Research ArticleAttitude and Altitude Control of Trirotor UAV by UsingAdaptive Hybrid Controller

Zain Anwar Ali1 Daobo Wang1 Suhaib Masroor2 and M Shafiq Loya3

1College of Automation Engineering Nanjing University of Aeronautics and Astronautics Nanjing Jiangsu 210016 China2School of Mechatronics and Automation Shanghai University Shanghai 201900 China3Department of Electronic Engineering Sir Syed University of Engineering and Technology Karachi 75300 Pakistan

Correspondence should be addressed to Zain Anwar Ali zainanwar86hotmailcom

Received 27 February 2016 Accepted 20 April 2016

Academic Editor Carlos-Andres Garcia

Copyright copy 2016 Zain Anwar Ali et alThis is an open access article distributed under the Creative Commons Attribution Licensewhich permits unrestricted use distribution and reproduction in any medium provided the original work is properly cited

The paper presents an adaptive hybrid scheme which is based on fuzzy regulation pole-placement and tracking (RST) controlalgorithm for controlling the attitude and altitude of trirotor UAVThe dynamic and kinematic model of Unmanned Aerial Vehicle(UAV) is unstable and nonlinear in naturewith 6 degrees of freedom (DOF) that is why the stabilization of aerial vehicle is a difficulttask To stabilize the nonlinear behavior of our UAV an adaptive hybrid controller algorithm is used in which RST controllertuning is performed by adaptive gains of fuzzy logic controller Simulated results show that fuzzy based RST controller gives betterrobustness as compared to the classical RST controller

1 Introduction

The automatic control of airborne machines has been achallenge to the researchers for numerous years Significantattention has been given to the control of UAVs [1] Sim-ple construction vertical taking off and landing (VTOL)capability and rapid steering are the main reasons of microhelicopter that attract military and civilian users UAVsare widely used in surveillance firefighting rescue trafficmonitoring and environmental monitoring scenarios [2 3]

There are two groups in which UAVs are categorizedthat is fixed and rotary wings In real-world tasks fixed-wing UAVs have existed for years in routine reconnaissanceassignments but they lack the hovering flying ability Rotor-crafts are foremost complex types of flying machineThey aremulti-input multioutput (MIMO) under actuated structurescapable of executing vertical takeoff and landing (VTOL)and also quick maneuvering turns Utmost vertical takeoffand landing flying machines depend on gyro equilibrium oraccelerometer systems to endure steady hovering flight [4ndash6]To fulfill the aforementioned necessities a multirotor UAV isbest available resolution for this Multirotor style UAV has

a number of categories together with birotor trirotor andquadrotor In this paper our main concern relates to trirotorUAV having three rotors situated in the midway from centerof gravity [7]

The trirotor UAVhas an issue of having a yawingmomentbrought in due to feedback torque from unpaired rotor Toovercome such condition a number of strategies of trirotorUAV have been established with their specific explanationssuch as single trirotor UAV having a servo motor connectedwith one of its rotor axes to diminish yaw moment by tiltingat certain angleThe other category of trirotor UAV is termedas coaxial trirotor and Draganflyer X6 might be reflected asthis type [8] It devises dual rotors mounted on every rotoraxis thus having overall six rotors Using two counterrotatingrotors on every axis the feedback torque has annulled Thisform of trirotor ensures an improved stability compared tothe solo trirotor UAV style

A trirotor UAV has four control parameters that isaltitude lateral longitudinal and angular moments whichprovides 6 degrees of freedom (DOF) and three Cartesiancoordinates that is 119909 119910 119911 [9] while the output includesrotational velocities translational velocities and rotational

Hindawi Publishing CorporationJournal of Control Science and EngineeringVolume 2016 Article ID 6459891 12 pageshttpdxdoiorg10115520166459891

2 Journal of Control Science and Engineering

angles Rotational and translational subsystems are incor-porated to establish sequential control due to the nonlinearbehavior of trirotor UAV Before the real flight test thesimulation of UAV parameters is necessary in this researchwe have to check all parameters which are highly unstableand nonlinear like control commands of UAV Euler anglesand translational and rotational velocity components [10]by resolving the error which is found in the yaw momentof unpaired rotor reaction produced by the turning effectldquotorquerdquo in a frame To nullify the tilt angle a Brushless DCMotor (BLDC) is installed in a triangular frame of trirotor

Different hybrid controller algorithms were previouslyapplied for controlling the attitude and altitude of UAVlike conventional Proportional Integral Derivative (PID)controller with Backstepping Scheme fuzzy based PID con-troller adaptive PID controller and Adaptive Sliding ModeController [11ndash14] but no one considers fuzzy based regu-lation pole-placement and tracking (RST) for controllingthe dynamics of trirotor UAV In this paper we use hybridcontroller scheme named as a fuzzy based RST controllerwhich was previously addressed by [15] The polynomialregulator of RST looks to be the remarkable substitute of thesystematic PID controller RST controller theory is totallybased on pole-placement algorithm and it has potential toexecute poles in the closed-loop system to handle in a distinctway the objectives of tracking and regulation

The robust RST controller of [16] is firstly applied in ourhighly unstable system and then after that fuzzy based RSTcontroller (F-RST) is applied in it taking the difference interms of attitude stability between controllers The overallperformance of RST is good between robustness and com-plexity but there are little transient errors to control thedynamics of the UAV as compared to our proposed F-RSTapproach

Themain contributions in this research are as follows (1)A novel algorithm to control the highly nonlinear system(2) fuzzy logic controller with fine tuning gains of RST(3) transient behavior of our system being realistic sameas the experimental point of view (4) the robustness andnullification of the rotor reaction already proven in yawcontrol

The paper is divided into six sections Section 1 definesthe introduction Section 2 defines the rigid body equationsof motion and the dynamics and representation of the UAVare defined in Section 3 The control approach and controlalgorithmare defined in Section 4Moreover simulations andresults are discussed in Section 5 Lastly the whole paper isconcluded in Section 6

2 Rigid Body Equations

The equations of motion of a rigid body are defined by thesecond law of Newton which expresses that the summationof all outside force acts in a body is equivalent to the timeperiod variation of the body momentum Moreover the sumof external forces in the body is also equivalent to the rate ofchange of angular momentum Trirotor has 6-DOF unstableand nonlinear equations of motion which can be expressedin ldquodifferentialrdquo equation

Following is the equation of motion The rotational orangular rates of the system are defined by (119901 119902 119903) and thetranslational velocity and its position are defined by (119906 V 119908)and (119909 119910 119911) Euler angles or attitude and external momentsof an aircraft fixed body are defined by (120593 120579 120595) and (119871119872119873)

[17ndash20]Rotational velocity components

119901 = minus sin 120579

119902 = sin120593 cos 120579 + 120579 cos120593

119903 = cos120593 cos 120579 minus 120579 sin120593

(1)

Translational velocity components

119906 =

(119898 + 119898119901V minus 119911 minus 119898119892 cos 120579 cos120593)119898119902

V =(119898 + 119898119902119908 minus 119909 minus 119898119892 sin 120579)

119903119898

119908 =

(119898V + 119898119903119906 minus 119910 minus 119898119892 cos 120579 sin120593)119901119898

(2)

Euler angles

120579 = minus119903 sin 120579 + 119902 cos120593

= 119901 + 119903 cos120593 tan 120579 + 119902 sin120593 tan 120579

= sec 120579 (119903 cos120593 + 119902 sin120593)

(3)

Aerodynamic moments

119871 = 119868119909 minus 119868119909119911119903 minus 119868119909119911119901119902 + 119902119903 (119868

119911minus 119868119910)

119872 = 119868119910 + 119868119909119911(1199012

minus 1199032

) + 119903119901 (119868119909minus 119868119911)

