Abstract
Many signals in engineering are periodic, or at least they can be well approximated by a periodic signal over a large time interval. This is true, for example, for most signals associated with engines, electrical motors and generators, converters, or machines performing a task over and over again. Thus, it is a natural control problem to try to track a periodic signal with the output of a plant, or (what is almost the same), to try to reject a periodic disturbance acting on a control system. We examine this problem in Sections 1 and 3 of this paper (Section 2 is for background). In Section 4 we shall indicate a way of generalizing these ideas to cope with superpositions of periodic signals of arbitrary periods.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Preview
Unable to display preview. Download preview PDF.
References
B.A. Francis and W.M. Wonham. The internal model principle for linear multivariable regulators. Appl. Math. Optim. 2 (1975), 170–194.
T. Georgiou and M.C. Smith. w-Stability of feedback systems. Systems & Control Letters 13 (1989), 271–277.
T. Georgiou and M.C. Smith. Graphs, causality and stabilizability: linear, shift-invariant systems on L 2[0,∞). Mathematics of Control, Signals, and Systems 6 (1993), 195–223.
S. Hara, Y. Yamamoto, T. Omata and M. Nakano. Repetitive control system: A new type servo system for periodic exogenous signals. IEEE Trans. Aut. Contr. 33 (1988), 659–668.
M. Green and D.J.N. Limebeer. Linear Robust Control. Englewood Cliffs, NJ: Prentice-Hall, 1995.
T. Inoue, M. Nakano and S. Iwai. High accuracy control of servomechanism for repeated contouring. Proc. of the 10th Annual Symp. on Incremental Motion Control, Systems and Devices 1981. 258–292.
T. Inoue, M. Nakano, T. Kubo, S. Matsumoto and H. Baba. High accuracy control of a proton synchrotron magnet power supply. Proc. of the IFAC 8th World Congress 1981. 216–221.
H. Logemann. Stabilization and regulation of infinite-dimensional systems using coprime factorizations. Analysis and Optimization of Systems: State and Frequency Domain Approaches for Infinite-Dimensional Systems. (R.F. Curtain, A. Bensoussan and J.L. Lions, Eds.). Vol. 185. LNCIS. Berlin: Springer-Verlag, 1993.
H. Logemann, R. Rebarber and G. Weiss. Conditions for robustness and nonrobustness of the stability of feedback systems with respect to small delays in the feedback loop. SIAM J. Control and Optim. 34 (1996), 572–600.
K.L. Moore. Iterative Learning Control for Deterministic Systems. Adv. in Ind. Control. London: Springer-Verlag, 1993.
R. Rebarber. Conditions for the equivalence of internal and external stability for distributed parameter systems. IEEE Trans. Aut. Contr. 38 (1993), 994–998.
E. Rogers and D.H. Owens. Stability Analysis for Linear Repetitive Processes. Vol. 175. LNCIS. Berlin: Springer-Verlag, 1992.
D. Salamon. Realization theory in Hilbert space. Mathematical Systems Theory 21 (1989), 147–164.
G. Weiss. Transfer functions of regular linear systems. Part I: characterizations of regularity. Trans. Amer. Math. Society 342 (1994), 827–854.
G. Weiss. Regular linear systems with feedback. Mathematics of Control, Signals, and Systems 7 (1994), 23–57.
G. Weiss and R.F. Curtain. Dynamic stabilization of regular linear systems. To appear IEEE Trans. Automatic Control.
Y. Yamamoto. Learning control and related problems in infinite-dimensional systems. Essays on Control: Perspectives in the Theory and its Applications. (H.L. Trentelman and J.C. Willems, Eds.). Boston: Birkhäuser, 1993. 191–222.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1997 Springer Science+Business Media New York
About this paper
Cite this paper
Weiss, G. (1997). Repetitive Control Systems: Old and New Ideas. In: Byrnes, C.I., Datta, B.N., Martin, C.F., Gilliam, D.S. (eds) Systems and Control in the Twenty-First Century. Systems & Control: Foundations & Applications, vol 22. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4612-4120-1_21
Download citation
DOI: https://doi.org/10.1007/978-1-4612-4120-1_21
Publisher Name: Birkhäuser, Boston, MA
Print ISBN: 978-1-4612-8662-2
Online ISBN: 978-1-4612-4120-1
eBook Packages: Springer Book Archive