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OPERATION ON SETS AND IT'S APPLICATIONS TO COMPUTER AIDED DESIGN OF ROBUST CONTROL SYSTEMS

集运算及其在鲁棒控制系统计算机辅助设计中的应用

基本信息

批准号：
63550311
负责人：
OHTA Yuzo
金额：
$ 0.45万
依托单位：
KOBE UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1988
资助国家：
日本
起止时间：
1988 至 1989
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-63550311/
关键词：
OPERATION ON SETS UNCERTAINTY ROBUST CONTROL COMPUTATIONAL GEOMETRY COMPUTER AIDED DESIGN ROBUST STABILITY 凸包問題制御系のCAD

项目摘要

Because of variation and uncertainty of system parameters, mathematical models Invariably give an imperfect description of real systems. Therefore, robustness is one of the most fundamental requirements for control systems. Main results of this research project may be summarized as follows:1. Polygon Interval Arithmetic. To treat uncertainty, we defined operations (addition, multiplication, and reversion) on sets consisting of all the convex polygons, which we call polygon interval arithmetic. We derived several important properties of polygon interval arithmetic. We also proposed an efficient algorithm to calculate addition of convex polygons.2. Robust Stability Analysis. (1)Stability of feedback systems can be analyzed by examining determinants of return differential matrix at every frequencies. A method based on the mapping theorem was used to calculate it, but it is very much time consuming. We proposed to use a method based on both polygon interval arithmetic and the mapping theorem to calculate determinants. (2)Stability of (nonlinear) systems can be examined by using Liapunov functions. We proposed a method to construct a Liapunov function via computational geometric technique to calculate convex hulls.3. RSRD(Robust Sequential Return Difference) method. We proposed RSRD method to design robust control systems, which uses polygon interval arithmetic, and which makes possible to design controllers of each loops "independently", and to guarantee the integrity.4. CAD(Computer Aided Design) System. We developed a CAD system to design robust control systems based on RSRD method. We also implemented a program to calculate stability margin of multi-input multi-output systems.

由于系统参数的多变性和不确定性，数学模型总是不能很好地描述实际系统。因此，鲁棒性是控制系统最基本的要求之一。本课题的主要研究成果可以总结如下：1.研究成果。多边形区间算法。为了处理不确定性，我们在由所有凸多边形组成的集合上定义了运算（加法、乘法和反演），我们称之为多边形区间算术。给出了多边形区间算法的几个重要性质。我们还提出了一种计算凸多边形加法的高效算法。鲁棒稳定性分析。(1)反馈系统的稳定性可以通过检查每个频率下返回微分矩阵的行列式来分析。采用了基于映射定理的计算方法，但计算时间较长。我们提出了一种基于多边形区间算法和映射定理的计算行列式的方法。(2)非线性系统的稳定性可以用Liapunov函数来检验。提出了一种利用计算几何技术构造Liapunov函数来计算凸壳的方法。稳健序列返回差分（RSRD）方法。提出了RSRD方法设计鲁棒控制系统，该方法采用多边形区间算法，使每个回路的控制器“独立”设计成为可能，并保证了系统的完整性。计算机辅助设计系统。开发了基于RSRD方法的鲁棒控制系统的CAD系统。我们还实现了一个计算多输入多输出系统稳定裕度的程序。