In this paper low-gain adaptive stabilization of undamped second order systems 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 low-gain PD-controller (proportional plus derivative controller). In the case where only position feedback is available, the adaptive stabilizer is constructed by a low-gain 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
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