Abstract: To address the time-varying and nonlinear characteristics of parameters in hydraulic position servo systems, this paper employs a fuzzy PID control algorithm to achieve online self-adjustment of PID parameters. Matlab simulations demonstrate that, compared to traditional PID control, fuzzy PID control exhibits advantages such as smaller overshoot, higher steady-state accuracy, and stronger robustness.
Keywords: servo valve; position servo system; fuzzy control; fuzzy PID
Abstract: The Fuzzy PID Control was proposed for modifying the parameters of PID online for time-varying nonlinear Hydraulic Position Servo System. The simulation results based on Matlab have shown that Fuzzy PID Control system has smaller overshoot, higher steady-state precision and stronger robustness than the traditional PID Control.
Keywords: Servo valve; Position Servo System; Fuzzy Control; Fuzzy PID
1. Introduction
Today, hydraulic servo systems are widely used in industrial and defense automation fields due to their advantages such as light weight, small size and large torque generation. However, due to factors such as oil leakage and oil contamination, hydraulic servo systems generally have phenomena such as 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 put forward for hydraulic servo control technology. Traditional PID control is difficult to achieve satisfactory control effect. In response to 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 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, thus having good practicality. However, fuzzy control alone is not easy to eliminate steady-state error and has high requirements for the computing performance of the controller [2], while the PID algorithm is simple and can eliminate steady-state error well. In this regard, this paper adopts a combination of fuzzy control and 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, this 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 by the servo valve, and then into hydraulic signals such as flow rate and pressure. These signals finally drive the hydraulic cylinder to move the load to complete the specified action.
Because the electro-hydraulic servo valve realizes both the conversion of electro-hydraulic signals and the amplification of hydraulic power, it plays a bridging role in the servo system and is the heart of the system. In this paper, the position servo system adopts a two-stage electro-hydraulic servo valve with a moving iron torque motor and nozzle baffle.
Based on the voltage, magnetic circuit and motion equation of the torque motor, the relationship between the nozzle baffle 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: ωsv is the natural frequency of the servo valve; ξsv is the damping ratio; ­­­­­­­Kq is the flow gain of the servo valve, which should be determined according to the actual no-load flow under the actual oil supply pressure, i.e., 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.
Furthermore, in this paper, the actuator is a hydraulic cylinder, and the load is pure inertia. Factors such as frame stiffness are not considered. The transfer function of the valve-controlled cylinder can be derived from the equations of motion as follows:
In the formula: Q0 is the no-load flow rate of the servo valve, with the same symbol 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;
The mathematical models (1) and (2) of the hydraulic controlled part in the hydraulic position servo control system are obtained through the above derivation. Then, based on PID control, the proportional, integral, and derivative parameters of PID are corrected by fuzzy control. This ensures that the system is in the optimal state under different conditions, thereby improving the system control accuracy and providing better real-time performance and robustness. Figure 2 shows 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 to achieve online adjustment of PID parameters. The inputs to fuzzy control are the error and the rate of change of error, and the outputs are the adjustment values of the three PID parameters Δkp, Δki, and Δkd. Based on the basic universe of discourse set for the hydraulic position servo system as [0.6, 0.6] and [0.3, 0.3], their corresponding fuzzy universes are both {-3, -2, -1, 0, 1, 2, 3}. Therefore, the quantization factor is now taken as the fuzzy set E of the error e and the rate of change of error ec, EC = {NB, NM, NS, Z, PB, PM, PB}, and its membership functions are shown in Figure 3.
Figure 3. Membership function of error
The fuzzy universes of discourse for the outputs Δkp, Δki, and Δkd of the fuzzy control are {-3, -2, -1, 0, 1, 2, 3}, {-0.06, }, and {-0.06}, respectively.
The fuzzy sets of the three output variables are {-0.04, -0.02, 0, 0.02, 0.04, 0.06} and {-0.3, -0.2, -0.1, 0, 0.1, 0.2, 0.3}, and their fuzzy sets are all {NB, NM, NS, Z, PB, PM, PB}. The membership functions of the three output variables are the same as those of the input error and the rate of change of error, all using trigonometric functions, which are not listed here.
After fuzzifying the precise quantities, based on the fuzzy sets and membership functions of each quantity, MAX-MIN fuzzy inference can be used to derive the fuzzy rule tables of the fuzzy output variables △kp, △ki, and △kd respectively. An important point is that the role of the three PID parameters and their interrelationships must be considered based on theoretical knowledge and engineering experience.
Based on the fuzzy output values derived from the fuzzy rules in Tables 1, 2, and 3, the actual precise values of the three PID parameters can be obtained through defuzzification, thereby enabling online adjustment of the PID. To achieve better fuzzy control performance, this paper uses a median-based defuzzification method.
4. MATLAB simulation results
A DYC1-40L electro-hydraulic servo valve was selected, with parameters: q <sub>n</sub> = 40L/min, and actual oil supply pressure. The hydraulic cylinder parameters are as follows: A step response simulation model of PID control and fuzzy PID control was established using Simulink in Matlab, and white noise interference with an amplitude of 1 was added to simulate the time-varying nature of the model. The simulation waveform is shown in the figure below:
5. Conclusion
Simulation results show that, with the same PID settings, adding fuzzy control to correct the PID parameters in real time can better control the controlled object. As shown in Figures 4 and 5, once the PID parameters are fixed, their applicability under time-varying conditions is greatly limited. In contrast, fuzzy PID, through online self-adjustment of parameters, keeps the control performance in an optimal state, exhibiting better control accuracy and robustness. Furthermore, when adjusting fuzzy control parameters, special attention should be paid to the roles of the quantization factor and the proportional factor.
References:
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