Design of robust performance control against real parameter variations

本研究的目的是建立一种针对系统真实的参数变化的鲁棒性能控制器的设计方法。鲁棒性能控制器是指保证系统稳定性和一定性能的控制器。真实的参数变化意味着由于系统故障、建模误差或系统参数变化引起的系统不确定性。本文的研究重点是：（1）建立描述系统故障的数学模型;（2）建立评价系统故障引起的系统性能恶化的指标;（3）建立控制器设计方法的理论;（4）建立设计控制器的算法;（5）开发实现该算法的CAD系统;（6）克服控制中的时滞，本文对这些问题进行了讨论，得到了几个重要结果。在这项研究中的讨论导致了一个通用的程序，例如，系统故障作为系统中的真实的参数变化。基于此过程，问题可以被视为鲁棒控制器的设计问题。得到了一种既能实现理想极点配置又能实现鲁棒稳定的控制器设计方法。利用两个有限维Riccati方程解决了控制时滞系统的鲁棒镇定问题。将鲁棒控制问题归结为非线性系统的控制设计问题。为了解决非线性控制问题，我们提出了一种基于增益调度的方法，将非线性控制问题转化为线性控制问题，并证明了该方法的有效性。开发了一些新的工具来实现我们的设计方法，并在CAD系统中成功地使用。

The objective of this research was to establish a design method for robust performance controllers against real parameter variations of systems. Robust performance controllers mean the controllers which assure stability and a prescribed level of some performance. Real parameter variations mean system uncertainties due to system failures, modeling errors or system parameter changes. This research, in particular, focused on the following points : (1) To develop a mathematical model to describe system failures ; (2) To developan index to evaluate deterioration ofsystem performance due to failures in systems ; (3) To establish a theory fordesign method of controllers ; (4) To develop an algorithm for designing controllers ; (5) To develop a CAD system to perform the algorithm ; (6) To overcome delay in control.These points were discussed in this paper, and several important results were obtained. The discussions in this research led to a general procedure for regarding, for example, system failures as real parameter variations in systems. Based on this procedure, problems can be treated as design problems of robust controllers. A design method of controllers which realize a desirable pole location and robust stability was obtained. A robust stabilization problem for systems with delay in control was solved by using two finite dimensional Riccati equations. The robustcontrol design problem was reduced to some control design problems for nonlinear systems. To solve the nonlinear control problem, we developed a method based on the so-called gain scheduling, which lead to a linear control problem, and showed its effectveness.Through this research, a CAD system in our laboratory was used. Some new tools for performing our design method were developed and used successfuly in the CAD system.