A one-step method of designing an observer-based modified repetitive-control system

Abstract

A method of designing a robust observer-based modified repetitive-control system for a class of strictly proper linear plants with periodic uncertainties has been developed. These plants have no direct path from the input to the output. First, the periodicity and continuity of repetitive control are exploited to construct a continuous-discrete two-dimensional (2D) model that allows the preferential adjustment of control and learning through regulation of the 2D feedback gains. Next, Lyapunov stability theory and the singular-value decomposition of the output matrix are used to establish two stability conditions. The conditions convert (a) the problem of designing the maximum cut-off angular frequency of the low-pass filter into a standard generalised eigenvalue optimisation problem, and (b) the problem of independently designing a state observer and a stabilising controller into a feasibility problem for linear matrix inequalities (LMIs). Two tuning parameters in one of the LMIs determine the selection of the 2D feedback gains. Then, the combination of two design conditions yields an iterative algorithm that simultaneously optimises the maximum cut-off angular frequency of the low-pass filter and the gains of the stabilising controller. It solves the trade-off problem between stability and tracking performance. Finally, a simulation example demonstrates the validity of the method.

Keywords:

• repetitive control
• state observer
• two-dimensional (2D) system
• linear matrix inequality (LMI)

Additional information

Funding

This work was supported in part by the National Natural Science Foundation of China [grant number 61203010], [grant number 61210011], [grant number 51374107]; Hunan Natural Science Foundation [grant number 11JJ4059]; Scientific Research Fund of Hunan Provincial Education Department [grant number 12B044].

Notes on contributors

Lan Zhou

Lan Zhou received her BS degree in 1998 from Hunan Normal University, Changsha, China; and MS degree in 2006 from Central South University, Changsha, China. From 2008 to 2010, she was a Joint Cultivation Doctoral Candidate of Japan and China. She received her PhD in control science and engineering from Central South University in 2011. She is an associate 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 a BS degree in engineering from Central South University, Changsha, Hunan, China, in 1983, an MS degree in 1990, and a PhD degree in 1993 in engineering from the Tokyo Institute of Technology, Tokyo, Japan. In 1993, he joined the Department of Mechatronics, School of Engineering, Tokyo University of Technology, and in April 2008, he transferred to the University's School of Computer Science, where he is currently a professor. He received the control engineering practice paper prize of the International Federation of Automatic Control (IFAC) in 1999 (jointly with M. Wu and M. Nakano). His research interests include the application of control theory, repetitive control, process control, Internet-based engineering education, and robotics.

Min Wu

Min Wu received the BS and MS degrees in engineering from Central South University, Changsha, China, in 1983 and 1986, respectively, and the PhD degree in engineering from Tokyo Institute of Technology, Tokyo, Japan, in 1999. Since July 1986, he has been a faculty member with Central South University, where he is currently a professor of automatic control engineering with the School of Information Science and Engineering. He was a visiting scholar at the Department of Electrical Engineering, Tohoku University, Sendai, Japan, from 1989 to 1990, a visiting research scholar at the Department of Control and Systems Engineering, Tokyo Institute of Technology, Tokyo, Japan, from 1996 to 1999, and a visiting professor at the School of Mechanical, Materials, Manufacturing Engineering and Management, University of Nottingham, Nottingham, UK, from 2001 to 2002. He received the control engineering practice paper prize of the International Federation of Automatic Control (IFAC) in 1999 (jointly with M. Nakano and J. She). His current research interests include robust control and its application, process control, and intelligent control. He is a senior member of IEEE.