THEORITICAL SYSTEM OF MULTIDIMENSIONAL SYSTEM AND ITS APPLICATION

多维系统理论体系及其应用

• 批准号: 10650425
• 负责人: SAITO Osami
• 金额: $ 0.9万
• 依托单位: Chiba University
• 依托单位国家: 日本
• 项目类别: Grant-in-Aid for Scientific Research (C)
• 财政年份: 1998
• 资助国家: 日本
• 起止时间: 1998 至 1999
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-10650425/
• 关键词: multidimentinal system; stability; Grobner Basis; Servo problem; optimal control; learning control; multipass; マルチパス制御; CAD; 状態方程式

The project deals with theoretical system of multidimensional system and its application to practical systems and has obtained the following results.(1) Stability and stabilization : The conventional stability theory and criterion depends on the system dimension. Here new theory and general criterion, independent on dimension, is studied based on Grobner Bases.(2) Practical nD system : The practical nD system is defined, as the domain of one independent variable of nD system is finite. The synthesis and analysis method of practical nD system, especially stabilization, stabilizing feedback compensatory and optimal control are investigated.(3) 2D model-following servo system : Two formulations of 2D model-following servo problem have been given. One is based on 2 variable polynomial ring. The other one is state variable formulation.(4) Application : The above results are applied to desinging the controller of non-unit memory linear multipass processes. Finaly the new CAD system with MAPLE, for multidimension system is developed.

本课题研究多维系统的理论体系及其在实际系统中的应用，取得了以下成果。(1)稳定性和镇定：传统的稳定性理论和判据依赖于系统的维数。在Grobner基的基础上，研究了与维数无关的新理论和一般准则。(2)实用nD系统：定义了实用nD系统，因为nD系统的一个独立变量的域是有限的。研究了实际nD系统的综合与分析方法，特别是镇定、镇定反馈补偿和最优控制。(3)二维模型跟踪伺服系统：给出了二维模型跟踪伺服问题的两种形式。一种是基于二元多项式环。另一种是状态变量法。(4)应用：将上述结果应用于非单位记忆线性多程过程的控制器设计。最后，用MAPLE开发了新的多维系统CAD系统。

项目成果

L. Xu, M. Yamada, O. Saito: "Development of nD Control System Toolbox for Use with MALTAB"Proceedings of 1999 IEEE International Conference on Control Application (CCA99). Auguat 22-27, Hawaii, 1543-1548 (1999)

L. Xu、M. Yamada、O. Saito：“与 MALTAB 一起使用的 nD 控制系统工具箱的开发”1999 年 IEEE 国际控制应用会议 (CCA99) 会议记录。

M. Yamada, L. Xu, O. Saito: "2D Model-Following Servo System and Its Applications to Linear Mutipass Processes"Proceddings of 14ィイD1thィエD1 IFAC World Congress Beijing. 240-246 (1999)

M. Yamada、L. Xu、O. Saito：“二维模型跟随伺服系统及其在线性多通道过程中的应用”第 14 届 IFAC 世界大会北京会议 240-246（1999 年）。

斉藤、天沼、早乙女: "入門電気回路"朝倉書店. 156 (2000)

Saito、Amanuma、Saotome：“电路入门”Asakura Shoten 156 (2000)。

L. Xu, J. Ying, O. Saito: "Feedback Stabilizaion for a Class of MIMO nD System by Grobner Basis Approach"Proceecings of 1ィイD1stィエD1 Int. Workshop on Multidimensional (ND) Systems (NDC'98) Zielana Gora, Poland, July. 1998.

L. Xu、J. Ying、O. Saito：“通过 Grobner Basis Approach 实现一类 MIMO nD 系统的反馈稳定”1D1 多维 (ND) 系统国际研讨会论文集 (NDC98) Zielana Gora，波兰，7 月1998。

M.Yamada,L.Xu.O.Saito: "2D Model Following Servo System" Multidimensional System and Signal Processing. Vel.10 No.1. 71-91 (1999)

M.Yamada，L.Xu.O.Saito：“二维模型跟随伺服系统”多维系统和信号处理。