Zero-error tracking control of uncertain nonlinear systems in the presence of actuator hysteresis

Abstract

In this paper, the problem of adaptive tracking control is addressed for a class of nonlinear systems with unknown constant parameters and unknown actuator nonlinearity. The actuator nonlinearity is modelled as the backlash-like hysteresis, which is described by a differential model. The prior knowledge on the control gain sign is not required, and only the assumption on the reference signal is made. By combining the adaptive backstepping technique with the Nussbaum gain approach, an adaptive compensation controller design approach is developed. It is proved that the proposed control approach can guarantee that all the signals in the closed-loop system are bounded, and the tracking error can converge to zero asymptotically despite the presence of the actuator hysteresis. Two simulation examples are included to illustrate the effectiveness of the proposed approach.

Keywords:

• adaptive control
• nonlinear systems
• tracking control
• backstepping
• hysteresis

Additional information

Funding

This work was supported by the National Natural Science Foundation of China [grant number 61104007], [grant number 61203048], [grant number 61374153], [grant number 61304066], [grant number 61104064]; China Postdoctoral Science Foundation funded project [grant number 2012M511465]; Shandong Postdoctoral Science Foundation funded project [grant number 201203031]; the Foundation of Key Laboratory of System Control and Information Processing, Ministry of Education, China; the project supported by the Young Core Instructor and Domestic Visitor Foundation from the Education Department of Shandong Province, China; and the programme for scientific research innovation team in colleges and universities of Shandong Province, China, the Natural Science Foundation of Anhui Province [grant number 1308085QF119].

Notes on contributors

Zhengqiang Zhang

Zhengqiang Zhang received the BSc and MSc degrees from Qufu Normal University, Qufu, China, in 2000 and 2003, respectively, and the PhD degree from the Nanjing University of Science and Technology, Nanjing, China, in 2011. Currently, he is with the School of Electrical Engineering and Automation, Qufu Normal University, Qufu, China. His current research interests include adaptive control, control of nonlinear systems, fault-tolerant control, and time-delay systems.

Hao Shen

Hao Shen received the BSc degree in Communication Engineering from Anhui University of Technology, Ma’anshan, China, in 2006, and the PhD degree in Control Theory and Control Engineering from Nanjing University of Science and Technology, Nanjing, China, in 2011. He is currently with the School of Electrical Engineering and Information, Anhui University of Technology. He has been doing postdoctoral research with Department of Electrical Engineering, Yeungnam University, Gyeongsan, Republic of Korea, since March 2013. His current research interests include stochastic hybrid systems, network control systems, robust control and filtering, and nonlinear systems.

Ze Li

Ze Li received the BSc degree from Nanjing University of Science and Technology, Nanjing , China, in 2005 and the PhD degree from Nanjing University of Science and Technology, Nanjing, China, in 2010 (combined M-PhD programme). Since February 2010, she has joined the College of Electronic and Information Engineering, Suzhou University of Science and Technology, Suzhou, China, where she is currently a lecturer. Her research interests include robust control and filtering, time-delay systems, stochastic systems, nonlinear systems, and fuzzy systems.

Shuzhen Zhang

Shuzhen Zhang is a master’s degree candidate at the School of Electrical Engineering and Automation, Qufu Normal University, Qufu, China. Her research interests include adaptive control and control of nonlinear systems.