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

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，并实现了这两种算法。一个是定义在凸多边形集合上的算术（我们称之为CPIA），另一个是定义在（不一定是凸）多边形上的算术（我们称之为NPIA）。运算是多边形的加法、乘法和求逆。2）增益裕度的计算我们提出了四种基于PIA的方法，它们是Gaston方法的改进，以及一种基于NPIA的方法，当传递函数的表达式是完全可分解的时，后者优于前者上级。3）鲁棒根轨迹法。我们提出了一种鲁棒的根轨迹方法，该方法能够分配代表性根，偶极子，4）鲁棒PID控制器的设计我们开发了一个用于设计PID控制器的CAD系统，该系统满足多种鲁棒性能。二自由度鲁棒系统CAD系统的开发我们开发了二自由度鲁棒系统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.