Research ArticleResearch of Control Strategy in the Large Electric CylinderPosition Servo System

Yongguang Liu, Xiaohui Gao, and Xiaowei Yang

School of Automation Science and Electrical Engineering, Beihang University, Beijing 100191, China

Correspondence should be addressed to Xiaohui Gao; hgaoxiaohui@126.com

Received 7 January 2015; Revised 1 March 2015; Accepted 3 March 2015

Academic Editor: Xinggang Yan

Copyright © 2015 Yongguang Liu et al.This is an open access article distributed under the Creative Commons Attribution License,which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

An ideal positioning response is very difficult to realize in the large electric cylinder system that is applied in missile launcherbecause of the presence of many nonlinear factors such as load disturbance, parameter variations, lost motion, and friction. Thispaper presents a piecewise control strategy based on the optimized positioning principle. The combined application of positioninterpolationmethod andmodified incremental PIDwith dead band is proposed and applied into control system.The experimentalresult confirms that this combined control strategy is not only simple to be applied into high accuracy real-time control systembut also significantly improves dynamic response, steady accuracy, and anti-interference performance, which has very importantsignificance to improve the smooth control of the large electric cylinder.

1. Introduction

The electric cylinder is a kind of actuator which can convertthe rotary motion of motor to linear motion by screw. Inrecent years, with the performance improvement of the servomotor and drive mechanism, the electric cylinder has madea significant breakthrough in the aspects of large stroke andheavy load, which will lead to a tendency of using it insteadof hydraulic cylinder in some industrial applications in thefuture [1, 2]. The electric cylinder has been widely appliedin military, medical, and industrial equipment because ofhigh transmission efficiency, excellent dynamic characteris-tic, high reliability, good environmental adaptability, compactstructure, and simple operation and maintenance [3–5]. Dueto load disturbance, parameter variations, friction, and othernonlinear factors in the position servo system, robust control,fuzzy control, self-adaptive control, internal model control,and sliding mode control can greatly improve the stabilityand anti-interference ability [6–17]. But these nonlinearcontrol algorithms are very difficult to be applied in thePLC controller or high accuracy real-time control systembecause of the complexity. Hence, this paper presents asimple piecewise control algorithmwhich respectively adoptsposition interpolation method and incremental PID with

dead band in different control stages. The final experimentalresult indicates that the dynamic response process is fast andsmooth and the positional accuracy is very high, which willpromote the application of large electric cylinders.

2. System Introduction

The erecting mechanism in the missile launching vehicle canerect the missile launcher from horizontal to tilted or verticalposition.The vehicle body, launcher, and driving mechanismcompose erecting mechanism which has been applied inmany kinds of missile launching vehicles (Figure 1). Asthe successful development of the large stroke and heavyload electric cylinder, it will replace the hydraulic cylinderand become the primary driving mechanism. This paperintroduces a large electric cylinder whose stroke is 1.5mand maximum output force is 30 t (ton), which can ensurethe missile launcher rotation range of 0–90∘ and positionalaccuracy of 0.05∘.The controller of the erectingmechanism isPLC and control cycle is 10ms.When the position instructionis 30∘ and conventional PID is applied in the controller, theposition response curve is shown in Figure 2. It indicates thatthe buffeting appears in the initial stage and system is unable

Hindawi Publishing CorporationMathematical Problems in EngineeringVolume 2015, Article ID 167628, 6 pageshttp://dx.doi.org/10.1155/2015/167628

2 Mathematical Problems in Engineering

Missilelauncher

Drivingmechanism

Velocitybody

Figure 1: Erecting mechanism of the missile launcher.

10 2 3 4 5 6 7 8 9 10

5

10

15

20

25

30

35

Time (s)

Posit

ion

(∘ )

InstructionResponse

Figure 2: Position response curve.

to meet the stability precision because of oscillation in theclose to desired position.

3. Modeling and SimulationBased on Simulink

In order to research the control strategy and apply it intocontrol system, the model of the erecting mechanism isestablished and the simulation is applied to analyze thereason of the buffeting appearing in the initial stage based onSimulink.

3.1. Modeling of the Erecting Mechanism. This paper estab-lishes the mathematical model of missile launcher that isdriven by electric cylinder and simulates based on Simulinkto analyze the reason of buffeting in the initial stage anddesign the controller.

Electric cylinder is mainly composed of servo motor,reducer, screw, and piston rod that can convert the rotarymotion of the servo motor to linear motion (Figure 3). Thetransmission schematic diagram is shown in Figure 4 and themathematic model is shown in

𝑢𝑎− 𝑢𝑞= 𝑖𝑎𝑅𝑎+ 𝐿𝑎

𝑑𝑖𝑎

𝑑𝑡

,

𝑇𝑎= 𝐾𝑚𝑖𝑎,

Servo motor

Screw

Piston rod

Screw nut

Reducer

Figure 3: Electric cylinder.

ua

uq

fa

La

wa

Ta

JbJa fb

Ph

�a

iFm

Figure 4: Transmission schematic diagram of the electric cylinder.

