Adaptive Control of Piezoelectric Actuators with Unknown Hysteresis

Abstract

Hysteresis phenomenon occurs in all smart material-based sensors and actuators, such as shape memory alloys, piezoceramics and magnetostrictive actuators (Bank & Smith, 2000; Tan & Baras, 2004). In order to study this phenomenon, different models were proposed (Brokate & Sprekels, 1996; Visintin, 1994). Normally, hysteresis models are classified into two categories, physics-based model such as Jiles-Atherton model (Jiles & Atherton, 1986) and phenomenology-based model such as Preisach operator (Brokate & Sprekels, 1996; Visintin, 1994) and Duhem model (Visintin, 1994). From control systems point of view, hysteresis is generally non-differentiable, nonlinear, and unknown. As a result, systems with hysteresis usually exhibit undesirable inaccuracies or oscillation and even instability. Mitigating the effect of hysteresis becomes necessary and important, thus it has received increasing attention in recent years (Tao & Kokotovic, 1995, Su, et al, 2000, Su, et al, 2005). Many of these studies are related to modeling of hysteresis and their control issues. With the development of artificial intelligent (AI), AI is being applied to dealing with nonlinearities in systems (Ge & Wang, 2002). Only a few studies have been carried out by using NN to tackle hysteresis modeling and compensation (Makaveev, et al, 2002; Kuczmann & Ivanyi, 2002; Beuschel et al, 1998; Zhao & Tan, 2006). In the paper (Makaveev, et al, 2002), a NN model is used to describe the hysteresis behavior in different frequencies with the knowledge of some properties of magnetic materials, such as loss separation property to allow the separate treatment of quasi-static and dynamic hysteretic effects. Beuschel et al used (Beuschel et al, 1998) a modified Luenberger observer and NN are used to identify a general model of hysteresis. These researches demonstrate that NN can work as an unknown function approximator to describe the characteristics of hysteresis. Recently, two papers (Zhao & Tan, 2006; Lin et al 2006) applied the approximation property of NN to coping with the identification of Preisach-type hysteresis in piezoelectric actuator, and the hysteresis estimation problem for piezo-positioning mechanism based on hysteresis friction force function, respectively. It should be noted that the aforementioned results share a common assumption that the output of hysteresis is measurable. In practical systems, smart actuators are integrated into the systems, which makes the measurement of output of hysteresis hard. Hence it is a challenge to design an observer for