Objective The optical tracking system has increasingly stringent requirements on the tracking precision, response time, and anti-interference ability of the servo table. Traditional control methods have shortcomings in terms of tracking precision and disturbance suppression. In order to enhance the control precision and anti-disturbance ability of the optical servo control system, this paper proposes a robust predictive control method with certain parameter self-regulation ability based on the continuous-time model.
Methods Firstly, the servo turntable system is modeled, and the influence of disturbances on the system state is analyzed. The linear extended state observer equation is constructed to estimate the uncertain disturbances in the system. Secondly, the derivation process of the turntable speed ring generalized predictive control law from the prediction model, performance indicators to the rolling optimization is given. The linear state model of the system is Taylor expanded to obtain the prediction model, and the system states of all orders are given by the state observer. The reference trajectory is output by the tracking differential. The optimization problem is solved based on the error-based performance index, and the current optimal control law is computed. Furthermore, the prediction domain update formula of the generalized predictive control is designed using the gradient descent idea, achieving self-adjustment, and the stability of the closed-loop control system is analyzed using Lyapunov theory, verifying the feasibility of the system. Finally, the simulation experiments show the improvement in tracking performance and disturbance rejection of the control method.
Results and Discussions Firstly, the simulation results of the improved GPC, linear model GPC, and cascade PID control methods are presented (Fig.5), and the tracking accuracy of the three methods is analyzed (Fig.10). The results show that the improved GPC has a 78.72% improvement in control accuracy compared to the cascade PID, and a 59.89% improvement compared to the linear GPC (Tab.2). Secondly, to verify the disturbance rejection capability of the control system, disturbances were added to the system, and the suppression performance of the three methods was compared (Fig.11-Fig.12). The results show that the improved GPC has a 58.95% improvement in the suppression of speed disturbance amplitude compared to the cascade PID (Tab.3); the improved GPC has a 56.91% improvement in the suppression of speed disturbance amplitude compared to the linear model GPC (Tab.4). Finally, the suppression ability of the three methods against sudden load addition was compared (Fig.12), and the tuning effect of the time domain parameters of the improved GPC was given (Fig.13). The robustness of the control method was verified by adjusting the parameters of the controlled object (Fig.14).
Conclusions The variable time-domain disturbance-resistant generalized predictive control algorithm is a sophisticated approach that leverages an extended state observer to effectively monitor system disturbances and states. By doing so, it can accurately predict the behavior of the controlled system and make adjustments accordingly. The prediction time-domain parameters are continuously updated using the gradient descent method based on the control error cost function, ensuring that the GPC remains adaptive and responsive to changes in the environment. In order to evaluate the performance of this enhanced GPC, a comprehensive comparison was conducted with cascade PID and linear model GPC, both operating within the same control bandwidth. The results revealed compelling advantages of the improved GPC over its counterparts. Specifically, it demonstrated an impressive 78.72% improvement in tracking accuracy compared to cascade PID, as well as a substantial 59.89% enhancement over linear model GPC. Furthermore, when it comes to speed disturbance suppression, the improved GPC showcased remarkable effectiveness by reducing amplitude by 58.95%, surpassing both cascade PID at 56%. These findings underscore not only the robustness but also the superior performance of this advanced algorithm in handling complex control tasks with high precision and efficiency.
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