Optimisation of control and learning actions for a repetitive-control system based on Takagi–Sugeno fuzzy model

Abstract

This paper deals with the problem of designing a two-dimensional (2D) modified repetitive-control system based on a Takagi–Sugeno (T-S) fuzzy model to achieve high tracking performance for a nonlinear plant. First, a nonlinear plant is represented by a T-S fuzzy model, and a modified repetitive controller with two repetitive loops is used to increases design flexibility. Next, a continuous-discrete 2D model is established to make use of the 2D characteristics in the modified repetitive-control system. Then, a sufficient stability condition is derived in terms of linear matrix inequalities. Three parameters are used to balance continuous control and discrete learning actions: one in a repetitive loop and two in a Lyapunov–Krasovskii functional. A particle swarm optimisation algorithm yields optimal parameters and the gains of the modified repetitive and state-feedback controllers. Finally, simulation and comparison results demonstrate the effectiveness of our method.

Keywords:

• Repetitive control
• Takagi–Sugeno (T-S) fuzzy model
• two-dimensional (2D) model
• linear matrix inequality
• particle swarm optimisation

Disclosure statement

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

Additional information

Funding

This work was supported by the National Natural ScienceFoundation of China [Grant Number 61733016], the National Key R&D Program of China [Grant Number 2018YFC0603405], the HubeiProvincial Technical Innovation Major Project [Grant Number 2018AA035], the 111 project [Grant Number B17040], and the FundamentalResearch Funds for the Central Universities [Grant Number CUG160705].

Notes on contributors

Manli Zhang

Manli Zhang received the B.S. degree in automation from China University of Geosciences, Wuhan, China, in 2018, where she is currently pursuing the Ph.D. degree in control science and engineering. Her current research interests include two-dimensional repetitive control and T-S fuzzy systems.

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 his Ph.D. degree in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1999. He was a faculty member of the School of Information Science and Engineering at Central South University from 1986 to 2014, and was promoted to Professor in 1994. In 2014, he moved to China University of Geosciences, Wuhan, China, where he is a professor in the School of Automation. He was a visiting scholar with the Department of Electrical Engineering, Tohoku University, Sendai, Japan, from 1989 to 1990, and a visiting research scholar with the Department of Control and Systems Engineering, Tokyo Institute of Technology, from 1996 to 1999. He was a visiting professor at the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK, from 2001 to 2002. His current research interests include process control, robust control, and intelligent systems. Dr. Wu is a Fellow of IEEE and a Fellow 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).

Luefeng Chen

Luefeng Chen received the B.S. degree in automation and the M.S. degree in control science and engineering from Central South University, Changsha, China, in 2009 and 2012, respectively, and the Ph.D. degree in computational intelligence and systems science from the Tokyo Institute of Technology, Tokyo, Japan, in 2015. He is currently an Associate Professor with the School of Automation, China University of Geosciences, Wuhan, China, where he was a Lecturer from 2015 to 2017. His current research interests include computational intelligence, human-robot interaction, intelligent system, pattern recognition, machine learning, emotion recognition and intention understanding, multi-robot behavior coordination, and intelligent control of industrial process. Dr. Chen was recipient of the Best Paper Award of the International Journal of Advanced Computational Intelligence and Intelligent Informatics in 2017 and the Best Paper Award in ASPIRE League Symposium 2012. He is a member of IEEE, the Chinese Association of Automation, the Chinese Association for Artificial Intelligence, and the Japan Society for Fuzzy Theory and Intelligent Informatics.

Shengnan Tian

Shengnan Tian received the B.S.degree in engineering from China University of Geosciences, Wuhan, China, in 2017. She is currently pursuing the Ph.D. degree in control science and engineering from China University of Geosciences, Wuhan, China. Her current research interests include repetitive control systems, fuzzy systems, and disturbance rejection.

Jinhua She

Jinhua She received the B.S. degree from Central South University, Changsha, China, in 1983, and the M.S. and Ph.D. degrees from the Tokyo Institute of Technology, Tokyo, Japan, in 1990 and 1993, respectively, all in engineering. 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, mobile learning, and assistive robotics. Dr She is a member of IEEE, Asian Control Association (ACA), the Society of Instrument and Control Engineers (SICE), Institute of Electrical Engineers of Japan (IEEJ), and the Japan Society of Mechanical Engineers (JSME). He was the recipient of the International Federation of Automatic Control (IFAC) Control Engineering Practice Paper Prize in 1999 (jointly with M. Wu and M. Nakano).