1 INTRODUCTION Test system of solenoid valve can perform many tests such as action performance test, sealing performance test, leakage test and life test. Many tests require that test system can supply precise pressure and even maintain pressure for a certain time. So realizing precise hydraulic pressure control is an important characteristic of solenoid test system. In this paper variable-voltage and variable-frequency (VVVF) technique is taken to adjust pressure of hydraulic system. The method of control VVVF hydraulic system is discussed and analyzed. Conventional PID control is widely used in industrial process control due to its simple algorithm, reliability and convenient parameter adjustment. In the non-linear, high-order, time-varying VVVF hydraulic system, however, conventional PID control often cannot satisfy the request of precise pressure control. Fuzzy controller is designed. Moreover, in order to observe the anti-disturbance performance of system this paper applies biology immune adjust principle and fuzzy control theory to design fuzzy immune self-adaptive controller which is used in VVVF hydraulic system, and gets favorable control effect finally. The remainder of this paper is organized as follows: In section II, mathematical model of hydraulic system is described. In section III the simulation results of PID is described. In sectio fuzzy control is described. In Section V fuzzy immune self-adaptive controller and simulation results are described. Concluding remarks are presented in section [1].

2 CONTROL MODEL AND MATHMATIC MODEL

2.1 Control model

The control model is composed by controller, frequency converter, electric motor, pressure sensor and hydraulic system which consist of pump, valves, accumulator etc. The control model is a negative feedback system by linking each model of main components. In figure 1 input variable is reference pressure 0P and output variable is practical

pressure P . e is selected as the error of inlet pressure of the tested valve, which is the difference of practical pressure P and the reference pressure 0P , and variable u is the control voltage of the frequency converter.

Fig 1. Principal of control model The purpose of control model simulation is to study and analyze the static and dynamic performance of the system and to find the optimal control parameters of the system. Of course, simulation is also very significant in the design and application of the VVVF hydraulic test system.

2.2 Mathematical Model

1. Formulas of converter and electric motor

The relationship between phase voltage 1U and current

frequency sf of the stator is given as:

Fuzzy Immune PID Control in VVVF Hydraulic system

Beitao Guo1,2, Hongyi Liu1, Yang Jiang1, Cao Yang1,Honghai Tian1

1. School of Mechanical Engineering & Automation, Northeastern University, Shenyang 110004, China

2.Shenyang Institute Of Chemical Technology, Shenyang 110034, China E-mail: guobabt@sohu.com

Abstract: This paper discusses and analyses precise hydraulic pressure control of VVVF hydraulic system. The mathematicalmodel of system is established and PID control law is adopted. Numerical simulation of PID controller is carried out with theSIMULINK of MATLAB. In the non-linear, time-varying VVVF hydraulic system, however, conventional PID control oftencannot satisfy the request of precise pressure control. This paper applies biology immune adjust principle and fuzzy controltheory to design fuzzy immune self-adaptive controller which is used in VVVF hydraulic system, and gets favorable controleffect. The MATLAB-based simulations show that fuzzy immune PID is effective in improving the control performance ofVVVF hydraulic system. Key Words: Mathematic model, PID, Fuzzy immune PID, Simulation

6154978-1-4244-2723-9/09/$25.00 c© 2009 IEEE

1(380 )

50 sbU f b−= • + (1)

1U phase voltage of stator

sf current frequency of stator

b compensating voltage value of stator.

Since the electric motor operates under the condition of VVV F, the moment equilibrium equation is specified as:

2 260 60

T Pn L T p

p

J dnT T B nm dt

π π− = + (2)

nT electromagnetism torque of electric motor

LT load breaking torque of electric motor;

TJ moment of inertia of motor shaft

pm magnetic antipode number of asynchronous motor;

TB torque of motor shaft;

pn motor speed.

2. Formula of pump

According to the performance of the flow rate and the pressure of the pump, the formula is given as:

0P pt pl

V dPQ Q QE dt

= − − (3)

PQ actual flow of pump;

PtQ theoretical flow of pump;

PlQ internal leakage of pump in low frequency;

0V cavity volume of pump;

E elastic modulus of oil;

P pressure of pump.

3. Formula of accumulator

Equilibrium equation of accumulator is given as:

2

1 ( )aS a a a a

a

dqP P m B qA dt

− = + (4)

sP outlet pressure of pump;

aP air pressure of accumulator;

am quality of oil cavity of accumulator;

aq flow of accumulator;

aB equivalent viscous damping coefficient of

accumulator;

aA area of oil cavity of accumulator.

4. Formula of hydraulic resistance of valves and pipes

The equivalent hydraulic resistance of valves and pipes is described as:

p PPQ G P= (5)

ppG hydraulic resistance coefficient of valves and

pipes;

pQ flow.

