## 4 Controller Design  
The open-loop transfer function of the valve-controlled hydraulic cylinder system is derived from Equation (15). This transfer function is a nonlinear function. Based on the literature [5], the Bode diagram of the variable motor speed-control system is analyzed. The Bode diagram of the system is illustrated in Figure 4, and the corresponding parameter values are provided in Table 1.  
By analyzing Figure 4, the amplitude margin of the open-loop system is found to be +7.76 dB, and the phase margin is +6.07 deg. Theoretically, the system is stable. However, the extremely small phase margin indicates a very low damping ratio, leading to significant overshoot and prolonged settling time. Additionally, the system exhibits poor robustness against parameter variations and external disturbances. Therefore, it is necessary to implement a controller for correction. Traditional PID control is simple to operate and easy to adjust. However, due to the strong nonlinearity of the speed-control system in hydraulic wind turbine generator sets, fixed PID parameter values cannot simultaneously satisfy both the dynamic and static performance requirements of the system. Therefore, this paper proposes the use of a fuzzy PID controller, which combines the high adaptability of the fuzzy control algorithm with the high precision of the PID controller to effectively manage the nonlinear system. The \begin{table}
\begin{tabular}{c c} \hline \hline
**Parameter** & **Parameter Value** \\ \hline \(K_{\beta\text{s}V}\) & \(1.25\times 10^{-5}\) \\ \(A_{p}\) & \(1.05\times 10^{-3}\) m\({}^{2}\) \\ \(V_{l}\) & \(5.0\times 10^{-4}\) m\({}^{3}\) \\ \(\beta_{e}\) & \(7.0\times 10^{8}\) Pa \\ \(m_{i}\) & \(2.5\) kg \\ \(B_{p}\) & \(1.78\times 10^{5}\) N\(\cdot\)s/m \\ \(K\) & \(6.23\times 10^{3}\) N\(\cdot\)m \\ \(F_{L}\) & \(50\) N \\ \(K_{ce}\) & \(5.0\times 10^{-12}\) m\({}^{5}\)/(N\(\cdot\)s) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: System parameters. Figure 4: Bode diagram of the open-loop system. principle of fuzzy PID control is illustrated in the figure. In this study, a two-input and three-output fuzzy controller is employed, where the inputs are the deviation, \(e\), and the deviation change rate, _ec_, and the outputs are the parameter adjustment values, _dkp_, _dKi_, and _dkd_. The fuzzy universes of discourse for these five variables are confined to the range of [\(-\)1,1] and divided into seven fuzzy subsets: [Negative Big, Negative Medium, Negative Small, Zero, Positive Small, Positive Medium, Positive Big], abbreviated as {NB, NM, NS, ZO, PS, PM, PB}. The fuzzy rule tables for _dKp_, _dKi_, and _dkd_ are presented in Table 2[30]. The corresponding three-dimensional response surfaces are depicted in the Figure 5.  
In hydraulic systems, mechanical stress on components like pumps, motors, and pipes is a major concern, while the time constant plays a crucial role in determining system responsiveness. Traditional fuzzy PID controllers, once designed, employ fixed fuzzy rules, defuzzification methods, and static quantization and proportional factors, which restrict their adaptability. Such limitations can lead to significant operational issues. For example, in hydraulic actuators, the inability of the controller to adjust to varying loads may prolong the time required to reach the target position (linked to the time constant), resulting in inefficient performance. Additionally, during sudden load changes, a fixed-parameter fuzzy PID controller often fails to provide an adequate response. Inadequate flow rate regulation under such conditions can cause a sharp pressure increase in the hydraulic motor, leading to elevated mechanical stress on system components. These issues highlight the constraints imposed by fixed proportional and quantization factors, which hinder the controller's effectiveness in managing the complex and variable demands of hydraulic systems.