Application of Least-Squares Support-Vector Machine Based on Hysteresis Operators and Particle Swarm Optimization for Modeling and Control of Hysteresis in Piezoelectric Actuators

Abstract

Nanopositioning systems driven by piezoelectric actuators are widely used in different fields. However, the hysteresis phenomenon is a major factor in reducing the positioning accuracy of piezoelectric actuators. This effect makes the task of accurate modeling and position control of piezoelectric actuators challenging. In this paper, the learning and generalization capabilities of the model are efficiently enhanced to describe and compensate for the rate-independent and rate-dependent hysteresis using a kernel-based learning method. The proposed model is inspired by the classical Preisach hysteresis model, in which a set of hysteresis operators is used to address the problem of mapping, and then least-squares support-vector machines (LSSVM) combined with a particle swarm optimization (PSO) algorithm are used for identification. Two control schemes are proposed for hysteresis compensation, and their performance is evaluated through real-time experiments on a nanopositioning platform. First, an inverse model-based feedforward controller is designed based on the LSSVM model, and then a combined feedback/feedforward control scheme is designed using a classical control strategy (PID) to further enhance the tracking performance. For performance evaluation, different datasets with a variety of hysteresis loops are used during the simulation and experimental procedures. The results show that the proposed method is successful in enhancing the generalization capabilities of LSSVM training and achieving the best tracking performance based on the combination of feedforward control and PID feedback control. The proposed control scheme outperformed the inverse Preisach model-based control scheme in terms of both positioning accuracy and execution time. The control scheme that uses the LSSVM based on nonlinear autoregressive exogenous (NARX) models has significantly less computational complexity compared to our control scheme but at the expense of accuracy.

Precision Motion Control of a Piezoelectric Actuator via a Modified Preisach Hysteresis Model and Two-Degree-of-Freedom H-Infinity Robust Control

“…Figure 20 shows the effectiveness of our controller on the considered nanopositioning system in reducing the hysteresis nonlinearity of the PEA, where it describes a highly linear relationship between the input and output. Tracking results with the suggested feedforward-feedback controller Table 5 shows the tracking performance for the proposed control scheme compared with the LSSVM-PID feedback controller, which has been proposed in our previous work [31]. It can be observed that the 2-DOF 𝐻 controller achieved better trajectory tracking performance than the traditional PID feedback controller, obtaining a 0.0212 µm RMSE on…”

“…PEA actuator (name of the company is unavailable) 0.03 PID-Modified Preisach [31] The feedforward compensator was designed by modified Preisach using PSO-LSSVM and the feedback controller was designed by incremental PID control.…”

“…Each training signal contains 500 samples (with a sample time of 0.02 s), and their amplitudes range from 0 to 6 V before amplification. In our previous work [ 31 ], we noted an interesting tradeoff between model complexity and accuracy and proved that the optimal number of operators is 55; thus, we used the same number in this study as well. Additionally, in the same previous paper, we presented a detailed discussion of the optimal tuning of PSO hyper-parameters used for training the model.…”

“…The experimental results indicated that the outputs could be predicted, but the output of the feedforward compensator accumulates errors over time in real-time control experiments due to the feedback [21,30]. In previous studies [31,32], the authors modified the Preisach model using a kernel-based machine learning method combined with a hysteresis memory to overcome the error accumulation limitation. The compensator has been constructed using two parts; hysteresis operators to solve the mapping problem and an inverse Preisach hysteresis model based on the LSSVM algorithm optimized by particle swarm optimization (PSO) and the improved PSO algorithms to estimate the density function.…”

Evaluation of Agricultural Machinery Operational Benefits Based on Semi-Supervised Learning

“…In this study, the optimization capability of particle swarm optimization (PSO) is selected to optimize the parameters of LSSVM [19][20][21] so as to further improve the model performance. The PSO algorithm updates its own speed and position after each iteration according to the optimal solution of the particle itself and the global optimal solution.…”