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引用次数: 9
摘要
我们给出了Byrnes等人(1999)对设计反馈律的几何方法的扩展的一个明确例子,该方法用于解决正则线性控制系统的调节器问题。上述文章中使用的方法基于另一篇论文(Byrnes et al., 1998),该论文处理了有界控制和观察算子的输出调节的无限维理论。在第一篇文章中,作者用无界输入和输出算子情况下某些调节器方程的可解性来描述状态和误差反馈调节器问题的可解性。本文给出了一维热方程设定值控制的一个简单例子。我们选择了一个简单的例子,其解析和数值解很容易获得,并且这些反馈设计策略的显式实现可以很容易地识别。
Example of output regulation for a system with unbounded inputs and outputs
We give an explicit example of an extension by Byrnes et al. (1999) of the geometric approach to the design of feedback laws for solving the regulator problem for regular linear control systems. The approach used in the above mentioned article is based on another paper (Byrnes et al., 1998) which treats the infinite dimensional theory of output regulation for bounded control and observation operators. In the first mentioned article, the authors have characterized the solvability of both state and error feedback regulator problems in terms of the solvability of certain regulator equations in the case of unbounded input and output operators. In this paper we present a simple example of set point control for a one dimensional heat equation. We have selected a simple example for which analytic and numerical solutions are readily obtained and the explicit implementation of these feedback design strategies can be easily identified.