## 5 Conclusions  
This paper proposes an ARC strategy for high-performance control of pump-controlled pitch systems in large wind turbines. Through theoretical analysis, numerical simulation, and physical experiments, the following main conclusions can be drawn:  
Figure 13: Comparison of pitch angle tracking errors between PID and ARC controllers during cylinder retraction.  
1. The proposed mathematical model for pump-controlled pitch systems effectively integrates the angular dynamics of the pitch mechanism and hydraulic system characteristics. The model considers major nonlinear factors, system parameter uncertainties, and wind speed disturbance effects, providing a reliable theoretical foundation for controller design.
2. PSO was used to optimize both the PID and ARC parameters under wind speed disturbance conditions. With the obtained optimal parameter combinations, the PID and ARC controllers showed similar tracking performance for sinusoidal signals, with PID performing slightly better than ARC, indicating that PID control can outperform ARC under specific conditions.
3. The simulation results demonstrate that when system parameters change due to various factors, the ARC controller maintains a small tracking error below 0.15\({}^{\circ}\), while the PID controller's error exceeds 1.5\({}^{\circ}\). The physical test bench results further confirm the practicality of this control strategy. During hydraulic cylinder reciprocating motion, especially in the retraction phase, the ARC controller shows excellent tracking performance with an error fluctuation range of approximately 0.1\({}^{\circ}\), significantly outperforming the PID controller's range of 0.7\({}^{\circ}\). This indicates that the proposed control strategy can effectively handle nonlinear characteristics and uncertainties in actual systems.  
This research offers valuable insights into energy-efficient design for wind turbine pitch systems. By adopting a pump-controlled solution combined with high-performance control strategies, system energy consumption can be reduced while maintaining control performance, which is significant for improving the overall efficiency of wind turbines. Future research will focus on developing control strategies that better address wind conditions and pitch system nonlinearities typically observed in wind turbine operation, while fully utilizing the energy-saving advantages of pump-controlled systems. Multi-objective optimization methods will be employed to further enhance the energy-saving effects while ensuring system stability and high performance.  
Conceptualization, T.Z. and B.Y.; methodology, B.Y. and G.C.; experiment, X.W. and Y.L.; software, X.W. and K.L.; investigation, K.L.; writing--original draft preparation, Y.L.; writing--review and editing, L.W.; analysis, L.W. and T.Z.; project administration, C.A.; funding acquisition, C.A. and G.C. All authors have read and agreed to the published version of the manuscript.  
This research was funded by the National Natural Science Foundation of China (U22A20178), the Research Fund Project of Xinjang Institute of Engineering (2024 xyg142605), the Autonomous Region Colleges and Universities Research Program (XJEDU2024P087), the Natural Science Foundation of Xinjang Uygur Autonomous Region (2022D01A244), and the Basic Research Funds for Universities of Xinjang (XJEDU2023P138).  
Not applicable.  
The original contributions presented in the study are included in the article, further inquiries can be directed to the corresponding author.  
Author [PERSON] was employed by the company Sichuan Chuanrun Intelligent Fluid Technology Co., Ltd. and author [PERSON] was employed by the company Shougang Jingtang United Iron & Steel Co., Ltd. The remaining authors declare that the re-search was conducted in the absence of any commercial or financial relationships that could be construed as a potential conflict of interest.