Design of a robust output-feedback-based modified repetitive-control system

Abstract

This paper concerns the problem of designing a robust output-feedback-based modified repetitive-control system for a class of strictly proper plants with periodic uncertainties. Exploiting the periodicity of repetitive control, a continuous-discrete two-dimensional (2D) model is built so that the control and learning actions can be adjusted preferentially by means of the control gains. The combination of the singular-value decomposition of the output matrix and the Lyapunov stability theory is used to derive a linear-matrix-inequality-(LMI-) based asymptotic stability condition. Two tuning parameters in the LMI regulate the choice of the parameters in the 2D control law and thereby enable the preferential adjustment of control and learning. A numerical example illustrates the tuning procedure and demonstrates the validity of the method.

Keywords:

• repetitive control
• output-feedback
• two-dimensional system
• linear matrix inequality (LMI)

Acknowledgements

This work was supported in part by the National Natural Science Foundation of China under Grant Nos. 61203010 and 61210011, Hunan Natural Science Foundation under Grant No. 11JJ4059 and Scientific Research Fund of Hunan Provincial Education Department under Grant No. 12B044.

Additional information

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 his BS in engineering from Central South University, Changsha, Hunan, China, in 1983; MS in 1990; and PhD 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 was transferred to the University's School of Computer Science, 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.