Performance Comparison of Two Altitude-Control Algorithms for a Fixed-Wing UAV

Mansoor Ahsan*, Kamran Shafique**, Atif Bin Mansoor*** and Muddassar Mushtaq*

*National University of Sciences and Technology, Islamabad, Pakistan **Pakistan Institute of Engineering and Applied Sciences, Islamabad, Pakistan

***Air University, Islamabad, Pakistan mahsan@cae.nust.edu.pk

Abstract—Uninhabited aerial vehicles (UAV) have proven their tremendous capabilities in military and civil applications. In a UAV, the onboard autopilot autonomously controls the aircraft flight and navigation. The altitude acquire-and-hold is an important function of autopilot, implemented using a control design algorithm that flies the UAV to commanded altitude and maintains it. Most of the commercially available autopilots use Proportional-Integral-Derivative (PID) controllers for altitude and heading control. In this paper, we present a performance comparison of two altitude-controller design techniques, the PID controller and the Phase Lead compensator. We have used a nonlinear mathematical model of the UAV Aerosonde in our work. The nonlinear model is lineraized around a stable trim condition and decoupled for linear controller design. The designed controllers are tested with the nonlinear model in view of small perturbation control theory. The results for the compensated linear and nonlinear models are presented. Our investigation reveals that Phase Lead compensator has inherent strengths compared to PID controller for UAV altitude acquire-and-hold in terms of better transient response, thus improving the payload performance during an altitude-change maneuver. The findings may lead to an effective approach in UAV autopilot design.

Keywords-autopilots; altitude-control; unmanned aerial vehicle; PID-control; Phase-Lead-compensator

I. INTRODUCTION Modern times have shown the overwhelming potential of uninhabited aerial vehicle (UAV) in diverse areas such as border and enemy reconnaissance, police surveillance, agricultural research, fire fighting, and geological surveys. The unchallenged capabilities of UAVs have paved ways for a pilot-less aviation in the future. Autopilot is the intelligent system onboard a UAV replacing the human pilot for all flight related operations. Development of UAVs involves expertise in different fields like aerodynamics, airframe structure, propulsion system and automatic flight control systems. Amongst all these systems, the automatic flight controller is of prime significance and is the main building block of the autopilot. This subsystem controls the UAV autonomously by generating various control signals for actuating control surfaces of the aircraft. Altitude-acquire-and-hold is an inherent function amongst the operations of an autopilot, which enables the aircraft to acquire a desired altitude and retain it till further instructions. In the recent past, a variety of

algorithms for navigation and control of a UAV have been proposed including the designs based on fuzzy logic [1], delayed feedback control [2], invertebrate neuronal models [3], neural network [4], multi agent systems [5], intelligent Proportional-Integral-Derivative (PID) control [6] and various other techniques [7] including nonlinear feedback linearization, sliding mode variable structure control, multiple model adaptive control and Back-stepping approach using Lyapunov function.

Most of the commercially available UAV autopilots use PID control loops for various control operations [15]. The autopilots by Micropilot [16] employ user definable PID feedback loops. The Picollo series autopilots by Cloud Cap Technology [17] exploit the strength of PID control to perform autonomous flight. Kestrel autopilot by Procerus Technologies offers real time PID graphers for onboard tuning of control gains [18]. Guidestar autopilot series by Athena Technologies uses PID control techniques for trajectory control in both altitude and heading [19]. PID control technique is widely used due to its past record of success, wide availability and simplicity of use [20]. PID controllers are generally used on UAVs owing to easy implementation, but these offer limitations in stability and robustness [15]. Phase Lead controllers in the feedback path are mostly employed in missile control systems to achieve stability and minimum overshoot [9], though these compensators can equally be well applied in the forward path after the error signal. This control technique has also been tested for aircraft control systems. A longitudinal motion autopilot using Phase Lead compensator has been designed for the F-16 aircraft nonlinear model in [10].

In this paper, we have compared the performance of PID controller and Phase Lead Compensator for altitude acquire-and-hold using the nonlinear mathematical model of a fixed wing UAV - Aerosonde. Both these techniques have been well documented in the control systems literature [8, 9]. Section II gives the details of nonlinear mathematical model of Aerosonde, followed by the linearized and decoupled longitudinal and lateral models. In Section III the details of PID Controller and Phase Lead Compensator design have been discussed. Section IV presents the simulation results of controllers for both linear and nonlinear aircraft models. The paper is concluded in Section V.

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II. NONLINEAR MODELING AND LINEARIZATION The AeroSim aeronautical simulation blockset [21] for

MATLAB/Simulink was used to incorporate a 6-Degree-of-Freedom (6-DoF) dynamic model of Aerosonde. This blockset provides a comprehensive set of tools for building dynamic models of manned / unmanned aircraft. The nonlinear mathematical model includes the following:

• Aerodynamic model using required forces and moments coefficients.

