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Adaptive stabilization of infinite-dimensional undamped second order systems without velocity feedback

Kobayashi T., Oya M.

Archives of Control Sciences

2004

Vol. 14, no. 1

73-84

In this paper adaptive stabilization of infinite-dimensional undamped second order systems is considered in the case where the input and output operators are collocated. the systems may have an infinite number of poles, and zeros on the imaginary axis. In the case where only position feedback is available, a parallel compensator is effective. The stabilizer is constructed by an adaptive p-controller for the augmented system which consists of the controlled system and a parallel compensator. The asymptotic stsbility of the closed-loop system is proved by LaSalle's invariance pronciple under compactness of the resolvent.

Adaptive stabilization of undamped flexible structures

Kobayashi T.

Control and Cybernetics

2001

Vol. 30, no 4

419-429

In this paper non-identifier-based adaptive stabilization of undamped flexible structures is considered in the case of collocated input and output operators. The systems have poles and zeros on the imaginary axis. In the case where velocity feedback is available, the adaptive stabilizer is constructed by an adaptive PD-controller (proportional plus derivative controller). In the case where only position feedback is available, the adaptive stabilizer is constructed by an adaptive P-controller for the augmented system which consists of the controlled system and a parallel compensator. Numerical examples are given to illustrate the effectiveness of the proposed controllers.