Abstract
This paper presents a modified repetitive control scheme comprising of a state error and a control input via delayed feedback to track periodic reference trajectories and/or attenuate disturbances. The closed-loop state error dynamics can be represented using a typical neutral delay system with an exogenous input to be attenuated. The sufficient conditions to achieve overall stability and H∞ performance to minimize state error are derived by applying a Lyapunov-Krasovskii functional and a Hamiltonian, which are expressed as an algebraic Riccati inequality (ARI) and a linear matrix inequality (LMI). Based on the derived conditions, it is shown that the repetitive controller design problem can be reformulated as an optimization problem with an LMI constraint to determine the state error feedback gain. Finally, a numerical example is presented to demonstrate the feasibility of the proposed method.
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S. Hara, Y. Yamamoto, T. Omata, and H. Nakano, “Repetitive control system: A new type servo system for periodic exogenous signals,” IEEE Trans. Autom. Control, vol. 37, no. 7, pp. 659–668, 1988.
T.-Y. Doh and J. R. Ryoo, “Robust approach to repetitive controller design for uncertain feedback control systems,” IET Control Theory & App., vol. 7, pp. 431–439, 2013.
T.-Y. Doh and M. J. Chung, “Repetitive control design for linear systems with time-varying uncertainties,” IEE Proc. — Control Theory & App., vol. 150, pp. 427–432, 2003.
T.-Y. Doh, J. R. Ryoo, and M. J. Chung, “Design of a repetitive controller: an application to the track-following servo system of optical disk drives,” IEE Proc. — Control Theory & App., vol. 153, pp. 323–330, 2006.
P. Lucibello, “Repetitive control of positive real systems via delayed feedback is Lyapunov asymptotically stable,” IEEE Trans. Autom. Control, vol. 52, no. 9, pp. 1748–1751, 2007.
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 & App., vol. 3, no. 9, pp. 1283–1292, 2009.
L. Zhou, J. She, and S. Zhou, “Robust ℌ∞ control of an observer-based repetitive-control system,” J. the Franklin Institute, vol. 335, pp. 4952–4969, 2018.
J. L. Schiff, The Laplace Transform: Theory and Applications, Springer-Verlag, Berlin, 1999.
K. Zhou, J. C. Doyle, and K. Glover, Robust and Optimal Control, Prentice-Hall, 1996.
S. Xu, J. Lam, and C. Yang, “ℌ∞ and positive-real control for linear neutral delay system,” IEEE Trans. Autom. Control, vol. 46, no. 8, pp. 1321–1326, 2001.
M. S. Mahmoud, Robust Control and Filtering for Time-Delay System, Dekker, 2000.
S. Boyd, L. E. Ghaoui, E. Feron, V. Balakrishnan, Linear Matrix Inequalities in System and Control Theory, SIAM, 1994.
R. Rabah, G. M. Sklyar, and A. V. Rezounenko, “Stability analyis of neutral type systems in Hilbert space,” J. Differential Equations, vol. 214, no. 2, pp. 391–428, 2005.
J. Hale, Theory of Functional Differential Equations, Springer-Verlag, New York, 1977.
G. Balas, R. Chiang, A. Packard, and M. Safonov, Robust Control Toolbox, The MathWorks, Inc., 2019.
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Recommended by Associate Editor Le Van Hien under the direction of Editor PooGyeon Park.
This research was supported by the research fund of Hanbat National University in 2017.
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Doh, TY., Ryoo, J.R. Design of Repetitive Control Systems Using a Delayed Control Input and a State Error. Int. J. Control Autom. Syst. 18, 3242–3246 (2020). https://doi.org/10.1007/s12555-019-0947-y
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DOI: https://doi.org/10.1007/s12555-019-0947-y