Active Vibration Control of a Dynamic Hysteresis System Using $\mu$ -Synthesis

This paper considers active vibration control of a dynamic hysteresis system with a piezoelectric actuator using acceleration sensors for data acquisition. A Hammerstein model is proposed with a BP neural network model and an autoregressive model with exogenous input representing, respectively, the static hysteresis and the rate-dependent characteristics. It is shown that the tracking errors of our model are less than 7% within a frequency range of 10–100 Hz, showing that the obtained model can describe the system hysteresis well. A <inline-formula> <tex-math notation="LaTeX">$\mu $ </tex-math></inline-formula>-synthesis strategy is used for vibration control with a nonlinear inverse compensation based on the obtained model. The experimental results show that the proposed robust control method can effectively attenuate the vibration with more than 60% vibration reduction within a frequency range of 35–80 Hz.