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Study of Control Theory Construction Based on Computer Algebra

基于计算机代数的控制理论构建研究

基本信息

批准号：
02650301
负责人：
SAITO Osami
金额：
$ 1.02万
依托单位：
Toyohashi University of Technology
依托单位国家：
日本
项目类别：
Grant-in-Aid for General Scientific Research (C)
财政年份：
1990
资助国家：
日本
起止时间：
1990 至 1991
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-02650301/
关键词：
Computer algebra Polynomial ring nD system Formula manipulation Matrix equation Practical stability Compensator CAD 2Dシステム 2ーDシステム

项目摘要

The aim of this study is to construct the new control system theory based on the computer algebra. In 1990, the main work was to research the 2-D system theory and the following results were obtained.1) Coprimeness of 2-D transferfunction and stability of 2-D system : The coprimeness is quite difference from the one of 1-D transferfunction. Then the concepts such as zero-coprimeness and factor coprimeness should be considered. In addition, minor coprimeness was necessary in the case of 2-d transferfunction matrix. Here the new concept - OMEGA -coprimeness was defined and consequently both coprimeness and stability condition for 2-D system could be discussed uniformly.2) Synthesis algorithms of stabilizable compensator for 2-D system : The algorithm is reduced to solving the bilateral matrix equation AX+BY=C. In this work the software package for the matrix equation has been developed based on REDUCE and it was clarified that there existed the deep relationship between the 2-D system and the computer algebra.In 1991, based on the above results, 2-D system theories were extended to the general n-D system theories and following results were obtained.3) Stability of n-D system : Recently the new stability concept for n-D system, -practical stability- was introduced. Here the synthesis algorithms of the practical stabilizable compensator were established. And the Computer Aided Design system was also developed.4) Dynamical simulation of n-D system : The dynamical response of n-D ststem is very complex. Then the user friendly simulator for n-D system was developed by using computer graphics and REDUCE.

本研究的目的是构建基于计算机代数的新的控制系统理论。1990年的主要工作是研究二维系统理论，得到了如下结果：1)二维传递函数的共生性与二维系统的稳定性：两者的共生性与一维传递函数的共生性有很大的不同。然后，应考虑零互质和因子互质等概念。此外，在二维传递函数矩阵的情况下，需要少量互质。2)二维系统可镇定补偿器的综合算法：算法归结为求解双边矩阵方程AX+BY=C。本文基于Reduced开发了求解矩阵方程的软件包，阐明了二维系统与计算机代数之间存在着深刻的联系。1991年，在上述结果的基础上，将二维系统理论推广到一般的n-D系统理论，得到了以下结果。3)n-D系统的稳定性：最近引入了n-D系统的新稳定性概念--实用稳定性。建立了实用的可镇定补偿器的综合算法。4)多维系统的动力学仿真：多维系统的动力响应非常复杂。在此基础上，利用计算机图形学和归约技术，开发了界面友好的多维系统模拟器。