Theoretical and experimental investigation study of discrete time rate‑dependent hysteresis modeling and adaptive vibration control for smart flexible beam with MFC actuators

Abstract

A new rate‑dependent hysteresis modeling and identification method, and a new adaptive filtering control algorithm is proposed to solve the hysteresis nonlinearity identification problem and adaptive parameter auto-tuning problem for vibration control of smart flexible beam employing MFC actuators. A Hammerstein model is proposed by composing asymmetric Bouc-Wen model and ARX model in series to for secondary path modelling to model the MFC actuator hysteresis and mechanical hysteresis of the flexible beam. To improve the convergence speed and performance for complex parameter identification of the Hammerstein model, an improved Jaya algorithm named hybrid Jaya is proposed which combines the mutation strategy of two kinds of DE algorithms as the individual update method of the proposed hybrid Jaya. To balance the convergence speed and steady-state error for active vibration control performance, a new variable tap-length and step-size FXLMS algorithm named FX-VSSFT-LMS algorithm is proposed and the adaptive parameters are auto-tuned by our proposed Hybrid Jaya algorithm. To verify the proposed Hammerstein model and adaptive filtering algorithm, a cantilever beam experimental platform with MFC actuators is constructed. Hybrid Jaya algorithm and Jaya algorithm were used to identify the Hammerstein model and Bouc-wen model of MFC actuator, and the improved effects of hybrid Jaya algorithm and Hammerstein model were compared and verified. The FX-VSSFT-LMS algorithm is compared with FX-VSSLMS algorithm with variable step size and FX-FTLMS algorithm with variable tap-length on the MFC cantilever beam. The experimental comparison proves that the Hammerstein model identified by the proposed Hybrid Jaya algorithm is effective and the FX-VSSFT-LMS algorithm has better convergence performance than FX-VSSLMS and FX-FTLMS algorithm.