Research on Multirate Digital Control Systems

多速率数字控制系统研究

基本信息

批准号：
60550294
负责人：
ARAKI Mituhiko
金额：
$ 0.9万
依托单位：
Kyoto 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：
1985
资助国家：
日本
起止时间：
1985 至 1986
项目状态：
已结题

来源：
https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-60550294/
关键词：
Multirate Digital Control System Freguency Response Method Pole Assignment Stability Margin Multirate-Input System Multirate-Output System Control System Design 強安定化可能性

项目摘要

State equations are derived for the multirate digital control systems by using an "extended state vector." Based on this equation, a Nyquisttype stability condition and theory of Gershgorin bands are established. Computer programs for the stability analysis and a simulator are completed. At the same time, the pole assignment problem is studied both for multirate-input systems and multirate-output systems. Assuming that the controlled object is completely controllable and observable, it was proved that arbitrary symmetric pole assignment of the closed loop system is possible, if the input multiplicities are set larger than or equal to the controllability indices in the case of multirate-input systems, and if the output multiplicities are set larger than or equal to the observability indices in the case of multirate-output systems. In addition, concerning the multirate-output case, it was shown that arbitrary symmetric pole assignment of the controller itself is possible if the output multiplicities are set larger than or equal to the observability indices of the angmented system (i.e. the system added with an integrator at each output). To study the performance of the control systems obtained by the above mentioned pole-assignment method, several examples are studied by using the stability-analysis programs and the simulator.

通过使用“扩展状态向量”，为多级数字控制系统得出状态方程。基于此方程，建立了Gershgorin带的NyquistType稳定性条件和理论。用于稳定性分析和模拟器的计算机程序已完成。同时，研究了杆分配问题，既已针对多次输入系统和多发出系统。假设受控的对象是完全可控制的和可观察的，则可以证明，如果将输入多重性设置为大于或等于多级输入系统的可控性指标，则可以证明对封闭环系统的任意对称杆分配，并且如果将输出多数率设置为多于多数级系统中的可观察性索引。此外，关于多次输出情况，如果将输出多重性设置为大于或等于Angmented系统的可观察性指标（即，每个输出添加的系统），则可以表明控制器本身的任意对称极点分配。为了研究通过上述极线分配方法获得的控制系统的性能，使用稳定性分析程序和模拟器研究了几个示例。