Time-varying unimodular function based robust right coprime factorization for nonlinear forced vibration control system

Abstract

In this paper, a new nonlinear forced vibration control scheme using an operator-based robust right coprime factorization approach is considered for forced vibration control on a flexible plate with piezoelectric actuator. First, for considering the effect of hysteresis nonlinearity from the piezoelectric actuator, the Prandtl-Ishlinskii (P-I) hysteresis model is used to describe it. Also, a dynamic model of flexible plate is given by the theory of thin plates. For guaranteeing the robust stability of the nonin-ear forced vibration control system, operator-based controllers are designed. Simultaneously, for improving forced vibration control performance, the time-varying unimodular function is constructed by the designed controllers. If the inverse of the time-varying unimodular function tends to zero by the operator-based controllers and designed compensator, the output can be made arbitrarily small. Finally, the effectiveness of the proposed nonlinear control system is confirmed by simulation results.