119873 = minus119868119909119911 + 119868119911119903 + 119868119909119911119902119903 + 119901119902 (119868

119910minus 119868119909)

(4)

The rotational and translational velocity of the aircraft interms of kinetic energy are written as

119879rotational = 05 lowast 119868119909 ( minus sin 120579)2 + 05

lowast 119868119910(120579 cos120593 + cos 120579 sin120593)

2

+ 05

lowast 119868119911( cos 120579 cos120593 minus sin120593)2

119879translational = 05 lowast 1198982

+ 05 lowast 1198982

+ 05 lowast 1198982

(5)

where 119868119909 119868119910 and 119868

119911are inertial moments and ldquo119898rdquo is the mass

about 119909- 119910- 119911-axis respectively

3 System Dynamics

The dynamics constraints and parameters of UAV are highlyunstable and nonlinear system is nearly similar to otheraircrafts which may help to design the controller for

Journal of Control Science and Engineering 3

1205912

z 1205913

120572

1205911x

y

f1

f2

f3

(a)

Rotor 1

Rotor 2

Rotor 3

q

r

uv

w

p

L

M

N

120∘120∘

120∘

(b)

Figure 1 Arrangement of trirotor UAV with (a) tilt angle and (b) system parameters

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors anticlockwise

Rotor 3Rotor 1Rotor 2

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors clockwise

Rotor 2Rotor 1Rotor 3

(b)

Figure 2 Roll Control Strategy with respect to anticlockwise (a) and clockwise (b) movement

the successful flight operation According to the momentumtheory which was proposed by Newton fluid axial velocityldquo119906rdquo through actuator is mostly greater than the speed ldquoVrdquowith which actuator is progressing through the air [21] Thegenerated thrust by the rotors equals the physique of the airpassing through the circle in a unit time The combination ofblade theory and momentum is derived from moments andaerodynamic forces Figure 1(a) shows the model of trirotoraerial vehicle in which two rotors are fixed in the body andone rotor is rotational called tilt rotor to nullify the reactiontorque effects It has an obvious benefit for the generation ofquick motion by using its tilt rotor but for the stabilizationof aerial vehicle it may require a very precise tilt angle[22 23]

The hovering state of trirotor blades depends uponthe propeller which becomes ineffective by increasing thenumber of blades on the propeller and limits its forwardflight speed By utilizing the momentum theory of helicopter

aerodynamics which is similar to trirotor UAV theory [24]there are three propellers which are fixed in the rotorsThe coefficient of thrust torque and nondimensional powerare used to elaborate the rotor characteristics which areindependent of rotor size in which radius of blade is denotedby ldquo119877rdquo angular velocity is given by ldquo120575rdquo area of blade is ldquo119860rdquoldquo120588rdquo is the air density shaft of rotor is ldquo119876rdquo thrust is ldquo119879rdquo andaerodynamics thrust coefficient is denoted by ldquo119862

1199051015840rdquo

1198621199051015840 =

119879

120588119860 (120575119877)2

1198621199021015840 =

119876

120588119860 (120575119877)2

119877

1198621199011015840 =

119875

120588119860 (120575119877)3

(6)

4 Journal of Control Science and Engineering

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Up)

Rotor 2Rotor 3Rotor 1

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Down)

Rotor 1Rotor 2Rotor 3

(b)

Figure 3 Pitch Control Strategy with respect to Nose-Up (a) and Nose-Down (b) conditions

0 1 2 3 4 5minus5

0

5

Time (s)

(deg

)

Tilt angle of rotors

Figure 4 Movement of yaw control

The power coefficient is written as

119875 = 119876120575 (7)

By putting the power coefficient

1198621199011015840 = 1198621199021015840 =

119876120575

120588119860 (120575119877)3=

119876

120588119860 (120575119877)2

119877

(8)

The UAV hovering identical incursion and constantcoefficient profile drag are supposed to be Cdo = 0015 thesupposition known as themodifiedmomentum theory whilerotor solidarity ratio is given as ldquo120590rdquo The induced power in

0 1 2 3 4 50

1000

2000

3000

4000

5000

x 04455y 3889

Altitude control of rotors

Time (s)

Spee

d in

RPM

Rotor 1Rotor 2Rotor 3

Figure 5 Altitude Control Strategy

the flight climbed mostly two or three times in excess of thepower profile Consider

1198621199011015840 = 119870radic

1198621199051015840

2

lowast 1198621199051015840 +

1

8

lowast 120590 lowast Cdo (9)

31 Representation of System The placement of the aerialvehicle is explained by using Euler angle responses havingaltitude and attitude control which rotates along 119909- 119910- and119911-axis It also presents the position of the center with respectto the Earth body frame and orientation of the aircraft isrepresented by (120593 120579 120595) [25] Newtonrsquos Euler base dynamics

Journal of Control Science and Engineering 5

Table 1 Dynamics amp constants of UAV

119909- 119910- 119911-axissystem

Aerodynamics forcecomponents

Translationalsubsystem components

Rotational subsystemcomponents Coordinates inertia

Roll (120593) 119909 119906 119901 119868119909

Pitch (120579) 119910 V 119902 119868119910

Yaw (120595) 119911 119908 119903 119868119911

Referenceinput

Desired UAVresponse

Trirotor dynamicsT S

R

minus

y(t)

Figure 6 Internal close-loop block diagram of RST controller

Eulerangles

Trirotor UAV dynamics

Angular ratesp q r

Desired (120593 120579 120595)

y(t)

minus

Fuzzy RSTcontrolsystem120593 120579 120595

Figure 7 Attitude hold condition of trirotor UAV

of rigid body movement depend on the rotational and trans-lational subsystems [26] Moreover the force componentsof aerodynamics components of translational and rotationalvelocity and moments are described in Table 1

The configuration of trirotor with tilt angle is shown inFigure 1(a) taken from [6] and system parameter is definedin Figure 1(b) from [3] in which the distance from the centrebody is denoted by ldquo119897rdquoThe forces which are created by rotorsR1 R2 and R3 are 119891

1 1198912 and 119891

3respectively and the torque

produced by the rotors is denoted by 1205911 1205912 1205913 The force

acting on the frame of the aircraft contains the thrust whichis vertical along the positive 119911-axis and we can say that

1198651199111015840 = 1198911+ 1198912+ 1198913lowast cos120572 (10)

The forces and torques of trirotor are written as

119891(119896)= 11987011990510158401205752

(119896)

120591(119896)= 11987012059110158401205752

(119896)

(11)

where 1198701199051015840 is thrust coefficient 119870

1205911015840 is torque coefficients and

120575 is the angular velocity of the rotor

4 Controlling Approach

The control strategy of trirotor is same as conventionalhelicopter theory The product of Euler angles controls

the orientation of flight The controlling approach of UAVconsists of roll pitch yaw and altitude control and tilt anglealso plays a vital role in the displacement of UAVThe ldquo1205751rdquo isrotor 1 ldquo1205752rdquo is rotor 2 and ldquo1205753rdquo is rotor 3 and the speed ofrotors is measured in round per minute (RPM)

Roll Control Strategy It is divided into two cases clockwiseand anticlockwise movement of rotors

(1) In clockwise rotation the speed of rotor 2 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor3 speed with about 2000RPM which is shown inFigure 2(a) Mathematically 1205752 gt 1205751 gt 1205753

(2) In anticlockwise rotation the speed of rotor 3 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor 2speed with about 2000RPM which is also shown inFigure 2(b) Mathematically 1205753 gt 1205751 gt 1205752

Pitch Control Strategy The two conditions for controlling thepitch of the trirotor are as follows One is Nose-Up and thesecond is Nose-Down it could be done by varying the speedof rotors

(1) For Nose-Up condition the speed of rotor 2 androtor 3 is the same about 4000 RPM as compared

