Robust Control of Multivariable Systems Subject to Structured Real Parameter Variations

本研究主要研究当被控对象受到一组真实物理参数的摄动时，控制系统的分析、综合和设计问题。这种模型存在于机器人、化工过程、飞行器控制、大型空间结构和许多其他工程系统中。这类对象被称为结构实参(SRP)对象。对于线性时不变多变量SRP系统，将考虑以下问题：(1)给定控制器的鲁棒性度量的确定。参数空间中稳定性超球体的大小(半径)是这种度量的一个候选。我们将研究确定这一半径的理论和计算算法。(2)开发一种综合控制器的程序，使其具有鲁棒性，即针对给定的一组对象参数漂移保持系统的闭环系统稳定性。这需要推广和发展哈里托诺夫发展的结果类型的综合版本。(3)开发了通过选择自由控制器参数来最大化鲁棒性度量的最大鲁棒性的设计方法。(4)对控制器参数进行适当测量和优化后，对期望响应的偏差和鲁棒性进行权衡的问题的表述和解决方法。

This research deals with the problem of analysis, synthesis and design of control systems when the plant is subject to perturbations of a set of real physical parameters. This type of model occurs in robotics, chemical processes, aircraft control, large space structures and many other engineering systems. Such plants are called structured real parameter (SRP) plants. For linear time-invariant multivariable SRP systems the following problems will be considered: (1) determination of a robustness measure for a given controller. One candidate for such a measure is the size (radius) of the stability hypersphere in parameter space. The theory and computational algorithm for determining this radius will be investigated. (2) The development of a procedure for the sythesis of a controller that robustifies, i.e. maintains closed loop stability of the system against a given set of ranges of plant parameter excursions. This requires a generalization and the development of a sythesis version of the type of results developed by Kharitonov. (3) The development of design procedures for maximal robustness by choosing the free controller parameters to maximize the robustness measure. (4) The formulation and solution of the problem of trading off robustness against deviations from the desired response measured suitably and optimized over the controller parameters.