压电作动器的率相关迟滞建模与跟踪控制

Abstract

A modeling method and a real-time trajectory tracking control strategy were proposed based on Hammerstein model to overcome the effect of rate-dependent hysteresis on piezoelectric actuators. First,by using modified Prandtl-Ishlinskii(MPI)model and the Autoregressive Model with Exogenous Input(ARX)to represent the static nonlinear part and the linear dynamic part of the Hammerstein model,respectively,a Hammerstein model was proposed to describe the rate-dependent hysteresis of piezoelectric actuators.Then,based on the proposed Hammerstein model,a compound control strategy with feed-forward adaptive inverse compensation and PI feed-back was designed.Finally,to verify the effectiveness of the proposed control strategy,a compound control strategy with feed-for-ward inverse compensation and PI feed-back was designed to compare with the proposed scheme.The experiments on the real-time tracking for single frequency signals and sweep signals with the amplitudes of 11μm,compound frequency signals and sinusoidal scanning signals with variable amplitudes were performed in a frequency of 100Hz,obtained results show that the root mean square error and the relative error between the reference input and the output of piezoelectric actuator are 0.280 8-0.437 3μm and 0.016 5-0.024 4respectively.As compared with the compound control strategy with feed-forward inverse compensation and PI feed-back,the proposed control strategy has better tracking accuracy and real-time ability.