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

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Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Submit your manuscripts athttpwwwhindawicom

VLSI Design

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Shock and Vibration

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Electrical and Computer Engineering

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Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

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Chemical EngineeringInternational Journal of Antennas and

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International Journal of

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Navigation and Observation

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DistributedSensor Networks

International Journal of

2 Journal of Control Science and Engineering

angles Rotational and translational subsystems are incor-porated to establish sequential control due to the nonlinearbehavior of trirotor UAV Before the real flight test thesimulation of UAV parameters is necessary in this researchwe have to check all parameters which are highly unstableand nonlinear like control commands of UAV Euler anglesand translational and rotational velocity components [10]by resolving the error which is found in the yaw momentof unpaired rotor reaction produced by the turning effectldquotorquerdquo in a frame To nullify the tilt angle a Brushless DCMotor (BLDC) is installed in a triangular frame of trirotor

Different hybrid controller algorithms were previouslyapplied for controlling the attitude and altitude of UAVlike conventional Proportional Integral Derivative (PID)controller with Backstepping Scheme fuzzy based PID con-troller adaptive PID controller and Adaptive Sliding ModeController [11ndash14] but no one considers fuzzy based regu-lation pole-placement and tracking (RST) for controllingthe dynamics of trirotor UAV In this paper we use hybridcontroller scheme named as a fuzzy based RST controllerwhich was previously addressed by [15] The polynomialregulator of RST looks to be the remarkable substitute of thesystematic PID controller RST controller theory is totallybased on pole-placement algorithm and it has potential toexecute poles in the closed-loop system to handle in a distinctway the objectives of tracking and regulation

The robust RST controller of [16] is firstly applied in ourhighly unstable system and then after that fuzzy based RSTcontroller (F-RST) is applied in it taking the difference interms of attitude stability between controllers The overallperformance of RST is good between robustness and com-plexity but there are little transient errors to control thedynamics of the UAV as compared to our proposed F-RSTapproach

Themain contributions in this research are as follows (1)A novel algorithm to control the highly nonlinear system(2) fuzzy logic controller with fine tuning gains of RST(3) transient behavior of our system being realistic sameas the experimental point of view (4) the robustness andnullification of the rotor reaction already proven in yawcontrol

The paper is divided into six sections Section 1 definesthe introduction Section 2 defines the rigid body equationsof motion and the dynamics and representation of the UAVare defined in Section 3 The control approach and controlalgorithmare defined in Section 4Moreover simulations andresults are discussed in Section 5 Lastly the whole paper isconcluded in Section 6

2 Rigid Body Equations

The equations of motion of a rigid body are defined by thesecond law of Newton which expresses that the summationof all outside force acts in a body is equivalent to the timeperiod variation of the body momentum Moreover the sumof external forces in the body is also equivalent to the rate ofchange of angular momentum Trirotor has 6-DOF unstableand nonlinear equations of motion which can be expressedin ldquodifferentialrdquo equation

Following is the equation of motion The rotational orangular rates of the system are defined by (119901 119902 119903) and thetranslational velocity and its position are defined by (119906 V 119908)and (119909 119910 119911) Euler angles or attitude and external momentsof an aircraft fixed body are defined by (120593 120579 120595) and (119871119872119873)

[17ndash20]Rotational velocity components

119901 = minus sin 120579

119902 = sin120593 cos 120579 + 120579 cos120593

119903 = cos120593 cos 120579 minus 120579 sin120593

(1)

Translational velocity components

119906 =

(119898 + 119898119901V minus 119911 minus 119898119892 cos 120579 cos120593)119898119902

V =(119898 + 119898119902119908 minus 119909 minus 119898119892 sin 120579)

119903119898

119908 =

(119898V + 119898119903119906 minus 119910 minus 119898119892 cos 120579 sin120593)119901119898

(2)

Euler angles

120579 = minus119903 sin 120579 + 119902 cos120593

= 119901 + 119903 cos120593 tan 120579 + 119902 sin120593 tan 120579

= sec 120579 (119903 cos120593 + 119902 sin120593)

(3)

Aerodynamic moments

119871 = 119868119909 minus 119868119909119911119903 minus 119868119909119911119901119902 + 119902119903 (119868

119911minus 119868119910)

119872 = 119868119910 + 119868119909119911(1199012

minus 1199032

) + 119903119901 (119868119909minus 119868119911)

119873 = minus119868119909119911 + 119868119911119903 + 119868119909119911119902119903 + 119901119902 (119868

119910minus 119868119909)

(4)

The rotational and translational velocity of the aircraft interms of kinetic energy are written as

119879rotational = 05 lowast 119868119909 ( minus sin 120579)2 + 05

lowast 119868119910(120579 cos120593 + cos 120579 sin120593)

2

+ 05

lowast 119868119911( cos 120579 cos120593 minus sin120593)2

119879translational = 05 lowast 1198982

+ 05 lowast 1198982

+ 05 lowast 1198982

(5)

where 119868119909 119868119910 and 119868

119911are inertial moments and ldquo119898rdquo is the mass

about 119909- 119910- 119911-axis respectively

3 System Dynamics

The dynamics constraints and parameters of UAV are highlyunstable and nonlinear system is nearly similar to otheraircrafts which may help to design the controller for

Journal of Control Science and Engineering 3

1205912

z 1205913

120572

1205911x

y

f1

f2

f3

(a)

Rotor 1

Rotor 2

Rotor 3

q

r

uv

w

p

L

M

N

120∘120∘

120∘

(b)

Figure 1 Arrangement of trirotor UAV with (a) tilt angle and (b) system parameters

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors anticlockwise

Rotor 3Rotor 1Rotor 2

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors clockwise

Rotor 2Rotor 1Rotor 3

(b)

Figure 2 Roll Control Strategy with respect to anticlockwise (a) and clockwise (b) movement

the successful flight operation According to the momentumtheory which was proposed by Newton fluid axial velocityldquo119906rdquo through actuator is mostly greater than the speed ldquoVrdquowith which actuator is progressing through the air [21] Thegenerated thrust by the rotors equals the physique of the airpassing through the circle in a unit time The combination ofblade theory and momentum is derived from moments andaerodynamic forces Figure 1(a) shows the model of trirotoraerial vehicle in which two rotors are fixed in the body andone rotor is rotational called tilt rotor to nullify the reactiontorque effects It has an obvious benefit for the generation ofquick motion by using its tilt rotor but for the stabilizationof aerial vehicle it may require a very precise tilt angle[22 23]

The hovering state of trirotor blades depends uponthe propeller which becomes ineffective by increasing thenumber of blades on the propeller and limits its forwardflight speed By utilizing the momentum theory of helicopter

aerodynamics which is similar to trirotor UAV theory [24]there are three propellers which are fixed in the rotorsThe coefficient of thrust torque and nondimensional powerare used to elaborate the rotor characteristics which areindependent of rotor size in which radius of blade is denotedby ldquo119877rdquo angular velocity is given by ldquo120575rdquo area of blade is ldquo119860rdquoldquo120588rdquo is the air density shaft of rotor is ldquo119876rdquo thrust is ldquo119879rdquo andaerodynamics thrust coefficient is denoted by ldquo119862

1199051015840rdquo

1198621199051015840 =

119879

120588119860 (120575119877)2

1198621199021015840 =

119876

120588119860 (120575119877)2

119877

1198621199011015840 =

119875

120588119860 (120575119877)3

(6)

4 Journal of Control Science and Engineering

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Up)

Rotor 2Rotor 3Rotor 1

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Down)

Rotor 1Rotor 2Rotor 3

(b)

Figure 3 Pitch Control Strategy with respect to Nose-Up (a) and Nose-Down (b) conditions

0 1 2 3 4 5minus5

0

5

Time (s)

(deg

)

