带有不确定干扰的无穷维振动系统的镇定

项目名称： 带有不确定干扰的无穷维振动系统的镇定

项目编号： No.61273129

项目类型： 面上项目

立项/批准年度： 2013

项目学科： 自动化技术、计算机技术

项目作者： 郭宝珠

作者单位： 中国科学院数学与系统科学研究院

项目金额： 80万元

中文摘要： 本项目旨在对带有外部一般有界干扰的无穷维振动系统设计边界反馈的镇定控制，包括基于滑模控制和自抗扰控制的状态反馈和输出反馈控制。对于输出反馈，另一个重要目标是设计基于滑模的关于"未知输入"，和基于自抗扰扰动控制的关于"扩张的状态观测器"的状态和干扰的观测器，并进而设计基于观测器的输出反馈控制以达到抵消或抑制干扰，实现系统稳定的目标。我们的系统具有两个主要特点：一是原系统可能不是稳定的（有有限个极点位于右半平面），或者是反稳定的（极点全部位于右半平面），在两种情况下控制都是必须的，系统的内部阻尼不足以使得系统稳定。二是系统的输入或者输出带有一般的有界干扰。这两个特点使得原先对于系统保守时的控制不能再用，Backstepping方法因此成为重新设计控制必须的手段。在研究的过程中以大量数值试验为辅助。在此研究的基础上，将理论结果用于柔性机器人的镇定。并在理论上推广到带干扰的高维偏微分振动系统控制。

中文关键词： 非线性系统；不确定；偏微分方程系统；反馈镇定；自抗扰控制

英文摘要： The objective of the project is to the boundary stabilization of the vibrating systems with general bounded external disturbance from both input and output. The disturbance has no dynamic model. Both state feedback and output feedback are considered. If the output feedback control is concerned, two approaches are adopted in investigations: sliding mode based control and active disturbance rejection based control, where the observer that is used to estimate both the state and disturbance is designed by sliding mode method with the"unknown inputs"; and by the active disturbance rejection control with the"extended state observer". There are two characteristics for the systems studied. First, the system may be un-stable (that is, there are possibly finitely many unstable poles located on the right complex plane); or anti-stable (all unstable poles are located on the right complex plane). Second, all systems have external disturbances. In both cases, the structural damping from system itself is not enough for the stabilization of the system, and hence control becomes necessary. The theoretical studies will be validated by numerical experiments. Based on the one-dimensional systems study, we shall try to generalize the method to solve the multi-dimensional vibrating systems with external disturbance.

英文关键词： Nonlinear system；uncertainty；partial differential equation system；feedback stabilization；active disturbance rejection control