Browse > Article
http://dx.doi.org/10.5302/J.ICROS.2014.13.1963

Design of H∞ Repetitive Control Systems using State Feedback  

Doh, Tae-Yong (Department of Electronic and Control Engineering, Hanbat National University)
Publication Information
Journal of Institute of Control, Robotics and Systems / v.20, no.1, 2014 , pp. 6-11 More about this Journal
Abstract
Repetitive control is a specialized control scheme to track and/or attenuate a periodic reference trajectory and/or disturbance. Most researches about repetitive control have been performed in the frequency domain. Recently, several approaches to deal with repetitive control systems in the state space are developed by representing a q filter as a state-space equation. This paper presents a design method of a repetitive control system in the state space to satisfy $H_{\infty}$ performance. The overall system is composed of a plant, a repetitive controller, and a state-feedback controller, which can be converted to a standard form used in $H_{\infty}$ control. A LMI (Linear Matrix Inequality)-based stability condition is derived for fixed state-feedback gains. Under a given q filter, another LMI condition is derived to improve $H_{\infty}$ performance and is employed to find state-feedback gains by solving an optimization problem. Finally, to verify the feasibility of the proposed method, a numerical example is demonstrated.
Keywords
repetitive control; q filter; standard form; Lyapunov-Krasovskii function; LMI (Linear Matrix Inequality); $H_{\infty}$ performance; stability;
Citations & Related Records
Times Cited By KSCI : 2  (Citation Analysis)
연도 인용수 순위
1 T.-Y. Doh and J. R. Ryoo, "Robust stability condition and analysis on steady-state tracking errors of repetitive control systems," International Journal of Control, Automation, and Systems, vol. 6, no. 6, pp. 960-967, 2008.   과학기술학회마을
2 K. S. Kim and T.-Y. Doh, "Repetitive controller design for a robust feedback control system," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 16, no. 7, pp. 668-673, Jul. 2010.   과학기술학회마을   DOI
3 T.-Y. Doh and J. R. Ryoo, "Robust approach to repetitive controller design for uncertain feedback control systems," IET Proc. Control Theory and Applications, vol. 7, no. 3, pp. 431-439, 2013.   DOI
4 T.-Y. Doh, J. R. Ryoo, and M. J. Chung, "Design of repetitive control: an application to the track-following servo system of optical disk drives," IEE Proc. - Control Theory and Applications, vol. 153, no. 3, pp. 323-330, May 2006.   DOI   ScienceOn
5 W. Chen, S. Chang, and W. Zhang, "Linear matrix inequality-based repetitive controller design for linear systems with time-varying input delay," IET Control Theory and Applications, vol. 4, no. 6, pp. 1071-1078, 2010.   DOI
6 J.-H. She, M. Wu, Y.-H. Lan, and Y. He, "Simultaneous optimization of the low-pass filter and state-feedback controller in a robust repetitive-control system," IET Control Theory and Applications, vol. 4, no. 8, pp. 1366-1376, 2010.   DOI
7 M. S. Mahmoud, Robust Control and Filtering for Time-delay Systems, Marcel Dekker, Inc., 2000.
8 K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, 1996.
9 P. Gahinet, A. Nemirovski, A. J. Laub, and M. Chilali, LMI Control Toolbox User's Guide, The MathWorks, Inc., 1995.
10 S. Hara, Y. Yamamoto, T. Omata, and H. Nakano, "Repetitive control system: a new type servo system for periodic exogenous signals," IEEE Transactions on Automatic Control, vol. 37, no. 7, pp. 659-668, 1988.
11 J. Li and T.-C. Tsao, "Robust performance repetitive control systems," ASME Journal of Dynamic Systems, Measurement, and Control, vol. 123, no. 3, pp. 330-337, 2001.   DOI
12 M.-C. Tsai and W.-S. Yao, "Design of a plug-in type repetitive controller for periodic inputs," IEEE Transactions on Control Systems Technology, vol. 10, no. 4, pp. 547-555, 2002.   DOI   ScienceOn
13 M.-C. Tsai and W.-S. Yao, "Analysis and estimation of tracking errors of plug-in type repetitive control system," IEEE Transactions on Automatic Control, vol. 50, no. 8, pp. 1190-1195, 2005.   DOI
14 T.-Y. Doh and M. J. Chung, "Repetitive control design for linear systems with time-varying uncertainties," IEE Proc. - Control Theory and Applications, vol. 150, no. 4, pp. 427-432, Jul. 2003.   DOI   ScienceOn
15 Q. Quan, D. Yang, K.-Y. Cai, and J. Jiang, "Repetitive control by output error for a class of uncertain time-delay systems," IET Control Theory and Applications, vol. 3, no. 9, pp. 1283-1292, 2009.   DOI