Tilt angle of rotors

Figure 4 Movement of yaw control

The power coefficient is written as

119875 = 119876120575 (7)

By putting the power coefficient

1198621199011015840 = 1198621199021015840 =

119876120575

120588119860 (120575119877)3=

119876

120588119860 (120575119877)2

119877

(8)

The UAV hovering identical incursion and constantcoefficient profile drag are supposed to be Cdo = 0015 thesupposition known as themodifiedmomentum theory whilerotor solidarity ratio is given as ldquo120590rdquo The induced power in

0 1 2 3 4 50

1000

2000

3000

4000

5000

x 04455y 3889

Altitude control of rotors

Time (s)

Spee

d in

RPM

Rotor 1Rotor 2Rotor 3

Figure 5 Altitude Control Strategy

the flight climbed mostly two or three times in excess of thepower profile Consider

1198621199011015840 = 119870radic

1198621199051015840

2

lowast 1198621199051015840 +

1

8

lowast 120590 lowast Cdo (9)

31 Representation of System The placement of the aerialvehicle is explained by using Euler angle responses havingaltitude and attitude control which rotates along 119909- 119910- and119911-axis It also presents the position of the center with respectto the Earth body frame and orientation of the aircraft isrepresented by (120593 120579 120595) [25] Newtonrsquos Euler base dynamics

Journal of Control Science and Engineering 5

Table 1 Dynamics amp constants of UAV

119909- 119910- 119911-axissystem

Aerodynamics forcecomponents

Translationalsubsystem components

Rotational subsystemcomponents Coordinates inertia

Roll (120593) 119909 119906 119901 119868119909

Pitch (120579) 119910 V 119902 119868119910

Yaw (120595) 119911 119908 119903 119868119911

Referenceinput

Desired UAVresponse

Trirotor dynamicsT S

R

minus

y(t)

Figure 6 Internal close-loop block diagram of RST controller

Eulerangles

Trirotor UAV dynamics

Angular ratesp q r

Desired (120593 120579 120595)

y(t)

minus

Fuzzy RSTcontrolsystem120593 120579 120595

Figure 7 Attitude hold condition of trirotor UAV

of rigid body movement depend on the rotational and trans-lational subsystems [26] Moreover the force componentsof aerodynamics components of translational and rotationalvelocity and moments are described in Table 1

The configuration of trirotor with tilt angle is shown inFigure 1(a) taken from [6] and system parameter is definedin Figure 1(b) from [3] in which the distance from the centrebody is denoted by ldquo119897rdquoThe forces which are created by rotorsR1 R2 and R3 are 119891

1 1198912 and 119891

3respectively and the torque

produced by the rotors is denoted by 1205911 1205912 1205913 The force

acting on the frame of the aircraft contains the thrust whichis vertical along the positive 119911-axis and we can say that

1198651199111015840 = 1198911+ 1198912+ 1198913lowast cos120572 (10)

The forces and torques of trirotor are written as

119891(119896)= 11987011990510158401205752

(119896)

120591(119896)= 11987012059110158401205752

(119896)

(11)

where 1198701199051015840 is thrust coefficient 119870

1205911015840 is torque coefficients and

120575 is the angular velocity of the rotor

4 Controlling Approach

The control strategy of trirotor is same as conventionalhelicopter theory The product of Euler angles controls

the orientation of flight The controlling approach of UAVconsists of roll pitch yaw and altitude control and tilt anglealso plays a vital role in the displacement of UAVThe ldquo1205751rdquo isrotor 1 ldquo1205752rdquo is rotor 2 and ldquo1205753rdquo is rotor 3 and the speed ofrotors is measured in round per minute (RPM)

Roll Control Strategy It is divided into two cases clockwiseand anticlockwise movement of rotors

(1) In clockwise rotation the speed of rotor 2 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor3 speed with about 2000RPM which is shown inFigure 2(a) Mathematically 1205752 gt 1205751 gt 1205753

(2) In anticlockwise rotation the speed of rotor 3 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor 2speed with about 2000RPM which is also shown inFigure 2(b) Mathematically 1205753 gt 1205751 gt 1205752

Pitch Control Strategy The two conditions for controlling thepitch of the trirotor are as follows One is Nose-Up and thesecond is Nose-Down it could be done by varying the speedof rotors

(1) For Nose-Up condition the speed of rotor 2 androtor 3 is the same about 4000 RPM as compared

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

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RoboticsJournal of

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Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 3

1205912

z 1205913

120572

1205911x

y

f1

f2

f3

(a)

Rotor 1

Rotor 2

Rotor 3

q

r

uv

w

p

L

M

N

120∘120∘

120∘

(b)

Figure 1 Arrangement of trirotor UAV with (a) tilt angle and (b) system parameters

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors anticlockwise

Rotor 3Rotor 1Rotor 2

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Roll control of rotors clockwise

Rotor 2Rotor 1Rotor 3

(b)

Figure 2 Roll Control Strategy with respect to anticlockwise (a) and clockwise (b) movement

the successful flight operation According to the momentumtheory which was proposed by Newton fluid axial velocityldquo119906rdquo through actuator is mostly greater than the speed ldquoVrdquowith which actuator is progressing through the air [21] Thegenerated thrust by the rotors equals the physique of the airpassing through the circle in a unit time The combination ofblade theory and momentum is derived from moments andaerodynamic forces Figure 1(a) shows the model of trirotoraerial vehicle in which two rotors are fixed in the body andone rotor is rotational called tilt rotor to nullify the reactiontorque effects It has an obvious benefit for the generation ofquick motion by using its tilt rotor but for the stabilizationof aerial vehicle it may require a very precise tilt angle[22 23]

The hovering state of trirotor blades depends uponthe propeller which becomes ineffective by increasing thenumber of blades on the propeller and limits its forwardflight speed By utilizing the momentum theory of helicopter

aerodynamics which is similar to trirotor UAV theory [24]there are three propellers which are fixed in the rotorsThe coefficient of thrust torque and nondimensional powerare used to elaborate the rotor characteristics which areindependent of rotor size in which radius of blade is denotedby ldquo119877rdquo angular velocity is given by ldquo120575rdquo area of blade is ldquo119860rdquoldquo120588rdquo is the air density shaft of rotor is ldquo119876rdquo thrust is ldquo119879rdquo andaerodynamics thrust coefficient is denoted by ldquo119862

1199051015840rdquo

1198621199051015840 =

119879

120588119860 (120575119877)2

1198621199021015840 =

119876

120588119860 (120575119877)2

119877

1198621199011015840 =

119875

120588119860 (120575119877)3

(6)

4 Journal of Control Science and Engineering

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Up)

Rotor 2Rotor 3Rotor 1

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Down)

Rotor 1Rotor 2Rotor 3

(b)

Figure 3 Pitch Control Strategy with respect to Nose-Up (a) and Nose-Down (b) conditions

0 1 2 3 4 5minus5

0

5

Time (s)

(deg

)

Tilt angle of rotors

Figure 4 Movement of yaw control

The power coefficient is written as

119875 = 119876120575 (7)

By putting the power coefficient

1198621199011015840 = 1198621199021015840 =

119876120575

120588119860 (120575119877)3=

119876

120588119860 (120575119877)2

119877

(8)

The UAV hovering identical incursion and constantcoefficient profile drag are supposed to be Cdo = 0015 thesupposition known as themodifiedmomentum theory whilerotor solidarity ratio is given as ldquo120590rdquo The induced power in

0 1 2 3 4 50

1000

2000

3000

4000

5000

x 04455y 3889

Altitude control of rotors

Time (s)

Spee

d in

RPM

Rotor 1Rotor 2Rotor 3

Figure 5 Altitude Control Strategy

the flight climbed mostly two or three times in excess of thepower profile Consider

1198621199011015840 = 119870radic

1198621199051015840

2

lowast 1198621199051015840 +

1

8

lowast 120590 lowast Cdo (9)

