Disturbed Zhang Dynamics Control for Triple-Integrator to Multiple-Integrator Systems: Design Formula Collection, Error Dynamics Equivalence, and Theoretical Analyses
Published in Proceedings of Chinese Control Conference, 2022
Recommended citation: K. Zheng, C. Hu, Y. Zhang, and X. Kang, "Disturbed Zhang Dynamics Control for Triple-Integrator to Multiple-Integrator Systems: Design Formula Collection, Error Dynamics Equivalence, and Theoretical Analyses," in Proceedings of Chinese Control Conference, Hefei, China, 2022, pp. 1--6. http://konzem.github.io/files/paper3.pdf
Abstract – In this paper, Zhang dynamics (ZD) is investigated and applied in a multiple-integrator system (MIS) with or without noise disturbance for tracking control. For illustration, the design procedure of ZD control (ZDC) for a triple-integrator system (TIS) is shown. Besides, the error dynamics of the TIS synthesized by the ZDC is presented, and its equivalent system comes to light. Moreover, theoretical analyses on the TIS equipped with the ZDC are given to substantiate its stability and convergence. For more generalization, the ZDC for the MIS is developed, and the corresponding error dynamics is exhibited. In addition, theoretical analyses on the MIS equipped with the ZDC are provided. Specifically, regardless of noise pollution, the tracking error and other ZD errors of the MIS synthesized by the ZDC are bounded and convergent.
Index Terms – Zhang dynamics control, multiple-integrator system, noise disturbance, tracking error, stability.