Abstract
Hysteresis is an inherent characteristic of piezoelectric materials that can be determined by not only the historical input but also the input signal frequency. Hysteresis severely degrades the positioning precision of piezoelectric micropositioning stages. In this study, the hysteresis characteristics and the excitation frequency effects on the hysteresis behaviors of the piezoelectric micropositioning stage are investigated. Accordingly, a rate-dependent asymmetric hysteresis Prandtl–Ishlinskii (RDAPI) model is developed by introducing a dynamic envelope function into the play operators of the Prandtl–Ishlinskii (PI) model. The RDAPI model uses a relatively simple analytical structure with fewer parameters and then other modified PI models to characterize the rate-dependent and asymmetric hysteresis behavior in piezoelectric micropositioning stages. Considering practical situations with the uncertainties and external disturbances associated with the piezoelectric micropositioning stages, the system dynamics are described using a second-order differential equation. On this basis, a corresponding robust adaptive control method that does not involve the construction of a complex hysteretic inverse model is developed. The Lyapunov analysis method proves the stability of the entire closed-loop control system. Experiments confirm that the proposed RDAPI model achieves a significantly improved accuracy compared with the PI model. Furthermore, compared with the inverse RDAPI model-based feedforward compensation and the inverse RDAPI model-based proportional–integral–derivative control methods, the proposed robust adaptive control strategy exhibits improved tracking performance.
Highlights
IntroductionMicrotechnology and nanotechnology are required in many industries for precision control
Two different dynamic input functions, hl(u, u) and hr(u, u), The parameters to be identified in the rate-dependent asymmetric hysteresis Prandtl-Ishlinskii (RDAPI) model inare selected to express the rate-dependent play operator
The proposed RDAPI model and the robust adaptive control strategy were tested on piezoelectric micropositioning stages to evaluate their efficiency
Summary
Microtechnology and nanotechnology are required in many industries for precision control. The rate-dependent hysteresis model requires further investigation Another challenge is eliminating the hysteresis nonlinearity of the piezoelectric micropositioning stage to achieve high-precision tracking control is another challenging topic. A nonlinear controller is designed to drive the controlled object and adjusts the control parameters online based on the tracking error to improve the control accuracy [42–46] This method omits the cumbersome inverse-model establishment process; its performance is unaffected by the inverse-model accuracy [47]. In contrast to the commonly used approach of constructing a complex hysteretic inverse model, the proposed control method directly uses the established RDAPI model to describe the hysteresis behavior, and the adaptive control laws are designed to eliminate hysteresis nonlinearity and uncertainties online. The proposed control method directly uses the established RDAPI model to describe the hysteresis behavior without constructing a complex hysteretic inverse model, and the robust adaptive method enhances the control accuracy and robustness.
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