• Propulsion model inclusive of engine and propeller sub-models.

• Inertial model specifying the centre of gravity (CG), mass and moments of inertia for the UAV.

• Atmosphere model [22].

• Earth model using the WGS-84 based coefficients to compute gravity and earth radius at each aircraft location.

• 6-DoF Equations of Motion implemented in body-axis of the aircraft.

The nonlinear dynamic model was linearized around a steady, level-flight trim condition. A linear aircraft model allows good insight into the aircraft’s natural modes of motions, resulting in the design of an effective controller [9]. According to the small perturbation theory a linearized system if asymptotically stable, carries the property of stability from nonlinear to linear regime [23]. Thus the controller designed for a system linearized around a stable equilibrium point will effectively control the nonlinear model within certain linear range of operation. The linearization gives a state-space based linear model of the UAV. For a steady and level-flight trim condition i.e. with approximately zero sideslip and roll angles, the system-matrix ‘A’ of the linear model has negligible values in the cross diagonal terms [9], thus facilitating the decoupling of the linear model into longitudinal and lateral sub-models. The longitudinal sub-model with the inputs of throttle and elevator is used to design the altitude controller. The decoupled longitudinal sub-model is given by (1).

l l l l lx A x B u= + (1)

Where xl is the time derivative of xl - the decoupled longitudinal state vector [u q h], where u is the velocity along body x-axis, q is pitch rate, is pitch angle and h is altitude of the UAV. ul is the control input, e elevator deflection angle. Al is the system matrix and Bl is the decoupled input matrix for the longitudinal sub-model. The longitudinal model represented by the state variables is given in (2).

The elements of the system matrix Al in (2) are in concise representation form of aerodynamic stability derivatives in the aircraft body axis [8, 9].

(2)

III. CONTROLLER DESIGN The altitude acquire-and-hold controller is designed with

two different control techniques, each using only elevator input to change the aircraft altitude, with a fixed thrust. In UAV autopilot designs, altitude control is mostly implemented with the elevator deflection whereas the throttle loop is closed with velocity feedback to control airspeed [24]. The likely reason for using elevator effort alone for altitude control is that UAVs are in general designed to be innately stable and do not require rapid maneuvering.

The linear dynamics of closed loop system are analyzed in terms of stability and control responses, i.e. overshoot and settling time [24].

A. PID Controller PID control is a widely used technique in various spheres

of control applications. The controller gains are applied to the measured variable through feedback and an “error” signal is generated by taking the difference between the measurement and a commanded set-point. The standard control law for the PID controller is given in (3).

0

( ) ( ) ( ) ( )t

p i d

du t K e t K e d K e t

dtτ τ= + + (3)

The controller is aimed to eliminate the error e(t) by adjusting the control input. The proportional term Kp in the controller generally ensures stability, the integral term Ki minimizes steady state errors and the derivative term Kd is tuned to improve the transient response.

Automatic flight control systems generously use PID controllers for various control functions. The frequency domain representation of the controller is given in (4) where ‘s’ is the Laplace variable.

2

( ) d p iic p d

K s K s KKG s K K s

s s

+ += + + = (4)

In our work, a root locus based PID controller is designed

for the altitude control, using the longitudinal sub-model of the UAV. A total of 3 successive loops are closed for the altitude controller as shown in Fig. 1. Reference input href is the commanded altitude. Kq is control gain for pitch rate loop, K for the pitch angle loop and Kh is the PID controller for altitude acquire-and-hold.

.

0 0

0 0

cos

sin

0

0 0 1 0 0

e

e

e

Xu Xq X g Xu u

q Zu Zq Z g Zqe

Mu Mq M M

hh

θ δ

θ δ

θ δ

θ

θδ

θ θ

−

−= +

Figure 1. Block Diagram for PID based altitude acquire-and-hold controller

The pitch rate information is fed back through a proportional gain to provide stability augmentation. The second loop is closed with the feedback of pitch angle and the final loop was closed by feeding back the altitude information to a PID controller. The difference between desired altitude and current aircraft altitude is the error signal e(t), acting as the reference input for the pitch angle control loop, and is minimized by PID control. A step command at the elevator is used as the reference input and the gains of the PID controller are tuned for altitude state to track the step input. The control law for altitude acquire and hold is given in (5).

