Controllability and Observability of Distributed Gyroscopic Systems

[+] Author and Article Information
B. Yang

Department of Mechanical Engineering, University of Southern California, Los Angeles, CA 90089-1453

C. D. Mote

Department of Mechanical Engineering, University of California at Berkeley, Berkeley, CA 94720

J. Dyn. Sys., Meas., Control 113(1), 11-17 (Mar 01, 1991) (7 pages) doi:10.1115/1.2896336 History: Received June 26, 1989; Revised February 05, 1990; Online March 17, 2008


Controllability and observability of a class of distributed gyroscopic systems under pointwise actuators and sensors are presented. The equations of motion are cast in a state space form, in which orthogonality of the eigenfunctions is obtained. The controllability and observability conditions in finite dimensions are obtained for a model representing a truncated modal expansion of the distributed system. In infinite dimensions the controllability and observability conditions are obtained through semi-group theory. In both the finite and infinite dimensional models the conditions of controllability and observability are evaluated through the eigenfunctions in an explicit form. The minimum number of actuators and minimum number of sensors needed to control and observe the system are determined by the largest eigenvalue multiplicity. The results are illustrated on vibration control of the axially moving string and the rotating circular plate.

Copyright © 1991 by The American Society of Mechanical Engineers
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