Adaptive Control of a Flexible String System With Input Hysteresis

In this brief, a vibration suppression scheme is investigated for a flexible string system with input hysteresis. The input hysteresis is formulated as a linear desired input and a “disturbance-like” term, whose unknown bound is then estimated by an adaptive law. Without constructing a hysteresis inverse, adaptive boundary control is designed to suppress the vibrations of the flexible string, cope with the uncertainties of system parameters, and tackle the hysteresis nonlinearities. Based on the extended LaSalle’s invariance principle, asymptotic stability of the closed-loop system is also manifested. Simulations are also provided to show the effectiveness of the designed control.

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