Rate-Dependent Hysteresis Modeling and Control of a Piezostage Using Online Support Vector Machine and Relevance Vector Machine

Hysteresis nonlinearity degrades the positioning accuracy of a piezostage and requires a suppression for precision micro-/nanopositioning applications. This paper proposes two new approaches to modeling and compensating the rate-dependent hysteresis of a piezostage driven by piezoelectric stack actuators. By formulating the hysteresis modeling as an online nonlinear regression problem, online least squares support vector machine (SVM) (LS-SVM) and online relevance vector machine (RVM) models are proposed to capture the hysteretic behavior. Both hysteresis models are capable of updating continually with subsequent samples. After a comparative study on modeling performances, an inverse model-based feedforward combined with proportional-integral-derivative feedback control is presented to alleviate the hysteresis effect. Experimental results show that the LS-SVM model-based control scheme is over 86% more accurate than the RVM model-based one in the motion tracking task, whereas the latter is 14 times faster than the former in terms of updating time. Moreover, both LS-SVM and RVM model-based control schemes can suppress the rate-dependent hysteresis to a negligible level, which validates the feasibility and effectiveness of the proposed approaches.

I. Introduction

A piezostage refers to a micro-/nanopositioning stage actuated by piezoelectric stack actuators (PSAs). In comparison with other types of actuators [1], PSA is capable of positioning with subnanometer resolution, rapid response, and large blocking force. Hence, it is widely adopted in diverse micro-/nanopositioning applications such as scanning probe microscopy [2], [3] and biological manipulation [4], [5]. Nevertheless, PSA introduces nonlinearity into the system due to the piezoelectric hysteresis and creep effects [6]. The hysteresis is embodied as a nonlinear relationship between the input voltage and output displacement and induces a severe open-loop positioning error as high as 10%–15% of the motion range of the positioning system. Therefore, the hysteresis has to be suppressed in high-precision application scenarios [7]–[9].