0

( ) { ( ( )) ( ( )) ( ( ))}

( ( )) ( ( )) (5)

t

q p ref i ref d ref

q q

du t K K K h h t K h h d K h h t

dt

K K t K q t

θ

θ

τ τ

θ

= − + − + −

− +

B. Phase Lead Compensator Phase Lead compensation is a control technique generally

used to improve the transient response of a dynamic system. This controller provides system stability by adding a positive contribution in the sum of angles in the angle criterion. The poles of the closed loop system are pushed towards left in the s-plane, thus improving stability as well as speed of the response. The general frequency domain description of the Phase Lead compensator is given in (6).

0

0

( )( )

( )c c

s zG s K

s p

−=

− (6)

Where z0 and p0 are the zero and pole of the compensator respectively and Kc is the controller gain. For the altitude controller, a pitch rate feedback is applied to the longitudinal sub-model for increasing the system damping.

A second and final loop is successively closed by applying Phase Lead compensation to the altitude feedback. The block diagram of the control loops is as shown in Fig. 2. Kq is control gain for pitch rate loop and Kh is the Phase Lead compensator for altitude control.

The difference between desired altitude and current aircraft altitude is the error signal acting as the reference input for the pitch rate control loop. The gains of the phase lead compensator, as well as the positions of its zero and pole are varied to track the step input at the elevator. The Laplace form of control law for altitude acquire-and-hold is given in (7).

Figure 2. Block Diagram for Phase Lead compensator based altitude

acquire-and-hold controller

0

0

( )( ) ( ) ( )

( )ref c q

s zU s h K h s K q s

s p

−= − −

− (7)

IV. SIMULATION RESULTS MATLAB/Simulink is used to simulate the linear and

nonlinear models of Aerosonde. Sampling frequency of 50 Hz is used for the simulation of nonlinear model, as it is the operating frequency of actuating servos installed on the UAV [21]. In view of previous work [10, 11, 12, 13, 14] regarding linear controller design for aircraft control, the design specifications for the altitude control were defined as Overshoot 10%, Settling Time 15 sec and zero Steady State Error.

A. PID Controller Root locus based control design technique is used to

develop PID controller for the linear model. The PID controller enables the altitude state to successfully track the step input at the elevator. The altitude response to elevator step input is sketched in Fig. 3. The linear model step response has a settling time of 14 sec and an overshoot of around 13%, with zero steady state error.

The linear PID controller is tested with the nonlinear Aerosonde model. The altitude acquire-and-hold results for the nonlinear model are exhibited in Fig. 4. Altitude in meters along y-axis is plotted against time in seconds along x-axis. The altitude plot shows a ‘Non Minimum Phase Effect’, as the altitude initially drops once the aircraft is commanded for a climb. This effect is due to the presence of a zero of the closed loop system in the right half s-plane. The nonlinear simulation results show a pronounced overshoot in climb as well as descend of the UAV.

B. Phase Lead Compensator Root locus technique is used for the Phase Lead controller

design. The altitude response to elevator step input, for the linear model controlled with Phase Lead compensator, is sketched in Fig. 5. The linear model step response has a settling time of approx. 37 sec and an overshoot of 8.26%, with zero steady state error.

Figure 3. Step Response for PID Controller

The linear Phase Lead compensator is tested with the nonlinear UAV model and the results for altitude control are exhibited in Fig. 6. Altitude in meters along y-axis is plotted against time in seconds along x-axis. The Phase Lead controlled aircraft takes longer time during climb in comparison with PID controlled aircraft, but the climb stays uniform with inconsequential overshoot.

Due to inherent role of aircraft, very low tolerances are

acceptable to strong transients. High overshoots in both longitudinal and lateral axes bring about severe discomfort to passengers in manned aircraft, and adversely affect the performance of payloads onboard a UAV. Therefore, a closed loop system with slower responses, against one with higher overshoots, is a preferable choice in aviation.

Figure 5. Step Response for Phase Lead compensator

V. CONCLUSION Most of the commercially available autopilots use PID

controller for altitude control. In this paper, we have compared the performance of PID controller and Phase Lead compensator for altitude acquire-and-hold functionality for a fixed Wing UAV – Aerosonde.

Our investigation reveals that Phase Lead compensator offers better transient response characteristics as compared to PID controller, while PID controller depicts shorter rise time to desired altitude but with pronounced overshoots. Whereas, the response by the Phase Lead controller although takes longer rise time, but offers negligible overshoot in the altitude as compared to the PID controller. Due to inherent role of UAVs, smaller transients are a desirable feature to optimize payload performance. So compared to the PID controller, Phase Lead compensator is a better choice for altitude acquire-and-hold controller in a UAV.

Figure 6. Altitude acquire-and-hold for nonlinear UAV model using Phase Lead compensator

Figure 4. Altitude acquire-and-hold for nonlinear UAV model using PID

controller

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