Abstract: To address the parameter uncertainty of hydraulic servo systems, a fuzzy model reference learning control method is proposed. This method adjusts the fuzzy rules of the fuzzy controller in real time through a learning mechanism, thereby enabling the object's output to track the output of the reference model. Furthermore, this method exhibits strong robustness. Simulation results verify its superiority. Keywords: hydraulic servo system; model reference control; fuzzy control; learning mechanism The Fuzzy Model Reference Learning Control of the hydraulic servo system Abstract: Contraposing the parameter uncertainty of hydraulic servo system, a Fuzzy Model Reference Learning Control (FMRLC) is proposed. This method can dynamically adjust the rules of fuzzy control mechanism by learning mechanism in real time, so that the output of the plant can follow the output of the reference model, and it can effectively moderate the unknown and time-varying external load disturbances. The simulation results show the effectiveness of this approach. Key words: hydraulic servo system; model reference control; fuzzy control; learning mechanism 0 Introduction The working environment of hydraulic systems is complex, and the system has considerable uncertainty, as well as changes in inertial load during operation, making it difficult for controllers designed in traditional theory to be applied in practice. A better way to solve this problem is to adopt adaptive control. The system requires small steady-state error and good speed, which brings great difficulties to the design of the control system. It is difficult to establish an accurate mathematical model for the hydraulic servo system, and traditional control strategies can no longer meet its precise control requirements. With the development of artificial intelligence control, fuzzy control, with its logic control method that does not rely on the accurate mathematical model of the controlled object, is well-suited for the control of hydraulic servo systems. In the design of the adaptive law of Model Reference Adaptive Control (MRAC) for hydraulic servo systems, a fuzzy model reference learning controller (FMRLC) designed by replacing the conventional adaptive mechanism with a fuzzy self-learning mechanism can achieve better control performance. 1 Mathematical Model of Hydraulic Servo System To make the problem specific and general, a valve-controlled hydraulic servo position system is selected as the research object. Through analysis of the system, its transfer function can be obtained as [1]: (where,) Where: K[sub]α[/sub] is the flow amplification coefficient of the valve; is the effective working area of ​​the hydraulic cylinder; ω[sub]n[/sub] is the natural frequency of the hydraulic cylinder; is the damping ratio of the power element; is the equivalent volume elastic coefficient of the liquid and the cylinder wall; M[sub]t[/sub] is the total mass of the piston and load; V[sub]t[/sub] is the total volume of the hydraulic cylinder; K[sub]ec[/sub] is the total flow pressure coefficient (elastic coefficient). Considering the influence of external load force interference, the block diagram of the controlled object of the entire hydraulic servo position system is shown in Figure 2. Where: r is the system reference input; y is the system output displacement; K[sub]a[/sub] is the servo amplification gain; K[sub]sv[/sub] is the static flow gain of the servo valve; K[sub]f[/sub] is the displacement sensor amplification factor. [align=center] Figure 2 Block diagram of hydraulic servo position system[/align] The open-loop transfer function of the system can be obtained as follows: (where the open-loop amplification factor) 2 Design of Fuzzy Model Reference Learning Controller The functional block diagram of the FMRLC is shown in Figure 3 [2-3]. It mainly consists of four parts: the controlled object, the adjustable fuzzy controller, the reference model, and the learning mechanism (adaptive mechanism). The FMRLC uses the learning system to observe the data in the fuzzy controller (e.g., r(KT) and y(KT), where T is the sampling period). This data is used to depict the current performance and automatic processing of the fuzzy control system, and then the fuzzy controller is automatically adjusted to achieve some given performance indicators. These performance indicators (closed-loop specifications) are set by the reference model shown in Figure 3. In conventional MRAC and similar methods, its conventional controller is adjustable, and the learning mechanism adjusts the fuzzy controller by searching to make the closed-loop system (the graph from r(KT) to y(KT)) behave like a given reference model (the graph from r(KT) to y[sub]m[/sub](KT). Basically, the fuzzy control system loop (lower part in Figure 3) operates so that y(KT) tracks y(KT) by processing u(KT), while the higher-position self-learning control loop (upper part in Figure 3), after searching, makes the controlled device output r(KT) track the reference model output y[sub]m[/sub](KT) by processing the fuzzy controller parameters. [align=center] Figure 3 Fuzzy Model Reference Learning Controller Principle[/align] 2.1 Fuzzy Controller The controlled object in Figure 3 has an input u(KT) and an output y(KT). Usually, the input of most fuzzy controllers is realized through some functions of the controlled device output y(KT) and the reference input r(KT). For this purpose, the input signals of the fuzzy controller are set as the error signal e(KT) of the reference output and the system output and the error signal change rate c(KT), which are defined as: Error Change Rate (e.g., pd fuzzy controller). Placing a smoothing filter between the reference input r(KT) and the total crossover point is necessary because such a filter ensures that only smooth and reasonable requirements are used by the fuzzy controller. (For example, a square wave input to r(KT) might be unreasonable for some known systems, which do not respond instantly.) Sometimes, if you want to find an optimal trajectory for an unreasonable reference input in the system, the FMRLC will continuously adjust the gain of the fuzzy controller until its variation meets the requirements. In Figure 3, we use a scaling gain added to the error e(KT) to change the error c(KT) and the control output u(KT) respectively. The first guess for these gains can be obtained as follows: the gain is selectable, and the typical range of values ​​cannot be obtained, so the values ​​will lead to saturation of the outermost input rate function of the