Pole placement method on a class of nonlinear systems with adaptive backstepping technique

Abstract

In this paper, a gain determining method for nonlinear adaptive backstepping technique is proposed by the pole placement method. By introducing a subsystem that can be linearised as a linear system, controller gains can be solved by the pole placement method. Compared with the existing techniques, the proposed method can achieve a transient performance like a linear system with the pole placement method instead of constraining the system in a predefined performance range. Meanwhile, the proposed method does not change the structure of adaptive backstepping controllers, which preserves the advantages of the original backstepping design and avoids increasing the computing effort for the control system. In addition, the applications of the proposed method are demonstrated by three examples, including a 2nd-order nonlinear system, a 3rd-order nonlinear system, and a single-link robot arm. The corresponding simulations are conducted, and the simulation results are illustrated and analysed. Moreover, comparative simulations are conducted to verify the proposed method.

Keywords:

• Adaptive control
• pole placement
• gain determining

Disclosure statement

No potential conflict of interest was reported by the author(s).

Additional information

Funding

This work was supported by the Natural Sciences and Engineering Research Council of Canada (NSERC) under Grants RGPIN-2017-05367.

Notes on contributors

Zhengqi Wang

Zhengqi Wang received the B.S. degree in automation from Tianjin University, Tianjin, China, in 2016 and the M.S. degree in electrical and computer engineering from Lakehead University, Thunder Bay, ON, Canada, in 2018. He is currently pursuing the Ph.D. degree in electrical and computer engineering at Lakehead University, Thunder Bay, ON, Canada. His research interests are in nonlinear control theory with applications in unmanned aerial vehicles and robotics.

Xiaoping Liu

Xiaoping Liu received his B.Sc. Degree in Automation in 1984, his M.Sc. Degree in 1987, and Ph.D. in Control Theory and Applications in 1989, all from Northeastern University in China. From 1989 to 2000, he was with the Department of Automatic Control at Northeastern University (China). He joined the Department of Electrical Engineering at Lakehead University in 2001. He is a member of the Professional Engineers of Ontario, Canada. His research interests include nonlinear control, adaptive control, robust control and their applications to real engineering systems.

Wilson Wang

Wilson Wang received his M.Eng. in industrial engineering from the University of Toronto (Toronto, Ontario, Canada) in 1998 and Ph.D. in mechatronics engineering from the University of Waterloo (Waterloo, Ontario, Canada) in 2002, respectively. From 2002 to 2004, he was employed as a senior scientist at Mechworks Systems Inc. He joined Lakehead University in 2004, and now he is a professor in the Department of Mechanical Engineering. His research interests include signal processing, artificial intelligence, machine learning, diagnostics and prognostics of engineering systems, smart sensors, intelligent control, and mechatronics.