Synthesis of Robust Controllers for Parameter Variations

该方案涉及两个综合问题：1）设计控制器 的规定的顺序，以稳定一个给定的系统和2）设计一个 稳定给定系统的规定阶控制器 包含在指定范围内具有不确定性的参数。 我们 建议建立控制器存在的条件， 为了获得有用的参数化（从控制系统设计者的 的观点）的所有控制器，解决上述问题。 所提出的问题是尚未解决的两个问题。 控制理论的问题。 现有的合成方法 （“观察”状态反馈，LQG，H和几何方法， 合成）可以以实际或令人满意的方式解决它们。 他们 在大多数工业应用中总是会立即出现， 完全缺乏一个综合理论来解决这个问题是一个 控制工程师在试图 将控制理论的结果应用于实践。 我们希望 解决上述困难问题的方法是基于最近的 结果推广了Kharitonov定理，使其适用于 控制系统和新技术的精确计算， 参数空间中的稳定球

This proposal deals with two synthesis problems 1) design a controller of a prescribed order to stabilize a given system and 2) design a controller of a prescribed order to stabilize a given system containing parameters subject to uncertainty in specified ranges. We propose to establish conditions for the existence of a controller and to obtain a useful parametrization (from the control system designer's point of view) of all controllers that solve the above problems. The problems proposed constitute two of the outstanding unsolved problems in control theory. None of the existing synthesis methods ("observed" state feedback, LQG, H , and geometric methods of synthesis) can solve them in a practical or satisfactory manner. They arise invariably and immediately in most industrial applications, and the complete lack of a synthesis theory to address this problem is a major stumbling block that control engineers encounter in attempting to apply the results of control theory to practice. Our hope that the difficult problems posed above can be solved is based on recent results which extend Kharitonov's theorem and make it applicable to control systems, and new techniques for the exact calculation of the stability ball in parameter space.