## 4 Experimental Results and Analysis
### Bench Test  
To further verify the control effect of PID and ARC, a physical test bed, as shown in Figure 11, was built for testing. The controller parameters are consistent with the software simulation parameters.  
Table 3 shows the test stand hydraulic components that were selected.  
Based on the PSO-optimized parameters, the PID and ARC controllers were implemented on the physical test bed to control the hydraulic cylinder in sinusoidal motion. The pitch angle was calculated based on the displacement of the hydraulic cylinder. The comparative tracking performance is illustrated in Figure 12.  
Figure 11: Pitch control system’s physical test bed.  
Figure 12: Experimental comparison of pitch angle tracking performance between PID and ARC controllers.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Serial Number** & **Component Name** & **Manufacturer** \\ \hline
1 & Temperature Sensor & Zhuhong (Wuxi, China) \\
2 & Pressure Sensor & Zhuhong \\
3 & Relief Valve & SUN (Houston, TX, USA) \\
4 & Two-Way Directional Valve & SUN \\
5 & Throttle Valve & SUN \\
6 & Accumulator & Liming (Zhoushan, China) \\
7 & Check Valve & Huade (Beijing, China) \\
8 & Displacement Sensor & Xiju (Wuhan, China) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Key components and manufacturers of the pump-controlled pitch system.  
The experimental results demonstrate that both the PID and ARC controllers can track the reference pitch angle effectively under physical test conditions. However, during the hydraulic cylinder retraction process (5-10 s), the ARC controller exhibits notably superior tracking performance compared to the PID controller. The tracking errors of both controllers are shown in Figure 13.  
The results indicate that the tracking error fluctuation range of the PID controller is approximately 0.7 degrees, while that of the ARC controller is about 0.1 degrees. This performance difference can be attributed to the asymmetric characteristics of the hydraulic cylinder, where the flow rates during extension and retraction are unequal. Since the PID parameters remain fixed while the ARC controller can adjust its response through parameter estimation via adaptive laws, the ARC controller demonstrates superior performance in handling both system nonlinearities and external disturbances.  
Based on the simulation and physical test bench results, the proposed ARC strategy demonstrates significant advantages in the pitch control system. In the numerical simulations, both the PID and ARC parameters were initially determined through empirical methods and then optimized using a Particle Swarm Optimization algorithm to obtain optimal parameter combinations under wind speed disturbances. With only wind speed disturbance, PID and ARC showed comparable sinusoidal signal tracking performance, with PID slightly outperforming ARC. In the parameter perturbation tests, the ARC strategy exhibited better robustness--even with system parameter changes, the maximum tracking error increment remained around 0.15\({}^{\circ}\), while PID's tracking error was significantly larger, reaching approximately 1.5\({}^{\circ}\), showing notably lower robustness than ARC. The physical test bench results corroborated the simulation findings--during hydraulic cylinder extension and retraction, the ARC controller's tracking error fluctuation range (approximately 0.1\({}^{\circ}\)) was significantly better than that of the PID controller (approximately 0.7\({}^{\circ}\)), demonstrating the feasibility of this control strategy in practical engineering applications. Particularly in handling internal and external disturbances and nonlinear issues such as hydraulic cylinder asymmetric characteristics, the ARC controller showed clear performance advantages through its parameter adaptation mechanism. These experimental results not only validate the effectiveness of the proposed control strategy but also provide a practical solution for precise control of pitch systems in large wind turbines.