Study of Control Theory Construction Based on Computer Algebra
Project/Area Number  02650301 
Research Category 
GrantinAid for Scientific Research (C).

Research Field 
計測・制御工学

Research Institution  Toyohashi University of Technology 
Principal Investigator 
SAITO Osami Toyohashi University of Technology Professor, 工学部, 教授 (50005526)

CoInvestigator(Kenkyūbuntansha) 
ABE Kenichi Toyohashi University of Technology Professor, 工学部, 教授 (70005403)

Project Fiscal Year 
1990 – 1991

Project Status 
Completed(Fiscal Year 1991)

Budget Amount *help 
¥1,600,000 (Direct Cost : ¥1,600,000)
Fiscal Year 1991 : ¥200,000 (Direct Cost : ¥200,000)
Fiscal Year 1990 : ¥1,400,000 (Direct Cost : ¥1,400,000)

Keywords  Computer algebra / Polynomial ring / nD system / Formula manipulation / Matrix equation / Practical stability / Compensator / CAD / 計算機代数学 / 多項式環 / nDシステム / 数式処理 / 行列方程式 / Practical安定 / 安定化補償器 / 2Dシステム / 2ーDシステム 
Research Abstract 
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 2D system theory and the following results were obtained. 1) Coprimeness of 2D transferfunction and stability of 2D system : The coprimeness is quite difference from the one of 1D transferfunction. Then the concepts such as zerocoprimeness and factor coprimeness should be considered. In addition, minor coprimeness was necessary in the case of 2d transferfunction matrix. Here the new concept  OMEGA coprimeness was defined and consequently both coprimeness and stability condition for 2D system could be discussed uniformly. 2) Synthesis algorithms of stabilizable compensator for 2D 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 2D system and the computer algebra. In 1991, based on the above results, 2D system theories were extended to the general nD system theories and following results were obtained. 3) Stability of nD system : Recently the new stability concept for nD 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 nD system : The dynamical response of nD ststem is very complex. Then the user friendly simulator for nD system was developed by using computer graphics and REDUCE.

Report
(4results)
Research Output
(18results)