5. Formula of pressure sensor 'P kP= (6)

k Pressure sensor coefficient;

P Pressure sensor feedback pressure

We use Laplace Transform to transfer above formulas from 1 to 6, and setup complex transfer function block diagram, then simplify the transfer function block diagram and get the closed-loop mathematic model. It is shown as follows

0( ) ( )1DEP S P SDEk

=+

(7)

2

'2

32u f pk k m

DRπ

= (8)

1BEBAC

=+

(9)

0

0

2

212

p

a a SPP

a a a a

qA V s VG s

nP s s Eω

ω ξ ω

=+ + +

+ +

(10)

30(1 ) 30 /

p

p T p

m AB

m B Am qπ η=

+ − (11)

2 2

'240

p fm kC

Rπ= (12)

The mathematic model is very complex and high-order model. Selecting principle of mathematic model parameters is according to work requirements of different components which conclude size, mass, material, working conditions,

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structure, etc. After selecting parameter simulation can be carried out in different control strategy and study the optimal control strategy.

3 PID CONTROL AND SIMULATION PID control simulation is carried out with SIMULINK of MATLAB. PID control model of SIMULINK is shown as figure 2 and simulation curve is shown as figure 3.

Fig 2. PID control model in SIMULINK OF MATLAB

Fig 3. Simulation curve of PID control model Numerical simulation results of PID closed-loop model shows that we cannot get satisfy control effectiveness and small excessive overshoot. PID control is weak in eliminating the static error and cannot attain high control precision in complex VVVF Hydraulic system.

4 FUZZY CONTROL AND SIMULATION Fuzzy control, an intelligent control method imitating the logical thinking of human and being independent on accurate mathematical model of the controlled object, can overcome some shortcomings of traditional PID. [2]. Fuzzy simulation program is compiled in MATLAB m-file. Fuzzy PID control simulation is shown as in figure 4. The result of simulation is satisfied. Therefore the fuzzy control and adopting advanced VVVF technology are used to solve the precise pressure supplying problem.

Fig 4. Simulation cure of fuzzy control model

5 FUZZY IMMUNE PID CONTROL AND SIMULATION

In order to observe the anti-disturbance performance of system This paper applies biology immune adjust principle and fuzzy control theory to design fuzzy immune self-adaptive controller which is used in VVVF hydraulic system. Immune is a kind of biology response. The biological immune system has a strong robustness and adaptability in the environment with massive disturbances and uncertainty [3].

5.1 Immune Controller

Based on regulation rules of biological immune system the basic immune controller can be described in figure 5.

Fig 5. Block diagram of immune feedback controller The above immune controller is based on the immune feedback mechanism. It is a nonlinear P controller, whose proportional coefficient is altered with the controller output. Unfortunately, it cannot efficiently compensate for the errors caused by the nonlinear disturbance. 5.2 Fuzzy Immune PID Controller Immune fuzzy PID is a non-linear controller based on immune theory of biology system and fuzzy theory. The structure of fuzzy immune PID controller is illustrated in figure 6 in which the fuzzy controller applied has two input variables and one output variable [4].

Fig 6. The fuzzy immune PID controller Fuzzy immune PID simulation program is compiled in MATLAB m-file. In order to test the robustness of system a disturbance is added and immune control tracking curve is shown in figure 7 and figure 8.

6156 2009 Chinese Control and Decision Conference (CCDC 2009)

Fig 7. Simulation cure of fuzzy immune PID controller

Fig 8. Simulation cure of error In figure 7 and figure 8 we can see that controller responses quickly to disturbance and simulation curve indicates that fuzzy immune PID control has good control effect and robustness. Fuzzy immune PID controller possesses good adaptability when the parameters of the controlled object are changed. The simulate results provided a theoretical basis for the design and application of VVVF hydraulic system.

6 CONCLUSION Based on the biological immune feedback regulation strategy and fuzzy logic, a fuzzy immune PID controller is proposed in this paper to control VVVF hydraulic system. Numerical simulation indicates that it has more advantages than conventional PID. Fuzzy immune PID controller has the remarkable properties such as fast response, good robustness and small overshoot. Moreover, it has a strong ability to adapt to the change of system parameters and anti-disturbance performance [5].

REFERENCES [1] Lee C. D, Chuang C. W. and Kao C. C, 2004, “Apply Fuzzy

PID Rule to PDA Based Control of Position Control of Slider Crank Mechanisms,” In Proc. of IEEE Int. Conf. on Cybernetics and Intelligent Systems (CIS) and Robotics, Automation and Mechatronics (RAM), Singapore, pp. 508~513.

[2] Fuzzy-PID Controller in Heating Ventilating and Air-Conditioning System,” In Proc. of the IEEE Int. Conf. on Mechatronics and Automation, China, pp. 2217~2222

[3] Kawafuku M, Sasaki M, Takahashi. Adaptive learning method of neural network controller using an immune feedback law[A]. In 1999 IEEE/ASME International Conference on Advanced Intelligent Mechatronics[C]. Piscataway NJ: IEEE, 641-646, 1999

[4] Wei W, Guo-hong Z: Artificial Immune System and Its Application in The Control System. Control Theory and Application, 158-160 , 19(2002)

[5] Kubota, A., Kato, H., Yamaguchi, H.: A new modelling of cavitating flows: a numerical study of unsteady cavitation on a hydrofoil section. J. Fluid Mech. 240, 59–96 (1992).

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