Online Hysteresis Identification and Compensation for Piezoelectric Actuators

Hysteresis in piezoelectric actuators (PEAs) causes significant position errors and limits the application of PEAs. Compensating hysteresis via inverse models is one of the most popular approaches to reduce its effects. However, the construction of an accurate model is very challenging since hysteresis is coupled with creep and high-order dynamics, and hysteresis properties are also affected by operating conditions and aging effects. To overcome these challenges, this article proposes an adaptive generalized Maxwell-slip (AGMS) algorithm to identify and compensate for hysteresis online. By evenly distributing the saturation deformations throughout the desired range, a linear relation between the output force and the spring stiffness is generated, which enables a low-computational-complexity algorithm, such as the recursive least-squares algorithm, to update the stiffness online. Since the GMS model is self-invertible, an inverse model can be further analytically constructed in real time and utilized to compensate for the hysteresis. Experimental and comparison studies are carried out. The results show that this approach relaxes the requirement on the precision of the model and is robust to the operating conditions due to the capability of updating model parameters online. The normalized root mean square tracking error is approximately 0.4%.

I. Introduction

Piezoelectric actuators (PEAs) are increasingly being employed in ultraprecision positioning due to their advantages of subnanometer resolution, frictionless operation, a rapid response speed, and a high mechanical bandwidth [1], [2]. However, it is also well known that PEAs suffer from hysteresis, which is a memory-related phenomenon and depends on both amplitude and frequency. Hysteresis is also coupled with creep and temperature effects [3]–[5]. Hysteresis can cause tracking errors of up to 15% of the working range and can even lead to instability [1], [6]. Thus, the complex nature of hysteresis poses a great challenge in attempts to achieve ultraprecision positioning and is receiving increasing attention.