Rate-dependent hysteresis modeling and compensation of piezo-driven flexure-based mechanism

Abstract

Updating parameters according to the driving rate of input, the rate-dependent Prandtl-Ishlinskii (PI) model is widely used in hysteresis modeling and compensation. In order to improve the modeling accuracy, two PI models identified at low and high driving rates separately are incorporated through a combination law. For the piezo-driven flexure-based mechanism, the very low damping ratio makes it easy to excite the structural vibration. As a result, the measured hysteresis loop is greatly distorted and the modeling accuracy of the identified PI model is significantly affected. In this paper, a novel time-efficient parameter identification method which utilizes the superimposed sinusoidal signals as the control input is proposed. This method effectively avoids the excitation of the structural vibration. In addition, as the driving rate of the superimposed sinusoidal signals covers a wide range, all the coefficients required for modeling the rate-dependence can be identified through only one set of experimental data. Hysteresis modeling and trajectory tracking experiments were performed on a 2-DOF piezo-driven flexure-based mechanism. The experimental results show that the combined hysteresis model maintains the modeling accuracy over the entire working range of the flexure-based mechanism. The mechanism’s hysteresis is significantly suppressed by the use of the inverse PI model as the feedforward controller; and better result is achieved when a feedback loop is also incorporated. The tracking performance of the flexure-based mechanism is greatly improved.