State estimation of non-linear piezoelectric stack actuator, hysteresis model

Abstract

The state estimation of a non-linear model of a piezoelectric stack actuator showing hysteresis is proposed. Model uncertainties related to hysteresis effect in piezoelectric stack actuators, most prominently in higher frequency zone; can make the closed-loop control system unstable. Furthermore it may lead to inaccurate open-loop control frequently causing harmonic distortions when the stack is driven with sinusoidal input signals. In order to solve the above issues, it is very important to determine an accurate non-linear model of the piezoelectric stack actuator. The Unscented Kalman Filter (UKF) algorithm is used to accurately estimate the states of the non-linear model of the piezo-electric stack actuator such that hysteresis effect can be accurately predicted. The states of the piezo-electric stack actuator model are assumed to be zero-mean Gaussian random variables (GRV). The UKF uses the Unscented Transformation (UT) method to choose the minimal number of samples points such that the true mean and covariance. of the GRV is completely captured. On propagation through the true non-linear model of the piezo-electric stack actuator, these sample points capture the posterior mean and covariance accurately to third order for Gaussian inputs. The accurately estimated model thereby assists studies aiming at a better understanding of the hysteresis effect as well as is useful in robust control system design. Preliminary results of this investigation are presented.