Research on Multirate Digital Control Systems

Research Project

Project/Area Number	60550294
Research Category	Grant-in-Aid for General Scientific Research (C)
Allocation Type	Single-year Grants
Research Field	計測・制御工学
Research Institution	Kyoto University
Principal Investigator	ARAKI Mituhiko Professor of Electrical Engineering, Faculty of Engineering, 工学部, 助教授 (60026226)
Project Period (FY)	1985 – 1986
Project Status	Completed (Fiscal Year 1986)
Budget Amount *help	¥1,400,000 (Direct Cost: ¥1,400,000) Fiscal Year 1986: ¥600,000 (Direct Cost: ¥600,000) Fiscal Year 1985: ¥800,000 (Direct Cost: ¥800,000)
Keywords	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
Research Abstract	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.