RESEARCH ON DEVELOPMENT OF CAD SYSTEM FOR ROBUST CONTROL SYSTEMS BY USING POLYGON INTERVAL ARITHMETIC

本文对所取得的成果进行了总结：1)多边形区间算法的定义与实现。提出了两种多边形区间算法，并分别进行了实现。一个是在凸多边形集合上定义的算法（我们称之为CPIA），另一个是在（不一定是凸的）多边形上定义的算法（我们称之为NPIA）。操作是加法，乘法和多边形的反演。在它们的实现中，我们使用了计算几何的最新结果。2)增益边际的计算我们提出了四种基于PIA的方法，分别是对Gaston方法的改进，以及一种基于NPIA的方法。当传递函数完全可分解时，后一种方法优于前一种方法。3)鲁棒根轨迹法。从实际应用的角度出发，我们提出了一种鲁棒的根轨迹方法，该方法能够分配代表根、偶极子和其他根的区域。4)鲁棒PID控制器的设计。开发了一套满足鲁棒性要求的PID控制器设计CAD系统。5)鲁棒二自由度系统CAD系统的开发。我们开发了鲁棒二自由度系统的CAD系统，该系统具有3)和4)中描述的功能，并采用经典的频率响应方法。

Results obtained by this project are summerlized as follows :1) Definition and Implementation of Polygon Interval Arithmetic.We proposed two kinds of the polygon interval arithmetic and implemented both of them. One is the arithmetic defined on the sets of convex polygons (we call this CPIA), and the other is that defined on (not necessarily convex) polygons (we refer this NPIA). Operations are the addition, the multiplication, and the inversion of polygons. In the implementation of them, we used recent results on computational geometry.2) Computation of Gain MarginWe proposed four method using PIA,which are improvement of the method proposed by Gaston, and one method using NPIA.The latter method is superior to the former when a totally decomposable expression of transfer functions.3) Robust Root Loci Method.In the practical points of view, we proposed a robust root loci method which is able to assign the regions of the representative roots, dipoles, and other roots.4) Design of Robust PID Controllers.We developed a CAD system for the design of PID controller which satisfies several robust performances.5) Development of CAD System for Robust 2 Degree of Freedom Systems.We developed CAD system for robust 2 degree of freedom systems which has functions described in 3) and 4), and classical frequency response method.