RIMI: Parametric Robust Control Design

所提出的项目涉及参数不确定性控制系统的各种分析和设计问题。具体地说，我们考虑传递函数系数是受扰动参数的线性或多线性函数的区间系统。该项目的主要目标是1)开发有效的方法来设计控制器，使其在大量参数不确定性下表现令人满意；2)扩展对各种类型控制系统的时域和频域特性的理解。本课题包括两个部分：新理论的发展和作为计算机辅助设计软件包的实现。我们提出解决的理论问题如下：1)重新审视经典的鲁棒成分控制设计和分析技术，发展新的鲁棒参数控制设计方法。2)发展时滞系统的相关理论。这包括确定具有固定控制器的时滞区间系统鲁棒稳定性的充分必要条件是什么，如何计算检验鲁棒稳定性，时滞区间系统的频域和时域特性是什么，以及如何在区间内调整可选参数以提高系统性能。3)发展处理多线性区间系统的等效理论和计算算法。4)研究区间系统的时域特性及其在控制暂态响应中的应用。5)开发了一种新的建模和识别技术，从给定的输入输出测试数据和标称线性识别模型中确定区间系统。项目的第二部分是构建一个高效的计算机辅助设计软件，将上述所有设计方法结合起来。本软件的基础系统是MATLAB。我们期望它将成为理论和实践工程师鲁棒参数控制设计和分析的宝贵工具。

The proposed project deals with various problems of analysis and design of control systems subject to parametric uncertainty. Specifically we consider interval systems whose transfer function coefficients are linear or multilinear functions of the parameters subject to perturbation. The main goals of this project are 1) to develop effective methodologies to design controllers that perform satisfactorily under large amounts of parametric uncertainties and 2) to expand understanding of time and frequency domain properties of various types of control systems. The project consists of two parts: development of new theory and its implementation as a computer aided design software package. The theoretical problems we propose to solve are as follows: 1) Reexamining the classical control design and analysis techniques with robustness ingredients and developing new design methodologies for robust parametric control design. 2) Developing relevant theory for time delay systems. This includes what is a necessary and sufficient condition to determine robust stability of a time delay interval system with a fixed controller, how to computationally check the robust stability, what are the frequency and time domain characteristics of a time delay interval system, and how to adjust selective parameters within their intervals to improve the system performance. 3) Developing equivalent theory and computational algorithms to deal with multilinear interval systems. 4) Developing theory to examine the time domain properties of interval systems and its use in controlling transient response. 5) Developing a new modeling and identification technique to determine an interval system from the given input - output test data and the nominal linear identified model. The second part of the project is to build an efficient computer aided design software to incorporate all the above design methods. The base system of this software is MATLAB. We expect it will be a valuable tool for robust parametric control design and analysis for both theoreticians and practicing engineers.