Aviation Engineering Innovations Conference st1

AEIC -2015-000

21-22 March 2015, Luxor, EGYPT

EFFECTS OF PARAMETERS PERTURBATION ON BEHAVIOR OF PID CONTROLLER

TUNED BY GENETIC ALGORITHM TECHNIQUE FOR HYDRAULIC SERVO SYSTEM

Magdy A. S. Aboelela1

Cairo University Giza, Egypt

M. A.Moustafa Hassan 2

Cairo University Giza, Egypt

Mohamed El- Sayed M. Essa3

I.A.E.T, Imbaba Airport Giza Egypt.

ABSTRACT

This paper deals with the tuning of classical Proportional- Derivative- Integral (PID) controller using Genetic Algorithm (GA) technique for position control of electro- hydraulic servo system. It also discusses the effects of parameter perturbation of a hydraulic system on the behavior of proposed controller. The hydraulic systems have many numbers of perturbations in parameters such as perturbation in supply pressure, Coulomb friction and viscous friction. The Hydraulic Servo System (HSS) plays an important role in industrial applications, especially inflight simulators and landing gear system of the aircraft. The main reason of using hydraulic systems in many applications is that, theycan provide a high torque and high force.The study has been investigated on simulation model and then verified experimentally in the laboratory.It was assumed that the system parameters have a perturbation of 20%.The simulation and experimental results show that the settling time and system overshoots are still around the same values in case of nominal parameters. It also shows that the proposed tuned PIDcontroller based on the Genetic Algorithm (GA) has the desired robustness to system uncertainties such as the perturbation of the pump’s supply pressure.As a general conclusion, one can conclude that the utilized PID controller has a good behavior anti parameter’s perturbation.

INTRODUCTION

Hydraulic control systems are widely used in many industrial fields due to their small size-to-power ratio and the ability to apply very large force and torque. In hydraulic control systems, the main purpose of control is to achieve a desirable response from the system. In light of this requirement, the development of the controller has been established for adjusting the output measured response to be as close as possible to the desired response.

1Prof. in Electrical Power and Machines Department, Cairo University, Email: aboelelamagdy@yahoo.com

2Prof. in Electrical Power and Machines Department, Cairo University, Email: drmmustafa1427@gmail.com

3Assistant Lecturer in I.A.E.T, Email: m.elameed_666@yahoo.com

Due to the importance of hydraulic systems in industrial applications, so many researchers have studied HSS. The dynamics of hydraulic systems are highly nonlinear as stated in ([Sohl and Bobrow, 1999]) and the system may be subjected to non-smooth and discontinuous nonlinearities due to directional change of valve opening, friction...etc. There have been some studies on analysis and implementation of the nonlinear tracking control law for HSS. This provided exponential stability for force tracking and position tracking to furnish an accurate friction model ([SohlandBobrow, 1999]).Nonlinear robust adaptive controller that is based on lyapunov theory with the ability of restraining the parameter perturbation for electro- hydraulic servo position with symmetry valves and control symmetry cylinder system is discussed in ([Shao and et. al, 2014]). An improved reaching law, and a sliding mode speed controller for an Electro-Hydraulic Velocity Servo System based on the improved reaching law and grey prediction compensator are presented in ([Wang and et al., 2012]).In ([Wang and et al., 2012]) the proposed control strategy can forecast and reject the disturbances and parameter perturbation. The assessment of the performance degradation of hydraulic servo system using a novel method based on fault observer and SOM (Self-organizing Map) network is introduced in ([LIU and et al., 2012]).The problem of online parameter-dependent controller synthesis for a position of electro-hydraulic servo systems driven by double-rod hydraulic actuators is investigated and discussed in ([Weng, Falu et al., 2012]). In this research the study of parameter perturbation and tuning of classical controller for position control of hydraulic servo system are discussed due to the importance of the use of electro-hydraulic servomechanism in aircraft flight control systems. Figure 1 shows the servo model of the control surface of the aircraft ([Edwards J., 1972]).

Figure 1. Aircraft control surface servo model

System Model

The studied hydraulic system is consisted of servo valve (Four way ), two cylinders with face to face connection and hydraulic power unit. The utilized mathematical model that describes the researched HSS is given in ([Essa, et al., 2014a]), which includes the most non-linear effects that are involved in the hydraulic system. The objective of investigate the simulation model and experimental hardware of the electro-hydraulic servo system is to design a suitable controller and check the behavior of controller anti parameter perturbation for position of electro-hydraulic servo system. The nonlinear model of a HSS is developed by simulation using SIMULINK / MATLAB program as stated in ([Essa, M.,2014b]).It describes the behavior of a servo system BOSCH REXROTH ([Mannesmann Rexroth, 2005]) servo valve. The problem that has been studied is illustrated in Figure 2, Figure 3 and Figure 4.

