Research Initiation: Robustness Properties of Multiple Loop Feedback Systems

线性多变量反馈系统具有许多单回路系统所不具备的特性，给设计带来了很大的困难。其中一个困难是，多变量系统的稳定裕度可能会因回路被破坏的位置而截然不同。一个更大的困难是，一个多变量反馈系统可能对只出现在一个环断点的不确定性具有良好的稳定裕度，但可能被同时出现在多个点的小扰动破坏。本研究的目的是了解多变量系统某一点的反馈特性（例如性能和鲁棒性）如何与其他回路断点的那些特性相关，并研究植物和补偿器的特性如何影响这种关系。研究中使用的技术包括一种从开环性质近似闭环的方法。本研究将有助于开发解决多变量控制系统设计问题的方法。

Linear multivariable feedback systems possess many properties not present in single-loop systems which pose great difficulty in design. One such difficulty is that multivariable systems can have radically different stability margins depending on where the loop is broken. An even greater difficulty is that a multivariable feedback system may possess good stability margins against uncertainty appearing at only one loop breaking point, yet may be destabilized by small perturbations appearing simultaneously at more than one point. The goal of this research is to understand how feedback properties, e.g. performance and robustness, at one point of a multivariable system are related to those properties at other loop breaking points and to investigate how properties of the plant and compensator affect this relation. The techniques used in the research include a method for approximating closed loop from open loop properties. This research should prove useful in developing methods for solving multivariable control system design problems.