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

TLDR

Hysteresis nonlinearity degrades the positioning accuracy of a piezostage and requires suppression for precision micro‑/nanopositioning applications. This paper proposes two new approaches to model and compensate the rate‑dependent hysteresis of a piezostage driven by piezoelectric stack actuators. The authors formulate hysteresis modeling as an online nonlinear regression problem, proposing online LS‑SVM and RVM models that update continually and use an inverse model‑based feedforward combined with PI‑D feedback control to alleviate hysteresis. Experimental results show that the LS‑SVM‑based control scheme is over 86 % more accurate than the RVM scheme, while the RVM updates 14 times faster, and both schemes suppress rate‑dependent hysteresis to a negligible level.

Abstract

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.