Adaptive Sliding Mode Control Based on Duhem Model for Piezoelectric Actuators

ABSTRACT

The strong hysteresis nonlinearity extremely limits the positioning precision of piezoelectric actuators (PZAs). For the purpose of eliminating hysteresis effect and achieving high precise output displacement of PZAs, an adaptive sliding mode control method is proposed in this paper. The proposed hybrid control method is composed of an adaptive control method and a sliding mode control method. The simulations are conducted to validate the effectiveness of the proposed control method. The simulation results show that the proposed control method restrains hysteresis behaviour of PZAs efficiently and reduces maximum relative error to 0.57%. In contrast, the existing works lack efficient methods to deal with the uncertain parameters of the hysteresis model. The proposed control method in this paper can effectively solve the existing problems and improve the positioning precision of the control system of PZAs.

KEYWORDS:

• Adaptive sliding mode control
• discretization
• Duhem model
• hysteresis
• inverse-based control
• piezoelectric actuators

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

Key Program of National Natural Science Foundation of China [grant number 2012CB821200]; National Natural Science Foundation of China [grant number 51105170]; Program of Science and Technology Development Plan of Jilin province of China [grant number 20140101062JC], [grant number 20140101082JC]; Program of Twelfth Five-Year Science and Technology Research Plan of Education Department of Jilin province of China [grant number 2014B023]

Notes on contributors

Miaolei Zhou

Miaolei Zhou was born in China in 1976. He received the BS and MS degrees in industrial electric automation from the Jilin Institute of Technology, China, in 1997 and 2000, and the PhD degree in control theory and control engineering from Jilin University, China, in 2004. Since 2000, he has worked in Jilin University, China. From 2006 to 2008, he was a postdoctoral researcher in the Tokyo University, Japan. Since 2014, he has been a professor with the control science and engineering, Jilin University, China. He is the author of more than 50 articles. His research interests include micro/nano drive and control technology, nonlinear control theory.

E-mail: [email protected]

Peng Yang

Peng Yang was born in China in 1990. He received the BSc degree in automation from Heilongjiang University of Science and Technology in 2013. Currently, he is a postgraduate student in College of Communication Engineering, Jilin University, China. His research interest is the hysteresis of piezoelectric actuators.

E-mail: [email protected]

Jingyuan Wang

Jingyuan Wang was born in China in 1988. She received the BSc degree in automation from Changchun University of Technology in 2011. She received the MS degree in College of Communication Engineering in Jilin University, China, in 2014. Her research interest is the hysteresis of piezoelectric actuators.

E-mail: [email protected]

Wei Gao

Wei Gao was born in China in 1974. He received the BS and MS degrees in industrial electric automation from the Jilin University of Technology, China, in 1996 and 1999, and the PhD degree in control theory and control engineering from Jilin University, China, in 2002. Since 1999, she has worked in Jilin University, China. Since 2004, she has been an associate professor with the control science and engineering, Jilin University, China. Her research interests include micro/nano drive and control technology, navigation and control of intelligent robot.

E-mail: [email protected]