## 1 Introduction
The outcomes from both simulations and practical experiments substantiated the efficacy of the suggested control strategy, confirming the successful attainment of a consistent speed output from the variable motor. Professor [PERSON] and his colleagues focused on the quantitative pump-variable motor speed-control system and adopted a fuzzy PID controller to achieve constant-speed control. The findings from the simulation revealed that the fuzzy PID controller markedly enhanced the efficacy of the speed-control system when juxtaposed with the traditional PID controller [17]. In the field of fuzzy PID control, [PERSON] et al. [18] combined PSO with fuzzy PID control for the speed regulation of DC motors and optimized the input and output gains of the fuzzy PID controller. The outcomes of the simulation illustrate that the refined controller displays outstanding capabilities in tracking trajectories accurately. [PERSON] et al. [19] introduced an enhanced genetic algorithm into the fuzzy PID control for a first-order inverted pendulum control system. The simulation validated the performance of the optimized algorithm, which effectively mitigates the issue of premature convergence inherent in traditional genetic algorithms. [PERSON] et al. [20] incorporated an enhanced Levy flight strategy into the particle swarm optimization algorithm for the temperature and humidity regulation of fruit and vegetable storage containers and subsequently optimized the fuzzy PID control. The simulation outcomes indicated that the enhanced algorithm achieves superior precision in controlling temperature and humidity. [PERSON] et al. [21] addressed the measurement-accuracy challenges of the MRTD tester by integrating an enhanced dung beetle algorithm into the fuzzy PID controller. Through simulations and experiments, they verified that the enhanced controller achieves significantly shorter regulation and ascension times, further underscoring the superiority of the control algorithm. [PERSON] et al. [22] focused on the temperature and humidity regulation of lithchi fresh-keeping equipment. They combined an enhanced PSO with a fuzzy PID controller. The simulation affirmed that the enhanced algorithm provides remarkable control efficacy and adeptly addresses the nonlinearity and hysteresis challenges inherent in the equipment. [PERSON] et al. [23] combined SDA (Spiral Dynamics Algorithm) and BFA (Bacterial Foraging Algorithm) for the fuzzy PID control of flexible robotic arms and validated the efficacy of the hybrid algorithm strategy. [PERSON] et al. [24] integrated the Whale Optimization Algorithm (WOA) with a fuzzy PID controller to address frequency regulation challenges in power systems. They verified that the optimized controller achieves excellent performance, although the approach suffers from slow convergence speed. [PERSON] et al. [25] presented GWO (the Grey Wolf Optimizer algorithm) as a novel approach for enhancing the fuzzy logic power system stabilizer. They confirmed that the optimized controller achieves a significantly faster system response time. Recently, the rapid progress in intelligent optimization approaches has resulted in their expanding use across various control-related applications. The integration of intelligent optimization algorithms with fuzzy PID control provides new perspectives for addressing the control challenges of complex nonlinear systems. In the context of speed control for hydraulic wind turbines, traditional PID controllers, despite their simple structure and ease of implementation, often fail to meet performance requirements under complex operating conditions, such as random wind speed fluctuations. To address this issue, researchers have suggested various control schemes. However, there remains relatively limited research on the combination of intelligent algorithms and fuzzy PID control.