Controllability and Observability of Distributed Gyroscopic Systems

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 eigenfunction is obtined. 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.