Figure 2. Valve-Cylinder Combinations with Varying Definitions ([Jelali and Kroll, 2003]).

The nonlinear state space model of the studied hydraulic servo system is described as follows.The state variables and the input variables are defined as �����, ��= ��� , ��= , ��= � , � = �� , ��= �� Where

�� Piston area

α Ratio of ring side area to piston side area

�� Friction Force (N)

�� Conversion Factor from volts to meters

�� Piston mass

Pressure in chamber A

� Pressure in chamber B

� Supply pressure

� Tank Pressure

� Flow rate in chamber A

�� Flow rate in chamber B

���, ��� Internal and external leakage flow

�� Valve input

��,���, ��� Piston position, velocity, acceleration, respectively

�� Valve spool position

�� Effective Bulk Modulus

� Time constant (sec.)

The previous equation can be written in state space form as follow

��� = �� (1)

��� = � !(#$)

(�� − '��)��-��(��) (2)

��� = )*(+,)-.(+$)

[(�(��, � ) − ���� + ���(��, ��)] (3)

��� = )*(+2)-3(+$)

[(��(��, � ) + '���� − ���(��, ��)] (5)

�� = - �4 � +

564 �� (6)

7 = 7��, + 8��+ ��9 �� =7: + ���� (7)

7� = 7��,� + 8�� − ��9'�� =7�: − ��'�� (8)

Where: S is the cylinder stroke. 7��,and7��,� are the pipeline volumes at A-side and B-

side respectively. The initial chamber volumes are assumed that the piston is centered such that these are equal. That is:

7: =7�: =7: The commonly used equation for calculation the effective bulk modulus �� for hydraulic cylinders is given by Equation (9) as given in ([Jelali and Kroll, 2003]).

�̅(<) = =�>?@+ ABC(=�D

D?@++ =�) (9)

Where =� = 50,=� =90, =� =3, � E#= 1800 MPa, and < E#= 28 MPa.

Experimental Setup The main purpose of experimental setup is to verify the simulation model for piston position of HSS and applying the controller design on practical system. Real time photo of the experimental HSS is illustrated in Figure 4. In the Experimental system, the two cylinders are connected to simulate hydraulic symmetric linear actuator. The hydraulic pump supplies the servo valve and actuator with a constant supply pressure (Ps). The PC sends an input voltage signal through an analog output port on the Data Acquisition Card (PCI-NI 6014) where it is converted from a digital to analog signal (inside PC), to the servo amplifier.

Figure 3. A Schematic Diagram of the Experimental System

Figure 4. Real Photo of Experimental Hardware

Genetic Algorithm (GA)

Genetic Algorithm (GA) is a very useful tool to search and optimize many engineering and

scientific problems such as airlines management revenue, artificial creative and automated

design for computers. GA was firstly proposed by Holland ([Sivanandam and Deepa, 2010]).It

is a stochastic optimization algorithm that was originally motivated by the mechanisms of

natural selection and evolutionary genetics.

The genetic algorithm consists of a population of individuals called chromosomes where each

one represents the solution of the studied problem (parameters of PID controller) which its

performance is evaluated based on fitness function ([Elbayomy, and et al., 2008]). A group of

chromosomes is selected to undergo to selection, crossover and mutation stages based on

the fitness of each individual. The application of selection, crossover and mutation operations

yields to create new individuals that give better solutions then the parents leading to optimal

solution.

The Integral Absolute Error (IAE) is used in this research as objective function in the

optimization stages and it is given in Equation 10. The objective function or the fitness function

is defined in Equation 11. The GA search will terminate when the fitness reach the maximum

value or the error be a minimum value as given in ([Essa, et al., 2014a]).In addition, the utilized

objective function of the optimization technique (GA) depends on the error criteria between

the reference step input (0.0278 m) and the feedback signal from the position transducer. The

main objective from the optimization is to compute the gains that can minimize the

performance index (IAE).

� Integral of Absolute Error (IAE)

IAE = F |H(I)|JIK: (10)

� Fitness function= 1/ IAE (11)

Results and Discussions

The step time of the utilized unit step in the simulation model and experimental hardware is

one second. The settling time, overshoot and PID/PI controller gains values for the simulation

and experimental system are shown in Table 1. At first it is important to test the system without

controllers to show the importance of using controllers in hydraulic system control, and this

has been shown in Figure 5. The results show in this case that there isn’t available settling

time and overshoots. As a result, it has been used PID/PI controllers in the position control of

HSS. Genetic Algorithm is used to find the optimal tuning or optimal PID/PI controller’s

parameters. The simulation results and experimental results show that using GA in tuning the

utilized controller gives a good results that summarized in better settling time and overshoots

in comparison with case without controllers. The step response of the simulation model and

experimental HSS hardware with PI/PID controller are illustrated in Figures 6 and 7. The

results also show that the controller that tuned by GA has a good anti- parameter’s

perturbation such that supply pressure variation and disturbance rejection as given in Figures

8 and 9.