31 Representation of System The placement of the aerialvehicle is explained by using Euler angle responses havingaltitude and attitude control which rotates along 119909- 119910- and119911-axis It also presents the position of the center with respectto the Earth body frame and orientation of the aircraft isrepresented by (120593 120579 120595) [25] Newtonrsquos Euler base dynamics

Journal of Control Science and Engineering 5

Table 1 Dynamics amp constants of UAV

119909- 119910- 119911-axissystem

Aerodynamics forcecomponents

Translationalsubsystem components

Rotational subsystemcomponents Coordinates inertia

Roll (120593) 119909 119906 119901 119868119909

Pitch (120579) 119910 V 119902 119868119910

Yaw (120595) 119911 119908 119903 119868119911

Referenceinput

Desired UAVresponse

Trirotor dynamicsT S

R

minus

y(t)

Figure 6 Internal close-loop block diagram of RST controller

Eulerangles

Trirotor UAV dynamics

Angular ratesp q r

Desired (120593 120579 120595)

y(t)

minus

Fuzzy RSTcontrolsystem120593 120579 120595

Figure 7 Attitude hold condition of trirotor UAV

of rigid body movement depend on the rotational and trans-lational subsystems [26] Moreover the force componentsof aerodynamics components of translational and rotationalvelocity and moments are described in Table 1

The configuration of trirotor with tilt angle is shown inFigure 1(a) taken from [6] and system parameter is definedin Figure 1(b) from [3] in which the distance from the centrebody is denoted by ldquo119897rdquoThe forces which are created by rotorsR1 R2 and R3 are 119891

1 1198912 and 119891

3respectively and the torque

produced by the rotors is denoted by 1205911 1205912 1205913 The force

acting on the frame of the aircraft contains the thrust whichis vertical along the positive 119911-axis and we can say that

1198651199111015840 = 1198911+ 1198912+ 1198913lowast cos120572 (10)

The forces and torques of trirotor are written as

119891(119896)= 11987011990510158401205752

(119896)

120591(119896)= 11987012059110158401205752

(119896)

(11)

where 1198701199051015840 is thrust coefficient 119870

1205911015840 is torque coefficients and

120575 is the angular velocity of the rotor

4 Controlling Approach

The control strategy of trirotor is same as conventionalhelicopter theory The product of Euler angles controls

the orientation of flight The controlling approach of UAVconsists of roll pitch yaw and altitude control and tilt anglealso plays a vital role in the displacement of UAVThe ldquo1205751rdquo isrotor 1 ldquo1205752rdquo is rotor 2 and ldquo1205753rdquo is rotor 3 and the speed ofrotors is measured in round per minute (RPM)

Roll Control Strategy It is divided into two cases clockwiseand anticlockwise movement of rotors

(1) In clockwise rotation the speed of rotor 2 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor3 speed with about 2000RPM which is shown inFigure 2(a) Mathematically 1205752 gt 1205751 gt 1205753

(2) In anticlockwise rotation the speed of rotor 3 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor 2speed with about 2000RPM which is also shown inFigure 2(b) Mathematically 1205753 gt 1205751 gt 1205752

Pitch Control Strategy The two conditions for controlling thepitch of the trirotor are as follows One is Nose-Up and thesecond is Nose-Down it could be done by varying the speedof rotors

(1) For Nose-Up condition the speed of rotor 2 androtor 3 is the same about 4000 RPM as compared

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

4 Journal of Control Science and Engineering

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Up)

Rotor 2Rotor 3Rotor 1

(a)

0 1 2 3 4 50

1000

2000

3000

4000

5000

Time (s)

Spee

d in

RPM

Pitch control of rotors (Nose-Down)

Rotor 1Rotor 2Rotor 3

(b)

Figure 3 Pitch Control Strategy with respect to Nose-Up (a) and Nose-Down (b) conditions

0 1 2 3 4 5minus5

0

5

Time (s)

(deg

)

Tilt angle of rotors

Figure 4 Movement of yaw control

The power coefficient is written as

119875 = 119876120575 (7)

By putting the power coefficient

1198621199011015840 = 1198621199021015840 =

119876120575

120588119860 (120575119877)3=

119876

120588119860 (120575119877)2

119877

(8)

The UAV hovering identical incursion and constantcoefficient profile drag are supposed to be Cdo = 0015 thesupposition known as themodifiedmomentum theory whilerotor solidarity ratio is given as ldquo120590rdquo The induced power in

0 1 2 3 4 50

1000

2000

3000

4000

5000

x 04455y 3889

Altitude control of rotors

Time (s)

Spee

d in

RPM

Rotor 1Rotor 2Rotor 3

Figure 5 Altitude Control Strategy

the flight climbed mostly two or three times in excess of thepower profile Consider

1198621199011015840 = 119870radic

1198621199051015840

2

lowast 1198621199051015840 +

1

8

lowast 120590 lowast Cdo (9)

31 Representation of System The placement of the aerialvehicle is explained by using Euler angle responses havingaltitude and attitude control which rotates along 119909- 119910- and119911-axis It also presents the position of the center with respectto the Earth body frame and orientation of the aircraft isrepresented by (120593 120579 120595) [25] Newtonrsquos Euler base dynamics

Journal of Control Science and Engineering 5

Table 1 Dynamics amp constants of UAV

119909- 119910- 119911-axissystem

Aerodynamics forcecomponents

Translationalsubsystem components

Rotational subsystemcomponents Coordinates inertia

Roll (120593) 119909 119906 119901 119868119909

Pitch (120579) 119910 V 119902 119868119910

Yaw (120595) 119911 119908 119903 119868119911

Referenceinput

Desired UAVresponse

Trirotor dynamicsT S

R

minus

y(t)

Figure 6 Internal close-loop block diagram of RST controller

Eulerangles

Trirotor UAV dynamics

Angular ratesp q r

Desired (120593 120579 120595)

y(t)

minus

Fuzzy RSTcontrolsystem120593 120579 120595

Figure 7 Attitude hold condition of trirotor UAV

of rigid body movement depend on the rotational and trans-lational subsystems [26] Moreover the force componentsof aerodynamics components of translational and rotationalvelocity and moments are described in Table 1

The configuration of trirotor with tilt angle is shown inFigure 1(a) taken from [6] and system parameter is definedin Figure 1(b) from [3] in which the distance from the centrebody is denoted by ldquo119897rdquoThe forces which are created by rotorsR1 R2 and R3 are 119891

1 1198912 and 119891

3respectively and the torque

produced by the rotors is denoted by 1205911 1205912 1205913 The force

acting on the frame of the aircraft contains the thrust whichis vertical along the positive 119911-axis and we can say that

1198651199111015840 = 1198911+ 1198912+ 1198913lowast cos120572 (10)

The forces and torques of trirotor are written as

119891(119896)= 11987011990510158401205752

(119896)

120591(119896)= 11987012059110158401205752

(119896)

(11)

where 1198701199051015840 is thrust coefficient 119870

1205911015840 is torque coefficients and

120575 is the angular velocity of the rotor

4 Controlling Approach

The control strategy of trirotor is same as conventionalhelicopter theory The product of Euler angles controls

the orientation of flight The controlling approach of UAVconsists of roll pitch yaw and altitude control and tilt anglealso plays a vital role in the displacement of UAVThe ldquo1205751rdquo isrotor 1 ldquo1205752rdquo is rotor 2 and ldquo1205753rdquo is rotor 3 and the speed ofrotors is measured in round per minute (RPM)

Roll Control Strategy It is divided into two cases clockwiseand anticlockwise movement of rotors

(1) In clockwise rotation the speed of rotor 2 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor3 speed with about 2000RPM which is shown inFigure 2(a) Mathematically 1205752 gt 1205751 gt 1205753