response. The gain can be determined through trial results with different inputs to the fuzzy controller (excluding the adaptive mechanism), and c(KT) can be determined after determining the conventional range of values. Using this approach, we choose a gain g[sub]c[/sub] such that the constant value of c(KT) does not cause the rate function of the outermost input to saturate. We choose g[sub]u[/sub] so that the output range is maximized to prevent the input of the controlled object from saturating (in reality, the input of the controlled object often saturates at some values). Obviously, these choices of gain do not always keep the system operational, so sometimes we need to adjust these gains by adjusting the overall FMRLC. To facilitate the implementation of the fuzzy controller using a normalized universe of discourse, the scaling factor of the controller is set such that the controller input satisfies: . Suppose the controller inference rule has the following form: where are linguistic variables related to the controller inputs e(KT), c(KT) and output u(KT). are the values ​​of the corresponding linguistic variables, respectively. In the design of the fuzzy adaptive law here, we make the input and output of the fuzzy controller uniformly divided according to the division shown in Figure 4. Among them, NVB, NB, NM, NS, Z0, PS, PM, PB, and PVB represent the linguistic variables of the input and output, and the fuzzy set of the fuzzy inverse model in the following description is also divided according to the division shown in Figure 4. 2.2 Reference Model The reference model and the controlled object have the same input, indicating the desired characteristics (overshoot, rise time, etc.) required by the control system. It can usually be described by linear or nonlinear, time-varying or time-invariant, discrete or continuous time system. In the design of the adaptive system, it is used as the design target and tracked with a certain accuracy. The general model reference adaptive control requires that the reference model must have the same order as the system model [3], which greatly limits its application range. Fuzzy Model Reference Learning Control Due to the role of the self-learning mechanism, the adjustment effect can be generated according to the difference between the self-learned modified reference model and the output of the controlled system and its rate of change. Therefore, a low-order system can be used as the reference model. The second-order reference model is taken as: (where the parameter values ​​are) 2.3 Learning Mechanism The learning mechanism adjusts the rule base of the direct fuzzy controller so that the output of the entire closed-loop system can track the ideal output of the reference model. The correction values ​​of these rule bases are obtained from the observation data of the control process, the reference model, and the fuzzy controller. The learning mechanism consists of two parts: the fuzzy inverse model and the knowledge base correction. The function of the fuzzy inverse model is to use the fuzzy system to complete the mapping between the error quantity (representing the deviation from the ideal value) and the process input p(KT) of the controlled object, so that it can be used to force it to tend to 0. The function of the knowledge base correction is to change the rule base of the fuzzy controller at any time by adjusting p(KT) online, thereby affecting the changes required in the process input to reduce the output error between the reference model and the controlled device. At the same time, the purpose of modifying the knowledge base can be achieved by adjusting the fuzzy relations implemented by the fuzzy controller. Since it is usually a high-dimensional matrix, in order to reduce the amount of computation and improve the computational efficiency, the method of directly adjusting the membership function of the fuzzy subset of the controller output linguistic variables is a good strategy. To make the tracking error y[sub]ε[/sub] approach zero, the knowledge base is modified to adjust the rule base of the fuzzy controller so that the output of the fuzzy controller at the previous moment is adjusted by P(KT) and then applied to the object. Assume that the input of the controller affects the output of the system within one sampling step, that is, u(KT-T) affects y(KT). Therefore, the correction mechanism forces the fuzzy controller to generate a desired output signal u(KT-T)+P(KT), which is applied to the object at time (KT-T) and thus makes y[sub]ε[/sub](KT) smaller. Assume that the fuzzy controller adopts a symmetric output membership function, and some uniformly partitioned membership functions of fuzzy subsets are defined on the fuzzy variable domain, denoted by . Therefore, the knowledge base correction can be accomplished by moving the center value of the fuzzy set membership function related to the controller output at the previous moment. Specifically, it can be divided into two steps: (1) Find the rules in the controller rules whose antecedents satisfy the following formula: Correct the center of the output membership function; rules that are not in the active set do not need to be corrected. 3 Simulation Study The system was simulated using Matlab[4]. The step response curves of the fuzzy model reference learning control algorithm and the traditional PID control algorithm are shown in Figure 5. The simulation results of FMRLC and traditional PID were compared. RM represents the output curve of the reference model. Through debugging, it can be seen from the simulation results that the parameters of FMRLC are adjusted faster. From the perspective of system response, its steady-state response process is faster than that of traditional PID. At the same time, the overshoot of FMRLC is smaller than that of traditional PID. It can be seen that FMRLC also has good robustness. [align=center] Figure 4 Partition of fuzzy input and output rate functions Figure 5 Step response curves of FMRLC and PID[/align] 4 Conclusion In view of the uncertainty of the parameters of the hydraulic servo system, a fuzzy model reference learning control method based on the learning self-adjustment mechanism is proposed. This method changes the inference rules of the fuzzy controller in real time through the self-learning adjustment of the learning mechanism, so as to improve the output adjustment accuracy of the fuzzy self-learning mechanism. Since this method has good robustness, it has high practical value in the controller design of hydraulic servo system.