Hysteresis modeling and compensation of a piezostage using least squares support vector machines

Abstract

Hysteresis effect degrades the positioning accuracy of a piezostage, and hence the nonlinearity has to be suppressed for ultrahigh-precision positioning applications. This paper extends least squares support vector machines (LS-SVM) to the domain of hysteresis modeling and compensation for a piezostage driven by piezoelectric stack actuators. A LS-SVM model is proposed and trained by introducing the current input value and input variation rate as the input data set to formulate a one-to-one mapping. By adopting the radial basis function (RBF) as kernel function, the LS-SVM model only has two free hyperparameters, which are optimally tuned by resorting to Bayesian inference framework. The effectiveness of the presented model is verified as compared with two state-of-the-art approaches, namely, Bouc–Wen model and modified Prandtl–Ishlinskii (MPI) model. In addition, the LS-SVM inverse model based feedforward control combined with an incremental proportional–integral–derivative (PID) feedback control is designed to compensate the hysteresis nonlinearity. Experimental results show that the LS-SVM model based hybrid control scheme is superior to the Bouc–Wen model and MPI model based ones as well as either of the stand-alone controllers. The rate-dependent hysteresis is suppressed to a negligible level, which validates the effectiveness of the constructed controller. Owing to a simple procedure, the proposed LS-SVM based approach can be applied to modeling and control of other types of hysteretic systems as well.