𝑇𝑎− 𝑇𝑏= 𝐽𝑎

𝑑2

𝜃𝑎

𝑑𝑡

+ 𝑓𝑎

𝑑𝜃𝑎

𝑑𝑡

,

𝑢𝑞= 𝐾𝑒

𝑑𝜃𝑎

𝑑𝑡

,

𝑇𝑏− 𝑇𝑚= 𝐽𝑏

𝑑2

𝜃𝑎

𝑑𝑡

+ 𝑓𝑏

𝑑𝜃𝑎

𝑑𝑡

,

𝑇𝑚=

𝐹𝑚𝑃ℎ

2𝜋𝜂𝑖

,

Δ𝐿 =

𝜃𝑎𝑃ℎ

2𝜋𝑖

,

(1)

where 𝑢𝑎is the input voltage of the armature winding; 𝑖

𝑎is

the current of the armature winding; 𝑅𝑎is the resistance of

the armature winding; 𝐿𝑎is the inductance of the armature

winding; 𝑇𝑎is the electromagnetic torque of the motor shaft;

𝐾𝑚is the electromagnetic torque coefficient; 𝑇

𝑏is the output

moment of motor; 𝐽𝑎is the moment of inertia of the motor

shaft; 𝑓𝑎is the viscous friction coefficient of the motor shaft;

𝜃𝑎is the output rotation angle of motor; 𝐾

𝑒is the voltage

coefficient; 𝑇𝑚is the output moment of electric cylinder; 𝐹

𝑚

is the loading force; 𝑖 is transmission ratio; 𝑃ℎis screw lead; 𝜂

is themechanical transmission efficiency; 𝐽𝑏is themoment of

inertia of the drive system;𝑓𝑏is the viscous friction coefficient

of the drive system; Δ𝐿 is the stretching-length of piston rod.Structural schematic diagram of the erecting mechanism

is shown in Figure 5 which describes the geometric rela-tionship and force status among vehicle body, launcher, andelectric cylinder.

Mathematical Problems in Engineering 3

h

O1l1

L

L 0

G

F m

𝛽

𝛼x

O

l

O2

Figure 5: Structural schematic diagram of the erecting mechanism.

Table 1: Main parameters of the missile launcher.

𝐾𝑒

/(V⋅radps−1) 𝐾𝑚

/(N⋅m⋅A−1) 𝐿𝑎

/H 𝑅𝑎

/Ω 𝜂

1.691 2.7 0.0025 0.058 0.8𝐽𝑏

/(kg⋅m2) 𝑓𝑏

/(N⋅m⋅radps−1) 𝑃ℎ

/m 𝑓𝑐

𝐺/N0.012 0.0063 0.02 0.3 68500𝑓𝑎

/(N⋅m⋅radps−1) 𝐽𝑎

/kg⋅m2 𝑖 𝑀𝑐

/kg 𝐿0

/m0.0153 0.0495 12 1200 2.56𝑥/m ℎ/m 𝑙/m 𝑙

1

/m 𝐽/(kg⋅m2)1.0265 1.5 5 3.101 15000

𝑂 is the pivot point of themissile launcher;𝑂1is the pivot

point of the electric cylinder;𝑂2is the joining point between

missile launcher and electric cylinder; 𝛼 is the rotation angleof themissile launcher;𝛽 is the horizontal angle of the electriccylinder; 𝐿

0is the original length of the electric cylinder; 𝐿 is

the length of the working electric cylinder; 𝐺 is the gravityof the missile launcher; 𝐹

𝑚is the output force of the electric

cylinder.The following equation shows the mathematic model of

the erecting mechanism:

𝐹𝑚cos𝛽 × 𝑥 sin𝛼 + 𝐹

𝑚sin𝛽 × 𝑥 cos𝛼 − 𝐺𝑙 cos𝛼 = 𝐽𝑑

2

𝛼

𝑑𝑡

,

sin𝛽 = 𝑥 sin𝛼 + ℎ𝐿

,

sin𝛼 =𝐿2

− 𝑙2

1

− 𝑥2

− ℎ2

2𝑥√ℎ2

+ 𝑙2

1

+ 𝛼0,

cos𝛼0=

ℎ

√ℎ2

+ 𝑙2

1

,

Δ𝐿 = 𝐿 − 𝐿0.

(2)

Figure 6 shows the block diagram of the missile launcherthrough combining (1) with (2). The main parameters of themissile launcher are shown in Table 1. Figure 7 shows theposition response in the simulation and experiment, whichproves the correctness of the model.