Table 1. Simulation and Experimental Hardware Results

Tunning

Method

Control

ler

Type

Kp

Ki

Kd

(sec.)Settling Time

% Over Shoot

Simulation Experimental Simulation Experimental

Genetic

Algorith

m (GA)

PID 52.7271 21.97 1.21 6.39 6.732 11.51 11.52

PI 30.82 13.56 0 7.20 7.551 18.7 18.7

Figure 5. Piston Position of HSS without Controller

Figure 6. Step Response of HSS Using GA and PI for Simulation and Experimental

System

0 2 4 6 8 10 12 14 16 18 20-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03(a) Step Response Of The System without Controller

Time (sec)

Pis

ton P

osi

tion (m

)

0 2 4 6 8 10 12 14 16 18 20-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035 Step Response with Genetic Algorithm Based On PI Controller

Time (sec)

Pis

ton

Dis

pla

ce

me

nt

(m)

Simulation Model- PI

Reference

Experimental System- PI

Figure 7. Step Response of HSS Using GA and PID for Simulation and Experimental

System

Figure 8. Effects of supply pressure variation on the Behavior of Experimental

Hardware

0 2 4 6 8 10 12 14 16 18 20-0.005

0

0.005

0.01

0.015

0.02

0.025

0.03

0.035 Step Response with Genetic Algorithm Based On PID Controller

Time (sec)

Pis

ton

Dis

pla

ce

me

nt

(m)

Simulation Model -PID

Reference

Experimental System - PID

Figure 9. Disturbance Rejection with PID/PI Controllers based on GA

Table. 2 Effects of supply pressure variation on Time Performance

Tunning

Method

Performanc

e Indix

Contro

ller

Type

Simulation Model

Experimental Hardware

Increasing in

pressure

supply of the

pump by 20%

Decreasing in

pressure

supply of the

pump by

20%

Increasing in

pressure

supply of the

pump by 20%

Decreasing in

pressure

supply of the

pump by 20%

Sett.

Time

(Sec.)

Over

shoot

(%)

Sett.

Time

(Sec.

)

Over

shoot

(%)

Sett.

Time

(Sec.

)

Over

shoo

t (%)

Sett.

Time

(Sec.)

Over

shoot

(%)

Genetic

Algorith

m (GA)

IAE PID 6.192 11.21 6.99 12.81 6.62 11.01 6.93 11.91

PI 7.12 17.9 7.8 19.87 7.13 18.1 7.85 19.7

Conclusion

In this paper, the tuning of PID controller using Genetic Algorithm (GA) technique and check

the performance of this controller against anti parameter perturbation and variation are

presented and discussed. From the results obtained it became clear that there is a slight

change in the values of settling time and the overshoots and that are considered acceptable

and very small, which shows that the use of controllers that have been tuned using genetic

algorithm works with high efficiency in the occurrence of a change in some parameters of

hydraulic system such as the change in supply pressure pump, an increase of or a decrease

of 20 percentage. The results also shows that the efficient use of GA for tuning the controllers

in the case of disturbance's occurrence. The future work is that use of different controllers

such as Fuzzy logic controller (FLC) tuned by Evolutionary Computational techniques and

using Fractional Order Controllers and verified the simulation results with experimental

hardware.

Acknowledgement

The Experimental Work was investigated in the laboratories of Institute of Aviation

Engineering and Technology (I.A.E.T), Imaba Airport , Giza, Egypt.

References

Edwards j. (1972). Analysis of an electro hydraulic aircraft control surface servo and comparison with test results. Flight Research Center, NASA, Washington, 1972. Elbayomy, Karam M., Jiao Zongxia, and Zhang Huaqing (2008). "PID controller optimization by GA and its performances on the electro-hydraulic servo control system." Chinese Journal of Aeronautics 21.4: 378-384, 2008. Essa M., Magdy A.S and Moustafa M. (2014a). Position control of hydraulic servo system using proportional-integral-derivative controller tuned by some evolutionary techniques. Journal of Vibration and Control (JVC), DOI: 10.1177/1077546314551445, 2014. Essa, M. (2014b). Position Control of Hydraulic Servo Systems Using Evolutionary Techniques. Master thesis, Faculty of Engineering (Cairo University), 2014. Jelali, M., and Kroll, A. (2003). Hydraulic servo-systems: modelling, identification and

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