Adaptive active vibration control for piezoelectric smart structure with online hysteresis identification and compensation

Smart structure vibration reduction based on adaptive active vibration control has become a hot research spot in recent years. A filtered-U least mean square algorithm based on an infinite impulse response filter structure is used to solve the interference of controller output to reference signal. The filtered-U least mean square algorithm is very suitable for the nonlinear vibration control of the flexible structure. This study focuses on the analysis and implementation of an adaptive active vibration control system for smart structure with a surface-bonded piezoelectric actuator. The piezoelectric actuator contained in the secondary path has nonlinear hysteresis property. The nonlinear hysteresis property will cause a nonlinear relationship between the structural vibration response and the control voltage, which deteriorates the robustness and control effect of the adaptive control. This study designs an improved version of the filtered-U least mean square algorithm with online hysteresis identification and compensation (filtered-U least mean square–online hysteresis identification and compensation) based on a discrete Prandtl–Ishlinskii model. The Prandtl–Ishlinskii model parameters of the nonlinear hysteresis property are identified online based on the least mean square algorithm. Based on the identified Prandtl–Ishlinskii model parameters, an inverse hysteresis compensator is established for feedforward compensation in the secondary path. Simulation results show that the proposed method can dynamically compensate the hysteresis nonlinearity of the secondary path, linearizing the nonlinear hysteresis. The vibration reduction effect of the proposed method is obviously better than that of other competing methods. A piezoelectric smart cantilever plate with PZT (or lead zirconate titanate, Pb (Zr, Ti)) actuators and sensors is designed to demonstrate the validity and efficiency of the proposed method by experiments. Experiment results demonstrate that the adverse effect of nonlinear hysteresis is eliminated well after feedforward hysteresis compensation is introduced; the unexpected frequency vibration caused by the hysteresis property is suppressed. The proposed methodology possesses an important advantage in application of the adaptive active vibration control of the piezoelectric smart structure.