3.2. Simulation of the Erecting Mechanism. In order tounderstand the reason of the buffeting that appears in the

initial stage more intuitively, we analyze all the elements inthe model applying the simulation environment. Figure 8describes the load of the electric cylinder when the missilelauncher erects from horizontal to vertical position, whichindicates that the load gets smaller with the increase of theangle. Figure 9 shows that the impact current in the servomotor can reach up to 300A which is far beyond the ratedcurrent 62A and lasts about 1 s. The fluctuant current in theservo motor leads to the buffeting in the initial stage. Theoverload current will seriously reduce the service life andeven damage the electric cylinder. Therefore, we must adoptcontrol algorithm to suppress the impact current and improvethe stability precision.

4. Design of the Controller

The ideal velocity curve should be trapezoid based onthe optimized positioning principle. Hence, the positionresponse process is divided into dynamic response andclose to desired position periods (Figure 10). The dynamicresponse is composed of accelerative, constant velocity, anddecelerating periods. The position interpolation method andincremental PID are applied to the dynamic response periodto ensure the steady accuracy and rapidity and incrementalPID with dead band is applied to close to desired positionperiod to ensure the stability precision. Since the incrementalPID cannot produce disturbance when switching controlparameters, the different control parameters applied in thedynamic response and close to desired position periods canavoid buffeting and enhance adaptability.

4.1. Position Interpolation Method. Position interpolationmethod is to add some new position instructions betweencurrent and desired position according to acceleration, veloc-ity, and control cycle of the system. It can make the dynamicresponse realize the ideal velocity curve through tracing thenew position instructions. If the current position instructionis 𝐿𝑖, the next control cycle position instruction is 𝐿

𝑖+1=

𝐿𝑖+ Δ𝐿, where Δ𝐿 can be obtained by:

Δ𝐿 =

{{{{{{{

{{{{{{{

{

𝑎𝑡 +

1

2

𝑎𝑇2

0 ≤ 𝐿𝑖≤

𝑉2

max2𝑎

𝑉2

max2𝑎

𝑉2

max2𝑎

< 𝐿𝑖≤ 𝐿 −

𝑉2

max2𝑎

𝑉max − 𝑎𝑡1 −1

2

𝑎𝑇2

𝐿𝑖> 𝐿 −

𝑉2

max2𝑎

.

(3)

𝑎 is themaximum acceleration of system requirement; 𝑡 isthe duration of the acceleration; 𝑇 is control cycle;𝑉max is themaximum velocity of system requirement; 𝑡

1is the duration

of the deceleration; 𝐿 is position instruction.

4.2. Incremental PID Control Algorithm. Incremental PIDis to obtain control output by accumulating the incrementΔ𝑈(𝑘). The sharp increase or decrease of the output canproduce buffeting. The output 𝑈(𝑘) of incremental PID is

4 Mathematical Problems in Engineering

InstructionController Controller

w ua iaKm

Ta

Ke

JbS + fb

wa

TbTm

1

S

Ph

2𝜋𝜂i

Ph

2𝜋i

𝜃a ΔL

Fm

L

L0

𝛽

l21 + x2 + h2

h

JS2

a1

JaS + fa− − −−

++

++

++

+

+

+

+−

1

LaS + Ra

2x√h2 + l21

0.5Gl cos

××

×

×

÷

÷

÷arc sin

arc sin

x sin

x sin

ar cos h

√h2 + l21

Figure 6: Block diagram of the missile launcher.

10 2 3 4 5 6 7 8 9 10

5

10

15

20

25

30

35

Time (s)

Posit

ion

(∘ )

ExperimentSimulation

Figure 7: Position response.

5

10

15

20

25

30

Position (∘)

0 10 20 30 40 50 60 70 80 90

Fm(t)

Figure 8: Load of the electric cylinder.

10 2 3 4 5 6 7 8 9 10

Time (s)

350

300

250

200

150

100

50

Curr

ent (

A)

Figure 9: Current in the servo motor.

t

w

Accelerativeperiod

Constant velocity

Deceleratingperiod

Close to desiredposition

Figure 10: Ideal velocity curve.

gradual change, which can avoid the chattering and integralsaturation. 𝑈(𝑘) can be obtained by

𝑈 (𝑘) = 𝑈 (𝑘 − 1) + Δ𝑈,

Δ𝑈 = Δ𝑈𝑝 + Δ𝑈𝑖 + Δ𝑈𝑑,

Δ𝑈𝑝 = 𝐾𝑝 (Δ𝑒 (𝑘) − Δ𝑒 (𝑘 − 1)) ,

Δ𝑈𝑖 = 𝐾𝑖 (Δ𝑒 (𝑘) − Δ𝑒 (𝑘 − 1)) × 𝑇,

Δ𝑈𝑑 =

𝐾𝑑 (Δ𝑒 (𝑘) − 2Δ𝑒 (𝑘 − 1) + Δ𝑒 (𝑘 − 2))

𝑇

,

(4)

where 𝑈(0) = 0, Δ𝑒(𝑘) = 𝐿 − 𝐿(𝑘), 𝐿 is desired position and𝐿(𝑘) is current position sampling, and Kp, Ki, and Kd are theparameters of the incremental PID.