(2) In anticlockwise rotation the speed of rotor 3 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor 2speed with about 2000RPM which is also shown inFigure 2(b) Mathematically 1205753 gt 1205751 gt 1205752

Pitch Control Strategy The two conditions for controlling thepitch of the trirotor are as follows One is Nose-Up and thesecond is Nose-Down it could be done by varying the speedof rotors

(1) For Nose-Up condition the speed of rotor 2 androtor 3 is the same about 4000 RPM as compared

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

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Active and Passive Electronic Components

Control Scienceand Engineering

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International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

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Shock and Vibration

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Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 5

Table 1 Dynamics amp constants of UAV

119909- 119910- 119911-axissystem

Aerodynamics forcecomponents

Translationalsubsystem components

Rotational subsystemcomponents Coordinates inertia

Roll (120593) 119909 119906 119901 119868119909

Pitch (120579) 119910 V 119902 119868119910

Yaw (120595) 119911 119908 119903 119868119911

Referenceinput

Desired UAVresponse

Trirotor dynamicsT S

R

minus

y(t)

Figure 6 Internal close-loop block diagram of RST controller

Eulerangles

Trirotor UAV dynamics

Angular ratesp q r

Desired (120593 120579 120595)

y(t)

minus

Fuzzy RSTcontrolsystem120593 120579 120595

Figure 7 Attitude hold condition of trirotor UAV

of rigid body movement depend on the rotational and trans-lational subsystems [26] Moreover the force componentsof aerodynamics components of translational and rotationalvelocity and moments are described in Table 1

The configuration of trirotor with tilt angle is shown inFigure 1(a) taken from [6] and system parameter is definedin Figure 1(b) from [3] in which the distance from the centrebody is denoted by ldquo119897rdquoThe forces which are created by rotorsR1 R2 and R3 are 119891

1 1198912 and 119891

3respectively and the torque

produced by the rotors is denoted by 1205911 1205912 1205913 The force

acting on the frame of the aircraft contains the thrust whichis vertical along the positive 119911-axis and we can say that

1198651199111015840 = 1198911+ 1198912+ 1198913lowast cos120572 (10)

The forces and torques of trirotor are written as

119891(119896)= 11987011990510158401205752

(119896)

120591(119896)= 11987012059110158401205752

(119896)

(11)

where 1198701199051015840 is thrust coefficient 119870

1205911015840 is torque coefficients and

120575 is the angular velocity of the rotor

4 Controlling Approach

The control strategy of trirotor is same as conventionalhelicopter theory The product of Euler angles controls

the orientation of flight The controlling approach of UAVconsists of roll pitch yaw and altitude control and tilt anglealso plays a vital role in the displacement of UAVThe ldquo1205751rdquo isrotor 1 ldquo1205752rdquo is rotor 2 and ldquo1205753rdquo is rotor 3 and the speed ofrotors is measured in round per minute (RPM)

Roll Control Strategy It is divided into two cases clockwiseand anticlockwise movement of rotors

(1) In clockwise rotation the speed of rotor 2 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor3 speed with about 2000RPM which is shown inFigure 2(a) Mathematically 1205752 gt 1205751 gt 1205753

(2) In anticlockwise rotation the speed of rotor 3 is4000 RPM greater than rotor 1 speed with about3000 RPM and rotor 1 speed is greater than rotor 2speed with about 2000RPM which is also shown inFigure 2(b) Mathematically 1205753 gt 1205751 gt 1205752

Pitch Control Strategy The two conditions for controlling thepitch of the trirotor are as follows One is Nose-Up and thesecond is Nose-Down it could be done by varying the speedof rotors

(1) For Nose-Up condition the speed of rotor 2 androtor 3 is the same about 4000 RPM as compared

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

6 Journal of Control Science and Engineering

Referenceinput e1

x

Adaptive fuzzy

dxdt

dxdt

dxdt

dxdt

dxdt

dxdt

x

x

x

Adaptive fuzzy

x

x

x

Adaptive fuzzy

x

x

MUX

Desired values e2

Adaptivefuzzy

DecentralizedRST

controller

System kinematic

modelControl

commands

TrirotorUAV constraints

Control signal ofvelocity

Control commands

ColLatLonPed

BLDCmotors

Aerodynamicforces and moments

Dynamics of TrirotorUAV

Desired valuesMeasured z 120593 120579 120595

y(t)

x y z

120593

120579120595

minusint

int

int

KR

KR

KR

KS

KS

KS

KT

KT

KT

zd 120593d 120579d 120595d

120575d1120575d2120575d3120575d4

1205751120575212057531205754

sum

sum

sum

sum

Figure 8 Simulink Matlab base block diagram of fuzzy RST controller

1

05

0

minus1 minus08 minus06 minus04 minus02 0 02 04 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoerrrdquo

Figure 9 Membership function of fuzzy logic controller for inputerror

1

05

00 0201 03 05 07 0904 06 08 1

ZERNESNEB PSS PSB

Input variable ldquoderrrdquo

Figure 10 Membership function of fuzzy logic controller for inputderivative error

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKR

Figure 11 Membership function of fuzzy logic controller for outputregulation gain (119865119870

119877)

1

05

0

ZER PSS PSB

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKS

Figure 12 Membership function of fuzzy logic controller for outputpole-placement gain (119865119870

119878)

1

05

0

ZER PSS PSM PSL

0 0201 03 05 07 0904 06 08 1

Output variable ldquo rdquoKT

Figure 13 Membership function of fuzzy logic controller for outputtracking gain (119865119870

119879)

0 1 2 3 4 50

05

1

15

2

25

Time (s)

Alti

tude

(m)

Figure 14 Altitude control of trirotor UAV

to the speed of rotor 1 which was about 2000RPM tocontrol the pitch Nose-Up condition which is shownin Figure 3(a) Mathematically 1205752 = 1205753 gt 1205751

(2) For Nose-Down the speed of rotor 1 is about4000 RPM as compared to the speed of rotor 2and rotor 3 which is equal to about 2000RPM tocontrol the pitch Nose-Down condition as shown inFigure 3(b) Mathematically 1205751 gt 1205752 = 1205753

Yaw Control Strategy To control the yaw moment we requireto achieve the desired lift the speed of all rotors increases

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 7

0 1 2 3 4 5minus05

0

05

1

15 Input altitude control versus time

Time (s)

Col

(ra

d)

(a)

0 1 2 3 4 5minus05

0

05

1 Input lateral control versus time

Time (s)

Lat

(rad

)

(b)

0 1 2 3 4 5

minus02

0

02

04

06

08

1

12

Input longitudinal control versus time

Time (s)

Lon

(rad

)

(c)

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

Ped

(rad

)

Input angular control versus time

(d)

Figure 15 Control commands of trirotor UAV

constantly while the thrust angle must change where ldquo120572rdquo isthe tilt angle which can be used for rapid turn in hazardousenvironment Figure 4 shows the change of tilt angle mathe-matically we can say that 1205751 = 1205752 = 1205753 with 120572 = 0

Altitude Control Strategy To maintain the desired altitudespeed of all rotors must be the same The speed of rotorsincreases frequently when reaching the desired altitude thespeed of all rotors is 4000 RPM which is shown in Figure 5in which angular velocity is also constant for all three rotorsMathematically 1205751 = 1205752 = 1205753

Control Algorithm Our proposed hybrid controller is char-acterized in this section in which the gains of RST controllerare utilized for the tuning of fuzzy logic controllerThe hybridcontrol algorithm is also used for the accurate tuning of eachinput parameter The close-loop response of RST controlleris shown in Figure 6 Figure 7 defines the attitude holdcondition of trirotor UAV and Figure 8 defines the completeblock diagram of overall control algorithm of our system

