Modeling and Control of Hysteresis Characteristics of Piezoelectric Micro-Positioning Platform Based on Duhem Model

Abstract

The hysteresis characteristic of piezoelectric micro-positioning platforms seriously affects its positioning accuracy in precision positioning. It is important to design an effective hysteresis model and control scheme. Based on the analysis of the Duhem model, this paper proposes to divide the hysteresis curve into two parts, the step-up section and the step-down section, to identify the model parameters, respectively, and a hybrid intelligent optimization algorithm based on the artificial fish swarm algorithm and the bat algorithm is proposed. The simulation experiment verified that the error of the improved model was reduced by 48.97%, which greatly improved the identification accuracy of the Duhem model. Finally, an inverse model of the Duhem model for the segmental identification of the improved artificial fish swarm algorithm is established, and a composite controller integrating feedforward, feedback and decoupling control is designed on the basis of the inverse model, and an experimental verification is carried out. The results show that the displacement errors of the composite controller under different voltage signals are all within 0.25%. Therefore, the established model can accurately express the hysteresis characteristics of the platform, and the use of the composite controller can effectively reduce the accuracy error caused by the hysteresis characteristics.

Modeling and identification of nonlinear hysteresis behavior of piezoelectric actuators using a computationally efficient phenomenological model and modified cuckoo search algorithm

“…For all three metrics, the lower the values of evaluation metrics, the better the model performance. The mathematical expressions of MAPE and SMAPE are given in equations (20) and (21).…”

“…Similar to the simulation process, eight types of frequencies from 10 Hz to 80 Hz are applied to the PZT actuator in the drive unit respectively, with sine wave voltages namely 0-20 V-0, 0-40 V-0, 0-60 V-0. Through the calculation of equations (11), (20) and (21), RMSW, MAPE and SMAPE of BW/PI models and the proposed model can be obtained respectively. The performance comparison results of the three models in terms of RMSE, MAPE and SMAPE are displayed in figures 12-19, according to different excitation frequencies and voltage levels, in the form of radar plots.…”

“…Different from physical models, phenomenological hysteresis models employ numerical equations directly to characterize nonlinear input and output relationships of hysteresis, without regard to the natural physical properties. Accordingly, phenomenological models are extensively applied in nonlinear hysteresis modeling of PZT actuators, such as Preisach model [9][10][11][12], Maxwell slip model [13,14], Prandtl-Ishlinskii (PI) model [15][16][17], Rayleigh model [18], Dahl model [19], Duhem model [20,21], Jiles-Atherton (J-A) model [22], neural networks model [23], frictional model [24], Bouc-Wen (BW) model [25][26][27], etc. Xiao and Li [12] developed a modified inverse Preisach model to characterize hysteretic responses of PZT actuators at a wide frequency range, where µ-density functions and weights were optimized by fast Fourier transform to realize the online rate-dependent compensation of PZT hysteresis in real-time.…”

Parameter identification of Duhem model based on antlion-fish swarm hybrid algorithm and robust backstepping sliding mode control for rate-dependent hysteresis of piezoelectric actuators

“…Where g(x, t) 6 ¼ 0, d(t) j j4D. Considering the last step (the second step) of backstepping design, combining sliding mode control to define sliding mode surface s = z 2 , Lyapunov function is still defined according to equation (20), then…”

“…Some studies have tried to develop different parameter identification methods. In addition to the classical least squares algorithm, 17 meta-optimization such as particle swarm algorithm (PSO), 18 genetic algorithm 19 and fish swarm algorithm (AF) 20 are applied to the parameter identification of the model. And some studies have verified that Antlion algorithm (ALO) is robust and simple.…”