In the first control period, Δ𝑒(𝑘 − 1) and Δ𝑒(𝑘 − 2) areboth 0, 𝑒(1) = 𝐿 is bigger, and 𝑇 = 0.01 s is smaller. Then,Δ𝑈𝑝 = 𝐾𝑝 × 𝑒(1) and Δ𝑈𝑑 = 𝐾𝑑 × 𝑒(1)/𝑇 are both bigger.Hence, Kp and Kd are both 0 in the first control period andadopt adaptable value in other control periods.

4.3. Incremental PID with Dead Band. When the missilelauncher reaches the close to desired position, it will produceoscillation and cannot satisfy the stability precision due tothe existence of nonlinear factors such as friction and lostmotion.Therefore, we adopt incremental PIDwith dead bandin the close to desired position.

Mathematical Problems in Engineering 5

Instruction−

e(k)|e(k)| ≤ e0

U(k) = 0

Yes

Yes

No

No

Kp = 0Kd = 0

Incremental PID with dead band

U(k) = U(k − 1)

U(k) Erectingsystem

Output

Flag(k) = 0

Flag(k) = 1 Flag(k − 1) = 0+ ΔUp

+ ΔUi

+ ΔUd

Figure 11: Flowchart of the incremental PID with dead band.

Instruction

−

−

−

L

e(k)

e(k)

Yes

Yes

No

No

Incremental PID

Incremental PID

U(k) Erectingsystem

Output

with dead band

Incremental PIDwith dead band

|e(k)| ≤ E0

Position interpolationmethod

L > E0

Figure 12: Flowchart of the control algorithm.

(1) Set the range of dead band 𝑒0that is little bigger than

stability precision.(2) As the displacement error |𝑒(𝑘)| ≤ 𝑒

0, the control

output is 0.(3) As the displacement error |𝑒(𝑘)| > 𝑒

0, the control

output is𝑈(𝑘) of the incremental PID.

Figure 11 shows the flowchart of the incremental PIDwithdead band.

In the position servo control system of the missilelauncher, the steps of the control algorithm are as follows.

(1) Set some parameters such as maximum acceleration𝑎, maximum velocity 𝑉max, and range of close todesired position 𝐸

0.

(2) As the displacement error |𝑒(𝑘)| ≤ 𝐸0, the incremen-

tal PID with dead band is adopted.(3) As the displacement error |𝑒(𝑘)| > 𝐸

0, position inter-

polation method and incremental PID are adopted.

Figure 12 shows the flowchart of the control algorithm.After applying this combined control algorithm to the

controller of position servo system in the missile launcher,Figures 13 and 14, respectively, show the position responseand current of the servo motor when the desired position is30∘. Figure 13 indicates that the dynamic response process isfast and smooth and the buffeting disappears in the initial

0 5 10 15

5

0

10

15

20

25

30

35

Time (s)

Posit

ion

(∘ )

−5

Figure 13: Position response.

stage. When the missile launcher arrives at the desiredposition, the steady state error is 0.02∘ which is in the rangeof stability precision. Figure 14 indicates that the maximumcurrent in the servo motor is 32A and overload and impactcurrent are both eliminated, which can prolong the servicelife of electric cylinder.

5. Conclusion

The bigger load and acceleration in the initial stage cause thefluctuation and impact current in the servo motor, which canproduce buffeting. The nonlinear friction and lost motionbring about the oscillation in the close to desired position.This paper proposes a piecewise control strategy based on

6 Mathematical Problems in Engineering

0 5 10 15

5

10

15

20

25

30

40

35

Time (s)

Curr

ent (

A)

Figure 14: Current in the servo motor.

the optimized positioning principle. Position interpolationmethod and incremental PID with dead band are, respec-tively, applied into dynamic response and close to desiredposition periods. The position interpolation method signif-icantly improves steady accuracy and rapidity performance,which can ensure the position response along the ideal curve.The incremental PID with dead band can largely enhance thestability precision.These control algorithms are easily appliedto the high accuracy real-time control system and acquireexcellent results, which will greatly promote the applicationof the large electric cylinder.

Conflict of Interests

The authors declare that there is no conflict of interestsregarding the publication of this paper.

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