A new control method for global stabilisation of translational oscillator with rotational actuator

ABSTRACT

A translational oscillator with a rotational actuator (TORA) is an underactuated mechanical system with two degrees of freedom. This paper presents a new method to solve the global stabilisation control problem for this underactuated system. First, a set of suitable state variables is chosen for the TORA. It transforms the system into a cascade affine nonlinear system. Then, a positive-definite Lyapunov function is constructed based on the structural characteristics of the system. A control law is designed to guarantee that the derivative of the Lyapunov function is non-positive. Finally, the global stability of the closed-loop control system is analysed using the Lasalle invariance principle. The condition on the control parameters is presented to globally stabilise the TORA at the origin. The effectiveness and robustness of the method are verified by a numerical example.

KEYWORDS:

• Translational oscillator with a rotational actuator (TORA)
• underactuated system
• Lyapunov function
• Lasalle invariance principle
• global stabilisation

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Ancai Zhang  http://orcid.org/0000-0003-3776-7945

Jinhua She  http://orcid.org/0000-0003-3165-5045

Jianlong Qiu  http://orcid.org/0000-0002-9886-3570

Chengdong Yang  http://orcid.org/0000-0003-3757-895X

Fawaz Alsaadi  http://orcid.org/0000-0003-0041-3158

Additional information

Funding

This work was supported in part by National Natural Science Foundation of China [grant numbers 61773193, 61703193, 61873348, and 61877033], by the program of JSPS (Japan society for the promotion of science) International Research Fellows [grant number 17F17791], and by the project of Young Teacher Growth Program of Shandong Province.

Notes on contributors

Ancai Zhang

Ancai Zhang received the B.S. degree in mathematics from Linyi University, Shandong, China, in 2005, and received the M.S. degree in applied mathematics, the Ph.D. degree in control science, and engineering from Central South University, Hunan, China, in 2008 and 2012, respectively. In 2012, he joined the School of Automation and Electrical Engineering, Linyi University. He carried out his study in Tokyo University of Technology, Tokyo, Japan, from October 2009 to October 2011with the support of the scholarship of Chinese Government, and the postdoctoral fellowship of Japan Society for the Promotion of Science (JSPS) from October 2017 to October 2018. His research interests include underactuated mechanical systems, nonlinear systems, and robotics.

Jinhua She

Jinhua She received the B.S. degree in engineering in 1983 from Central South University, Changsha, Hunan, China, and received the M.S. degree in 1990 and the Ph.D. degree in 1993 in engineering from the Tokyo Institute of Technology, Tokyo, Japan. In 1993, he joined the School of Engineering, Tokyo University of Technology, where he is currently a professor. His research interests include the application of control theory, repetitive control, process control, Internet-based engineering education, and robotics.

Jianlong Qiu

Jianlong Qiu received the M.S. and Ph.D. degrees in Applied Mathematics from Southeast University, Nanjing, China in 2000 and 2007, respectively. From August 2008 to January 2013, he was a Postdoctoral in the School of Automation, Southeast University, Nanjing, China. He is currently the Dean and the Professor of School of Automation and Electrical Engineering, Linyi University. His research interests include complex systems and complex networks, control theory, and application.

Chengdong Yang

Chengdong Yang received the B.S. degree in Mathematics and Ph.D. degree in Computer Science from Harbin Engineering University in 2007 and 2011, respectively. From 2015 to 2018, he was a postdoctoral researcher in School of Automation, Southeast University, China. He is currently a professor in Linyi University. His current research interests include complex networks, multi-agent systems, distributed parameter systems, and feature selection.

Fawaz Alsaadi

Fawaz Alsaadi received the B.S. and M.Sc. degrees in computer science from King Abdulaziz University, Jeddah, Saudi Arabia, and University of Denver, Denver, Colorado, USA in 1998 and 2006, respectively. He received the Ph.D. degree in biometric security from the University of Colorado Springs, Colorado Springs, USA, in 2017. He is currently an assistant professor of the Information Technology Department within the Faculty of Computing and Information Technology, King Abdulaziz University. He has research interests in control theory and applications and biometric recognition.