The semantics levels of the fuzzy based RST controller arereferred to as negative below (NEB) negative small (NES)zero (ZER) positive small (PSS) and positive big (PSB) in

Table 2 If-then rule of fuzzy logic controller for119870119877

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER ZER ZER ZER ZERNES ZER PSS PSS PSS ZERZER PSS PSS PSS PSS PSSPSS PSB PSS PSS PSS PSSPSB PSB PSB PSB PSB PSB

which ldquoerrrdquo is the error and ldquo119889119890119889119905rdquo is its derivative Thefuzzy controller if-then rules are shown in Tables 2ndash4 forthe tuning of fuzzy based regulation pole-placement andtracking (RST) gains denoted as119870

119877 119870119878 and119870

119879

The membership function of fuzzy logic controller inputerror ldquoerrrdquo and derivative of input ldquo119889errrdquo are shown in Figures9 and 10 having ranges minus1 to 1 and amplitude is about 0 to 1

The outputs of fuzzy (RST) controller are referred to asregulation gain (119870

119877) pole-placement gain (119870

119878) and tracking

gain (119870119879) The semantic levels are allocated as zero (ZER)

positive small (PSS) and positive big (PSB) and their ranges

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

8 Journal of Control Science and Engineering

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

Phi (

rad)

Roll angle versus time

F-RSTRST

(a)

0 1 2 3 4 5minus2

0

2

4 Pitch angle versus time

Time (s)

Thet

a (ra

d)

F-RSTRST

(b)

0 1 2 3 4 5

minus2

0

2

4

Time (s)

Sie (

rad)

Yaw angle versus time

F-RSTRST

(c)

Figure 16 Comparison of F-RST with RST controller for Euler angle responses

Table 3 If-then rule of fuzzy logic controller for 119870119878

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB PSS PSB PSB PSB PSBNES PSS PSS PSS PSS PSBZER ZER PSS PSS PSS PSBPSS ZER PSS PSS PSS PSSPSB ZER PSB PSB PSB PSS

Table 4 If-then rule of fuzzy logic controller for 119870119879

119889119890119889119905

ErrorNEB NES ZER PSS PSB

NEB ZER PSS PSS PSS ZERNES PSS PSS PSM PSS PSSZER PSM PSS PSM PSM PSMPSS PSM PSM PSM PSS PSLPSB PSL PSM PSM PSS PSL

and amplitude are 0 to 1 After defuzzification the output offuzzy logic controller is change into crisps which is shown inFigures 11ndash13

The output of fuzzy logic controller is used as an adaptivegain for the RST controller and can be written as

119906119865119877(119905) = 119891

119877(119890119909

119889119890119909

119889119905

)119870119877119890119909(119905)

119906119865119878(119905) = 119891

119878(119890119909

119889119890119909

119889119905

)119870119878int

119905

0

119890119909(119905)

119906119865119879(119905) = 119891

119879(119890119909

119889119890119909

119889119905

)119870119879

119889119890119909(119905)

119889119905

(12)

in which RST controller gains in (12) are defined as regulationgain (119870

119877) pole-placement gain (119870

119878) and tracking gain

(119870119879) whereas the gain values are tuned manually after that

accurate tuning of the system parameters is performed by119865119870119877 119865119870119878 and 119865119870

119879

And outputs of fuzzy controllers are

119865119870119877= 119891119877(119890119909

119889

119889119905

119890119877)

119865119870119878= 119891119878(119890119909

119889

119889119905

119890119878)

119865119870119879= 119891119879(119890119909

119889

119889119905

119890119879)

(13)

TheRST controller is defined as119877 = (1199022+1199030119902+1199031) 119878 = (119878

01199022

+

1198781119902 + 1198782) 119879 = (119879

0119902 + 1198791)1198600

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 9

0 1 2 3 4 5minus05

0

05

Time (s)

p (r

ads

)

(a)

0 1 2 3 4 5minus05

0

05

1

15

2

Time (s)

q (r

ads

)

(b)

0 1 2 3 4 5minus05

0

05

1

Time (s)

r (ra

ds)

(c)

Figure 17 Rotational velocity responses

And finally the fuzzy RST controller for altitude andattitude stabilization control of trirotor UAV can be writtenas

119906119865-RST

(119909119910119911)

(119905) = 119865 [

119879

119877

] lowast (119906119888(119905)) minus 119865 [

119878

119877

] 119910 (119905) (14)

with 119905 = 0 1 2 The same controller is designed for 119910 119911 120593 120579 120595

5 Simulation Results and Discussions

The effectiveness of our proposed hybrid adaptive fuzzy RSTcontroller is presented in this section along with the non-linear simulations for the attitude and altitude stabilizationcontrol of trirotor UAV on Matlab Simulink and comparefuzzy RST controller with the conventional RST controllerThe simulation is done for 119909- 119910- and 119911-axis along withattitude control Table 5 defines the parameter of trirotorUAV The UAV subsystem is divided into rotational andtranslational subsystems Initial errors in the system arecontrolled and stabilized by rotational subsystem and attitudeangle is converging to zero to realize the hovering state Thetranslational components depend on Euler angles howeverthe Euler angles and rotational subsystem do not depend ontranslational subsystem

Table 5 Parameters of trirotor UAV

Parameters 119868119909

119868119910

119868119911

119897 MassValues 03105 02112 02215 03050 0785Si units kgm2 kgm2 kgm2 m kg

Figure 15 shows the altitude lateral longitudinal andangular control of UAV The rise time and settling time foreach input channel are between 1 to 2 seconds along withminor ldquobumpsrdquo The altitude of the UAV is set to ldquounityrdquo asshown in Figure 14 Figure 16 shows the attitude responsehaving different initial angles but after that it will convergeto zero which means that it will easily hold the attitudecontrol of UAV The rotational and translational velocity rateresponses are shown in Figures 17 and 18 and both convergeto the desired values easily

The sampling time was set to 02 seconds for every simu-lation which was done in five seconds Our proposedmethodconverges to desired responses abruptly and efficiently asshown in Figures 16ndash19The initial conditions of Euler anglesare 120593 = 054 120579 = 24 120595 = 25 radians and referenceinput control commands are 119909

119889= 119910119889= 120595 = 0ms and

119911119889= 1m while 119906 = V = 0 and 119908 = 1 are translational

velocity components The rotational velocity converges tozero to maintain the desired attitude hold position easily the

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

10 Journal of Control Science and Engineering

0 1 2 3 4 5minus2

minus15

minus1

minus05

0

05

1

15

2

Time (s)

u (m

s)

(a)

0 1 2 3 4 5minus15

minus1

minus05

0

05

1

15

2

Time (s)

v (m

s)

(b)

0 1 2 3 4 50

05

1

15

2

Time (s)

w (m

s)

(c)

Figure 18 Translational velocity responses

0 1 2 3 4 5minus1

minus05

0

05

1

Time (s)

x (m

s)

(a)

0 1 2 3 4 5minus1

0

1

2

3

Time (s)

y (m

s)

(b)

0 1 2 3 4 50

05

1

15

Time (s)

z (m

s)

(c)

Figure 19 Position rate and altitude of trirotor UAV

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

Journal of Control Science and Engineering 11

results in Figures 15ndash18 show that our proposed algorithmhasbetter robustness

All the simulated constraints of UAV yield to originaltrimmed conditions especially in the Euler angle responsesshown in Figure 16 our proposed algorithm with the con-ventional RST controller In Figure 18 translational velocityis 119906 = V = 0 119908 = 1 which means it easily controlledthe attitude of UAV without any overshoot undershoot andtransient error and settling time response is also better thanthe previously adaptive RST controller The results show thatour proposed controller is able to stabilize the attitude anglesand altitude of trirotor UAV

