非线性重复控制系统的扰动动态补偿与鲁棒性设计研究

How to construct a simple, effective method of estimating and compensating for unmatching disturbances is a bottleneck and a difficult point in the disturbance rejection problem for nonlinear repetitive-control systems. This project will investigate the problem of how to design a nonlinear repetitive-control system that dynamically compensates for any disturbances for a class of nonliner plants that perform periodic control tasks. For a nominal nonlinear system with disturbances, we will first design a disturbance estimator and a compensator by employing the dynamic gain technique to dynamically estimate and compensate for the effect of the disturbances even in transient state. Next, we will establish a new structure for a nonlinear repetitive-control system that contains a disturbance estimator and compensator, a repetitive controller, and a feedback controller. Then, we will develop a method of designing the new nonlinear repetitive-control system based on the relationships among the parameters of the control system, its stability, disturbance rejection performance, and repetitive control performance. And we also derive an algorithm to search for the best combination of the parameters of the disturbance estimator and compensator, and the repetitive controller. For a class of nonlinear plants with uncertain nonlinear dynamics, we will build a structure for a robust nonlinear repetitive-control system that dynamically compensates for the uncertainties. Finally, we will devise a method of designing the robust nonlinear repetitive-control system based on the uncertainties compensation. We will demonstrate the validity of the method through simulations and experiments on a motor control system. The objective of this project is to develop a new and effective method of disturbances rejection and robust design for nonlinear repetitive-control systems. This project has significant theoretical and practicalmeaning, and contributes to the fields of repetitive-control and nonlinear control.

构建一种简单、有效的非匹配扰动估计和补偿方法是解决当前非线性重复控制系统扰动抑制问题的瓶颈与难点。本项目针对具有周期性控制任务的非线性系统，研究基于扰动动态补偿的非线性重复控制系统设计方法。采用动态增益技术，构建扰动估计器和补偿器，实现对各种非匹配扰动的实时估计和动态补偿，建立基于扰动估计器、补偿器、重复控制器和反馈控制器的系统结构；寻找系统参数与稳定性、扰动抑制性能和重复控制性能的关系，提出基于扰动动态补偿的非线性重复控制系统设计方法，以及扰动动态补偿和重复控制的同步优化设计方法；针对含有不确定非线性动态的系统，提出基于不确定性补偿的鲁棒非线性重复控制系统设计方法；通过仿真分析和电机控制系统实验，探讨基于扰动动态补偿的重复控制应用。本研究将为非线性重复控制系统扰动抑制与鲁棒性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。

本项目针对具有周期性控制任务的伺服系统，研究了基于扰动动态补偿的非线性重复控制系统设计方法。采用动态增益技术，构建了扰动估计器和补偿器，实现对各种非匹配扰动的实时估计和动态补偿，建立了基于扰动估计器、补偿器、重复控制器和反馈控制器的系统结构。通过分析系统参数与稳定性、扰动抑制性能和重复控制性能的关系，提出了基于扰动动态补偿的非线性重复控制系统设计方法，以及扰动动态补偿和重复控制的同步优化设计方法。针对含有不确定非线性动态的系统，提出了基于不确定性补偿的鲁棒非线性重复控制系统设计方法。通过仿真分析和电机控制系统实验，探讨了基于扰动动态补偿的重复控制应用。本研究为非线性重复控制系统的扰动抑制与鲁棒性设计提供了一种新颖的和有效的方法，解决了非匹配扰动估计和补偿这个难点问题，促进了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。

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