基于非线性补偿的重复控制系统及鲁棒性设计

This project will investigate the problem of how to design a repetitive control system that compensates for nonlinearities for a class of nonlinear systems that perform periodic control tasks. For a nominal plant with nonlinearities, a model of a nonlinear repetitive control system will first be established based on an exploration of the characteristics of nonlinearities and their influence on system performance. Next, a feasible condition for the compensation of nonlinearities will be derived. And a method of designing an estimator and a compensator for the nonlinearities will be developed. Then, a new structure for a repetitive control system will be created. It will contain the new estimator and compensator, a repetitive controller, and a feedback controller. A method of designing the repetitive controller and the feedback controller based on the relationships among the parameters of the control system, and its stability and control performance will be established. For a certain class of nonlinear plants with uncertainties, a structure for a robust repetitive control system that compensates for the nonlinearities will be created; and the conditions for robust stability and robust performance will be investigated. Then, the design problem will be considered; and conditions for the parameters of the estimator and the compensator, and for the parameters of the repetitive controller and the feedback controller, will be established. A method of tuning those parameters will also be devised. Finally, the validity of the method will be demonstrated through simulations and experiments on a mechatronic control system. The objective of this project is to develop a new and effective design method for nonlinear repetitive control systems. This project will have significant theoretical and practical results. Moreover, it will spur advances in the fields of repetitive control and nonlinear control.

针对一类具有周期控制任务的非线性系统，本项目研究一种基于非线性补偿的重复控制系统设计方法。通过分析非线性特性对重复控制系统性能的影响，建立非线性重复控制系统的模型描述；探讨非线性补偿的可行性条件和方法，研究非线性特性估计器和补偿器的设计方法；建立基于非线性估计器、补偿器、重复控制器和反馈控制器的系统结构模型，寻找重复控制器、反馈控制器参数与系统稳定性和控制性能之间的关系，提出重复控制器和反馈控制器的设计方法；研究不确定性条件下基于非线性补偿的鲁棒重复控制系统结构，以及满足系统鲁棒稳定性和鲁棒性能的条件，讨论非线性估计器和补偿器与重复控制器和反馈控制器的设计条件，提出系统的参数整定方法；通过计算机仿真和机电控制系统实验，探讨基于非线性补偿的重复控制应用。本项目的研究将为非线性重复控制系统设计提供一种新颖的和有效的方法，促进重复控制和非线性控制理论与应用的发展，具有重要的科学意义和应用价值。

本项目通过分析一类具有周期控制任务的非线性系统，研究了一种基于非线性补偿的重复控制系统设计方法。首先，通过分析重复控制过程，构建了描述连续的控制行为和离散的学习行为的二维数学模型。通过将外部扰动与非线性作为总扰动，提出了针对各类典型非线性特性的EID方法，实现了对各种典型非线性特性的估计与补偿。在基于非线性补偿的重复控制系统设计方面，基于非线性重复过程的二维数学模型，将重复控制方法应用于非线性系统补偿，设计了改进型二维重复控制器；结合LMI方法与Lyapunov稳定性定理，在理论上获得了二维鲁棒稳定条件；基于该条件提出了估计器、补偿器、控制器的参数设计方法，实现了非线性重复控制系统的设计。针对带有不确定性的非线性系统，通过结合二维重复控制与鲁棒控制，研究了使带有不确定性的非线性重复控制系统满足鲁棒稳定性和鲁棒控制性能的条件，给出了非线性估计器和补偿器与重复控制器和反馈控制器的设计条件，提出了对该类系统的参数整定方法。通过计算机仿真和机电控制系统实验，探讨基于非线性补偿的重复控制应用。本项目的研究将为非线性重复控制系统设计提供了一种新颖的和有效的方法，促进重复控制和非线性控制理论与应用的发展，具有重要的科学意义和应用价值。