Modeling and Internal Model Control of Piezo-Positioning Actuator

Piezo-positioning actuators are widely used in the field of precision control, but they have significant hysteresis nonlinearity of their own, which seriously affects the positioning accuracy of piezo-positioning actuators. In order to accurately describe the rate-dependent hysteresis nonlinearity of the piezo-positioning actuator, this paper uses the Hammerstein model to model the dynamic hysteresis nonlinearity, which is described by the Prandtl-Ishlinskii model and the linear dynamic part described by the transfer function model obtained by the Hankel matrix system identification method. The control strategy is the two-degree-of-freedom internal-mode control scheme with a feedback filter. In the internal-mode control, the feedforward controller is designed using the minimum-phase approximation method for the presence of a non-minimum-phase link in the nominal model and the stability analysis of the control scheme and the parameter selection of the feedback filter are implemented based on the small-gain theorem. The experimental results show that the relative modeling error of the Hammerstein model established in this paper is less than 2.42% within 80Hz and the root mean square error is less than 0.3551μm, which can effectively describe the hysteresis nonlinearity in the experimental frequency band. Under the control strategy of this paper, the signals in the experimental frequency band can be tracked effectively with the relative error less than 6.08% and the root mean square error less than 1.2744μm, which can meet the needs of practical engineering and prove the effectiveness of the proposed control strategy.