Operator‐based robust non‐linear vibration control for an L‐shaped arm with unknown load by using on‐line wavelet transform

Abstract

An L-shaped arm with unknown load driven by a linear pulse motor is studied in this work. To control the motor motion and the arm vibration, an operator-based non-linear control is designed using an on-line discrete wavelet transform (DWT). First, the dynamics of the L-shaped arm vibration is modelled by considering the arm as a two-dimensional Euler–Bernoulli beam. The relationship between the load and the arm vibration is given. Second, by using the on-line DWT in the operator-based non-linear control, the proposed control for the system is designed. The wavelet transform is used to estimate the load and remove the influence of some undesired uncertainties. The operator-based right coprime factorisation method is used to guarantee the robust stability of the motor-arm system. The piezoelectric actuator is utilised to further reduce the arm vibration. The hysteresis of the piezoelectric actuator is compensated by using a Prandtl–Ishlinskii hysteresis model. Finally, simulation results are demonstrated to validate the proposed control.