Improving disturbance-rejection performance in a modified repetitive-control system based on equivalent-input-disturbance approach

ABSTRACT

This paper presents a method to actively reject aperiodic disturbances and to suppress uncertainties in a modified repetitive-control (RC) system, based on an equivalent-input-disturbance (EID) approach. The influences of aperiodic disturbances and uncertainties on the input channel are estimated by an EID estimates and then rejected by incorporating the estimation into a repetitive control law. First, how to construct an EID-based modified repetitive-control system is described, in which a correction is introduced to the amount of the delay of the repetitive controller to enhance the steady-state tracking performance. Next, a linear-matrix-inequality-(LMI)-based stability criterion is derived by employing the Lyapunov functional method. Two tuning parameters introduced in the LMI can manipulate the preferential adjustment of the robust stability and learning efficiency and thus improve both transient and steady-state performances. Then, an optimisation algorithm is presented to produce optimal controller gains. Finally, simulations exhibit the design procedure in detail, and the superiority of the proposed method in this paper is demonstrated through comparisons with some conventional RC and $H_{\mathrm{\infty }}$ RC methods.

Keywords:

• Repetitive control
• aperiodic disturbance
• disturbance estimation and rejection
• linear matrix inequality (LMI)

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 numbers 61673167, 61873348, and 61503132].

Notes on contributors

Lan Zhou

Lan Zhou received the B.S. degree in 1998 from Hunan Normal University, Changsha, China, and the M.S. degree in 2006 from Central South University, Changsha, China. From 2008 to 2010, she had been a Joint Cultivation Doctoral Candidate of Japan and China. She received her Ph.D. degree in control science and engineering from Central South University in 2011. She is a Professor of control theory and control engineering with the School of Information and Electrical Engineering, Hunan University of Science and Technology, Xiangtan, China. Her current research interests include robust control, repetitive control, and control application.

Jinhua She

Jinhua She received the B.S. degree in engineering from Central South University, Changsha, China, in 1983, and the M.S. and Ph.D. degrees in engineering from the Tokyo Institute of Technology, Tokyo, Japan, in 1990 and 1993, respectively. In 1993, he joined the School of Engineering, Tokyo University of Technology, Tokyo, 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.

Xian-Ming Zhang

Zhang Xian-Ming received the M.Sc. degree in applied mathematics and the Ph.D. degree in control theory and engineering from Central South University, Changsha, China, in 1992 and 2006, respectively. In 1992, he joined Central South University, where he was an Associate Professor with the School of Mathematics and Statistics. From 2007 to 2014, he was a Post-Doctoral Research Fellow and a Lecturer with the School of Engineering and Technology, Central Queensland University, Rockhampton, QLD, Australia. From 2014 to 2016, he was a Lecturer with the Griffith School of Engineering, Griffith University, Gold Coast, QLD, Australia. In 2016, he joined the Swinburne University of Technology, Melbourne, VIC, Australia, where he is currently a Senior Lecturer with the School of Software and Electrical Engineering. Dr. Zhang was a recipient of the National Natural Science Award (Second Class) in China in 2013, jointly with Prof. M. Wu and Prof. Y. He. His current research interests include state estimation/filtering, event-triggered control, networked control, security control, neural networks, multi-agent systems, and time-delay systems.

Zhu Zhang

Zhu Zhang received the B.S. degree in electrical engineering from Hunan Institute of Engineering in 2004, the M.S. degree in power electronics from the South China University of Technology in 2007, and the Ph.D. degree in electrical engineering from Hong Kong Polytechnic University, Hong Kong, in 2012. From 2007 to 2009, he was a Research Assistant with the Power Electronics Research Center, Hong Kong Polytechnic University. From 2012 to 2013, he had been a research associate with the Electrical Engineering Department, Hong Kong Polytechnic University. Since 2013, he has been a lecturer with College of Information and Electrical Engineering, Hunan University of Science and Technology. His research interests include power electronics and power transmission, and intelligent control.