Research on Fuzzy PID Control of Hydraulic Position Servo System

1. Introduction

Nowadays, hydraulic servo systems are widely used in automation fields such as industry and national defense due to their advantages of light weight, small size, and large torque generation. However, due to factors such as oil leakage and oil contamination, hydraulic servo systems generally have time-varying parameters, nonlinearity, and especially nonlinearity of flow in valve-controlled power mechanisms. With the increasing requirements for control accuracy, higher and higher requirements are also placed on hydraulic servo control technology. Traditional PID control is difficult to achieve satisfactory control effects. To address this problem, many different modern control strategies have emerged in recent years, such as neural network control, adaptive control, fuzzy control, and predictive control. These control methods have made great progress in theory, but there are still some practical problems that need to be solved in hydraulic servo control [1].

Fuzzy control does not require an accurate mathematical model of the controlled object and can introduce expert experience, so it has good practicality. However, it is not easy to eliminate steady-state errors using fuzzy control alone, and it has high requirements on the controller's computing performance [2]. The PID algorithm is simple and can effectively eliminate steady-state errors. In this regard, this paper combines fuzzy control with PID control, and uses fuzzy control to correct PID parameters in real time, which improves the control accuracy and robustness of the system and has good practicality.

2. Hydraulic position servo system

Figure 1 Structure diagram of hydraulic position servo system

As shown in Figure 1, the hydraulic position servo system consists of an amplifier, an electro-hydraulic servo valve, a hydraulic cylinder, a load, and a position sensor. The input signal is amplified and sent to the electro-hydraulic servo valve. The low-power electrical signal is converted into a valve core displacement signal through the servo valve, and then converted into hydraulic signals such as flow and pressure. These signals finally drive the hydraulic cylinder to drive the load to complete the specified action.

Because the electro-hydraulic servo valve realizes the two functions of electro-hydraulic signal conversion and hydraulic power amplification, it plays the role of a bridge in the servo system and is the heart of the system. In this article, the position servo system adopts a two-stage electro-hydraulic servo valve with a moving iron torque motor, nozzle and baffle.

Based on the voltage, magnetic circuit and motion equation of the torque motor, the relationship between the nozzle flapper displacement and the motor deflection angle, and the motion equation and flow equation of the main valve (symmetrical four-way slide valve) [3], the transfer function of the electro-hydraulic servo valve can be derived as follows:

In the formula: ω _sv is the natural frequency of the servo valve; ξ _sv is the damping ratio; Kq is the servo valve flow gain, which should be determined according to the actual no-load flow under the actual oil supply pressure, that is , qn is the rated flow of the servo valve, ps is the actual oil supply pressure, psn is the specified valve pressure drop of the servo valve, generally psn=7MPa, and In is the rated current of the servo valve.

In addition, the actuator in this article is a hydraulic cylinder, and the load is pure inertia, without considering factors such as frame stiffness. The transfer function of the valve-controlled cylinder can be derived from the motion equation as follows:

Where: Q0 is the no-load flow rate of the servo valve, , the symbols have the same meaning as before; P is the effective area of ​​the hydraulic cylinder piston; ωh is the hydraulic natural frequency; ξh is the hydraulic damping ratio;

Through the above derivation, the mathematical model (1) (2) of the hydraulic controlled part in the hydraulic position servo control system is obtained. Then, on the basis of using PID control, the three parameters of PID proportion, integration and differentiation are corrected through fuzzy control. In this way, the system can be guaranteed to be in the optimal state under different conditions, thereby improving the system control accuracy, and having better real-time and robustness. As shown in Figure 2, the block diagram of the designed hydraulic position servo fuzzy PID control system.

Figure 2 Hydraulic position servo fuzzy PID control system

3. Fuzzy PID control

This paper uses fuzzy control method to achieve online adjustment of PID parameters. The input of fuzzy control is error and error change rate, and the output is the adjustment amount of three PID parameters △kp, △ki and △kd. According to the basic domain of the hydraulic position servo system setting [0.6, 0.6], the basic domain of is [0.3, 0.3], and the corresponding fuzzy domain is {-3, -2, -1, 0, 1, 2, 3}, so the quantization factor is now the fuzzy set E of error e and error change rate ec, EC = {NB, NM, NS, Z, PB, PM, PB}, and its membership function is shown in Figure 3:

Figure 3. Member number function of error

The fuzzy domains of the fuzzy control outputs △kp, △ki and △kd are {-3,-2,-1,0,1,2,3}, {-0.06,

The membership functions of the three output variables are the same as those of the input error and error change rate, and all use trigonometric functions, which are not listed here one by one.

After fuzzifying the precise quantity, the fuzzy rule tables of the fuzzy output variables △kp, △ki and △kd can be derived respectively according to the fuzzy sets and membership functions of each quantity by using MAX-MIN fuzzy reasoning. It is very important to consider the effects of the three PID parameters and their relationship based on theoretical knowledge and engineering experience.

According to the fuzzy output inferred by the fuzzy rules in Tables 1, 2, and 3, the actual accurate values ​​of the three PID parameters can be obtained through defuzzification, thereby realizing online adjustment of the PID. In order to achieve better fuzzy control effect, this paper uses the median defuzzification method.

4. MATLAB simulation results

Select the DYC1-40L electro-hydraulic servo valve, whose parameters are: q _n =40L/min, actual oil supply pressure . The hydraulic cylinder parameters are: . Simulink is used in Matlab to establish the step response simulation model of PID control and fuzzy PID control, and white noise interference with an amplitude of 1 is added to simulate the time variation of the model. The simulation waveform is as follows:

5. Conclusion

The simulation results show that when the PID setting parameters are the same, adding fuzzy control to modify the PID parameters in real time can better control the controlled object. As can be seen from Figures 4 and 5, once the PID parameters are fixed, their applicability under time-varying conditions is greatly restricted, while the fuzzy PID can keep the control performance in the optimal state through online self-adjustment of parameters, with better control accuracy and robustness. In addition, when adjusting the fuzzy control parameters, special attention should be paid to the role of the quantization factor and the proportional factor.