6 Conclusion

Fuzzy based RST control algorithm is used to control theunstable and nonlinear behavior of trirotor UAV Howeverthe translational and rotational subsystems are used toachieve the desired attitude and altitude The robustnessof our algorithm is demonstrated by using the computersimulation which shows the effectiveness of the controllerthat has better transient responsewith very lowovershoot andundershoot to achieve the desired attitude At last the trirotorconverges very fast according to the desired position

Competing Interests

The authors declare that they have no competing interests

Acknowledgments

This work is sponsored by the National Natural ScienceFoundation of China (NSFC) under Grant no 61503185 andsupported by Key Laboratory of College of Automation Engi-neering Nanjing University of Aeronautics andAstronauticsNanjing 210016 China

References

[1] S Ding and S Li ldquoStabilization of the attitude of a rigidspacecraft with external disturbances using finite-time controltechniquesrdquo Aerospace Science and Technology vol 13 no 4-5pp 256ndash265 2009

[2] D Kastelan M Konz and J Rudolph ldquoFully actuated tricopterwith pilot-supporting controlrdquo IFAC-PapersOnLine vol 48 no9 pp 79ndash84 2015

[3] M K Mohamed Design and control of UAV system a Tri-Rotor aircraft [Doctor of Philosophy] University of ManchesterManchester UK 2012

[4] A Haider and M Sajjad ldquoStructural design and non-linearmodeling of a highly stable multi-rotor hovercraftrdquo ControlTheory and Informatics vol 2 no 4 pp 24ndash35 2012

[5] D-W Yoo Control system design and vision based collisionavoidance of multi-rotor UAV [MS thesis] KAIST 2011

[6] A B Chowdhury A Kulhare andG Raina ldquoA generalized con-trol method for a Tilt-rotor UAV stabilizationrdquo in Proceedingsof the IEEE International Conference on Cyber Technology inAutomation Control and Intelligent Systems (CYBER rsquo12) pp309ndash314 IEEE May 2012

[7] J-T Zou and H Tso ldquoThe development of tri-rotor aerialvehiclerdquo Advanced Science Letters vol 13 no 1 pp 245ndash2502012

[8] H Kim and D J Lee ldquoNonlinear attitude stabilization andtracking control techniques for an autonomous Hexa-Rotorvehiclerdquo inWireless Communications Networking and Applica-tions pp 1279ndash1292 Springer India 2016

[9] J T-Y Wen and K Kreutz-Delgado ldquoThe attitude controlproblemrdquo IEEE Transactions on Automatic Control vol 36 no10 pp 1148ndash1162 1991

[10] H Wong M S de Queiroz and V Kapila ldquoAdaptive track-ing control using synthesized velocity from attitude mea-surementsrdquo Automatica A Journal of IFAC the InternationalFederation of Automatic Control vol 37 no 6 pp 947ndash953 2001

[11] J L Junkins M R Akella and R D Robinett ldquoNonlinearadaptive control of spacecraft maneuversrdquo Journal of GuidanceControl and Dynamics vol 20 no 6 pp 1104ndash1110 1997

[12] B Xiao Q Hu and Y Zhang ldquoAdaptive sliding mode faulttolerant attitude tracking control for flexible spacecraft underactuator saturationrdquo IEEE Transactions on Control SystemsTechnology vol 20 no 6 pp 1605ndash1612 2012

[13] M K Mohamed and A Lanzon ldquoDesign and control of noveltri-rotor UAVrdquo in Proceedings of the UKACC InternationalConference on Control (CONTROL rsquo12) pp 304ndash309 IEEECardiff UK September 2012

[14] C Papachristos K Alexis and A Tzes ldquoTechnical activitiesexecution with a TiltRotor UAS employing explicit model pre-dictive controlrdquo in Proceedings of the 19th IFAC World Congresson International Federation of Automatic Control (IFAC rsquo14) pp11036ndash11042 Cape Town South Africa August 2014

[15] Z Chen K Xie and G Xie ldquoDesign and simulation of fuzzycontroller based on RSTrdquo Journal of Electronics and InformationTechnology vol 25 2003

[16] Z A Ali D B Wang and M Aamir ldquoDesign a robust RSTcontroller for stabilization of a tri-copter UAVrdquo Pakistan Journalof Engineering Technology amp Science vol 5 no 1 2015

[17] D W Yoo H D Oh D Y Won and M J Tahk ldquoDynamicmodeling and stabilization techniques for tri-rotor unmannedaerial vehiclesrdquo International Journal of Aeronautical and SpaceSciences vol 11 no 3 pp 167ndash174 2010

[18] B Xiao Q Hu and Y Zhang ldquoFault-tolerant attitude controlfor flexible spacecraft without angular velocity magnitudemeasurementrdquo Journal of Guidance Control andDynamics vol34 no 5 pp 1556ndash1561 2011

[19] J-T Zou K-L Su and H Tso ldquoThe modeling and implemen-tation of tri-rotor flying robotrdquo Artificial Life and Robotics vol17 no 1 pp 86ndash91 2012

[20] J-S Chiou H-K Tran and S-T Peng ldquoAttitude control of asingle tilt tri-rotor UAV SYSTEM dynamic modeling and eachchannelrsquos nonlinear controllers designrdquoMathematical Problemsin Engineering vol 2013 Article ID 275905 6 pages 2013

[21] Y D Song and W Cai ldquoQuaternion observer-based model-independent attitude tracking control of spacecraftrdquo Journal ofGuidance Control and Dynamics vol 32 no 5 pp 1476ndash14822009

[22] D A Ta I Fantoni and R Lozano ldquoModeling and control ofa tilt tri-rotor airplanerdquo in Proceedings of the American ControlConference (ACC rsquo12) pp 131ndash136 Montreal Canada June 2012

[23] A Kacar Attitude and altitude control of a triple tilt-rotorunmanned aerial vehicle [PhD thesis] Atilim UniversityAnkara Turkey 2013

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

12 Journal of Control Science and Engineering

[24] D-W Yoo H-D Oh D-Y Won and M-J Tahk ldquoDynamicmodeling and control system design for tri-rotor UAVrdquo inProceedings of the 3rd International Symposium on Systems andControl in Aeronautics and Astronautics (ISSCAA rsquo10) pp 762ndash767 Harbin China June 2010

[25] S Yoon S J Lee B Lee C J Kim Y J Lee and S Sung ldquoDesignand flight test of a small tri-rotor unmanned vehicle with a LQRbased onboard attitude control systemrdquo International Journal ofInnovative Computing Information and Control vol 9 no 6 pp2347ndash2360 2013

[26] D-W Yoo D-Y Won and M-J Tahk ldquoOptical flow based col-lision avoidance of multi-rotor UAVs in urban environmentsrdquoInternational Journal of Aeronautical and Space Sciences vol 12no 3 pp 252ndash259 2011

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of

International Journal of

AerospaceEngineeringHindawi Publishing Corporationhttpwwwhindawicom Volume 2014

RoboticsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Active and Passive Electronic Components

Control Scienceand Engineering

Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

International Journal of

RotatingMachinery

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporation httpwwwhindawicom

Journal ofEngineeringVolume 2014

Submit your manuscripts athttpwwwhindawicom

VLSI Design

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Shock and Vibration

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Civil EngineeringAdvances in

Acoustics and VibrationAdvances in

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Electrical and Computer Engineering

Journal of

Advances inOptoElectronics

Hindawi Publishing Corporation httpwwwhindawicom

Volume 2014

The Scientific World JournalHindawi Publishing Corporation httpwwwhindawicom Volume 2014

SensorsJournal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Modelling amp Simulation in EngineeringHindawi Publishing Corporation httpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Chemical EngineeringInternational Journal of Antennas and

Propagation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

Navigation and Observation

International Journal of

Hindawi Publishing Corporationhttpwwwhindawicom Volume 2014

DistributedSensor Networks

International Journal of