Precision tracking control of a piezoelectric-actuated system

Abstract

In this paper, precision tracking control of piezoelectric-actuated systems is discussed. In order to obtain precision tracking control, a modified Prandtl–Ishlinskii (MPI) model is used to model the hysteresis nonlinearity. Then, the inverse MPI model is used to reduce the hysteresis nonlinearity, and a sliding-mode controller is used to compensate for the remaining nonlinear uncertainty and disturbances. In general, the piezoelectric-actuated system can be modeled as a linear model coupled with a hysteresis. When the linear model is identified, it is used to design the sliding-mode controller. Finally, this design method is applied to the motion control of a nano-stage, and experimental results are presented to verify the usefulness of this method.

Introduction

Piezoelectric actuators are becoming increasingly important in today's positioning technology due to the requirements of nanometer resolution in displacement. It is well known that the piezoelectric actuator has many advantages such as: (1) there are no moving parts; (2) the actuators can produce large forces; (3) they have almost unlimited resolution; (4) the efficiency is high; (5) response is fast. However, it also has some disadvantages such as: (1) hysteresis behavior; (2) drift in time; (3) temperature dependence. The hysteresis characteristics are generally nondifferentiable nonlinearities and are usually unknown, and this often limits system performance via undesirable oscillations or instability. Therefore, it is difficult to obtain an accurate trajectory tracking control.

Recently, several methods have been reported for the trajectory tracking control of a piezoelectric-actuated system. Ge and Jouaneh [2], [3] used a combination of a proportional integral derivative (PID) feedback controller with a feedforward controller that included the Preisach model of hysteresis. Their experimental results showed that the tracking performance was improved greatly. However, the result in Ref. [2] is only valid for a sinusoidal trajectory, and the method in Ref. [3] needs to train the model by using reference input before the control can be started. Ku et al. [7] combined a PID feedback controller with an adaptive neural network feedforward controller to control a nanopositioner that was actuated by a piezoelectric actuator. Cruz-Hernandez and Hayward [1] proposed a variable phase method. They utilized an operator to shift the periodic input signal by a phase angle that depended on the amplitude of the input signal and then used this operator to reduce the hysteresis nonlinearity. Huang and Lin [4] proposed a new hysteresis model based on two first-order transfer functions in parallel with two parameters determined from experiment. Adaptive control is also an approach to the inverse control of plants with hysteresis behavior. Tao and Kokotovic [9] developed an adaptive hysteresis inverse model and cascaded it with the system so that the effects of hysteresis nonlinearity could be reduced. Xu [11] utilized an adaptive neural network inverse controller to compensate for the hysteretic behavior of a piezoelectric actuator and a proportional integral controller in the outer loop to overcome the remaining nonlinear uncertainty. Furthermore, Hwang et al. [6] utilized an offline learned neural network model to reduce the effect of hysteresis and then designed a discrete-time variable structure controller to overcome the remaining uncertainty. They also reinforced this method [5] by using a recurrent neural network to improve the control performance. However, the computational burden of the controller that was designed by their method was heavy. Shen et al. [12] utilized an integer sliding-mode controller to compensate for the nonlinearity and disturbances in piezoelectric-actuated systems.

Kuhnen and Janocha [13] and Kuhnen [14] proposed a modified Prandtl–Ishlinskii (MPI) model for the hysteresis nonlinearities. This model also has been extended to model rate dependent hysteresis phenomena [15] and hysteresis with rate-dependent creep effects [16]. The main advantages of the MPI model over the Preisach model are that it is less complex, and its inverse can be computed analytically. In this paper, the MPI model is applied to model the hysteresis nonlinearity. Then, the inverse MPI model is used to reduce the hysteresis nonlinearity, and a sliding mode controller is designed to compensate for the remaining nonlinear uncertainty and disturbances. In this study, the sliding-mode uncertainty (disturbance) estimation and compensation scheme [8], [10], [12] is used to design the feedback controller. Finally, this design method is applied to the motion control of a nano-stage. The experimental results verify the usefulness of this method.