Design of robust performance control against real parameter variations

本研究的目的是建立一种针对系统实际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稳定性和某些性能达到规定水平的控制器。实际参数变化是指由于系统故障、建模错误或系统参数变化引起的系统不确定性。本研究主要集中在以下几个方面：(1)建立描述系统故障的数学模型；(2)制定指标，评价系统故障对系统性能的影响；(3)建立了控制器设计方法的理论；(4)开发控制器设计算法；(5)开发一个CAD系统来执行算法；(6)克服控制延迟。本文对这些问题进行了讨论，并得到了一些重要的结果。本研究中的讨论导致了一个通用的程序，例如，将系统故障视为系统中的真实参数变化。在此基础上，问题可视为鲁棒控制器的设计问题。给出了一种既能实现理想极点位置又能实现鲁棒稳定性的控制器设计方法。利用两个有限维Riccati方程求解了一类控制时滞系统的鲁棒镇定问题。将鲁棒控制设计问题简化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所谓增益调度的方法来解决线性控制问题，并证明了它的有效性。通过本研究，使用了我们实验室的CAD系统。开发了一些新的工具来执行我们的设计方法，并成功地应用于CAD系统中。

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.