Stable control strategy for a second-order nonholonomic planar underactuated mechanical system

Abstract

This paper presents a stable control strategy for a planar four-link active–passive–active–active (APAA) underactuated mechanical system. The control objective is to move its end-point from any initial position to any target position. First, the controllers are designed to move the first link to the target angle which ensures the target position is within the reachable area of the planar three-link passive–active–active (PAA) system. Meantime, the system is reduced to a planar virtual Pendubot. Then, the periodic controllers are designed based on the nilpotent approximation model to make the first link return to the target angle and all angular velocities converge to zeroes, where the fuzzy modulating is added to adjust the convergence of angular velocities. Thus, the system is reduced to a planar virtual PAA system. Next, the control is divided into two stages, and based on the angle constraint relationships, the target angles of the planar virtual PAA system for the target position are obtained by using the online particle swarm optimisation algorithm. Each stage controllers are designed according to the target angles, so the end-point of the planar APAA system is controlled to the target position. Finally, the validity of the control strategy is demonstrated via simulations.

Keywords:

• Underactuated mechanical system
• position control
• nilpotent approximation
• PSO algorithm

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61773353], the Hubei Provincial Natural Science Foundation of China [grant number 2015CFA010] and the 111 Project [grant number B17040].

Notes on contributors

Xuzhi Lai

Xuzhi Lai received her B.S., M.S., and Ph.D. degrees in engineering from Central South University, Changsha, China, in 1988, 1991 and 2001, respectively. From 1991 to 2014, she was a Faculty Member of the School of Information Science and Engineering, Central South University, as a full professor. From 1998 to 1999, she was a visiting scholar with the Department of Mechatronics, School of Engineering, Tokyo University of Technology, Tokyo, Japan. From 2004 to 2006, she was a visiting scholar with the Department of Mechanical Engineering, University of Toronto, Toronto, ON, Canada, and with the School of Engineering, University of Guelph, Guelph, ON, Canada. In 2014, she joined the China University of Geosciences, Wuhan, China, where she is currently a professor in the School of Automation. Her research interests include intelligent control, robot control and nonlinear system control.

Peiyin Xiong

Peiyin Xiong received his B.S. and M.S. degrees, in 2004 and 2007, respectively, from School of Computer Science and Mathematics, Changsha University of Science & Technology. He obtained the Ph.D. degree in engineering from Central South University, in 2017 Changsha, China. He is a faculty member of the School of Information and Electrical Engineering, Hunan University of Science and Technology. His current research interests include nonlinear system control and intelligent control.

Min Wu

Min Wu received his B.S. and M.S. degrees in engineering from Central South University, Changsha, China, in 1983 and 1986, respectively, and the Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999. From 1986 to 2014, he was a faculty member of the School of Information Science and Engineering, Central South University, as a full professor. From 1989 to 1990, he was a visiting scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, and from 1996 to 1999, a visiting research scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology. From 2001 to 2002, he was a visiting professor with the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK. In 2014, he joined the China University of Geosciences, Wuhan, China, where he is currently a professor in the School of Automation. His research interests include robust control, process control, and intelligent systems. Prof. Wu is a senior member of the Chinese Association of Automation. He received the IFAC Control Engineering Practice Prize Paper Award in 1999 (together with M. Nakano and J. She).