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Modeling, Simulation and Optimization of Complex Processes pp 383–392Cite as

Stability of Higher Order Repetitive Control

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Summary

Repetitive control (RC) and iterative learning control (ILC) apply to repeating situations, and iteratively adjust the command to a feedback control system aiming to converge on zero tracking error. Thus, these forms of control solve an inverse problem, but instead of doing so numerically with a mathematical model, it is done iteratively with the real world hardware. ILC restarts the system before each run, while repetitive control applies to executing a periodic command or eliminating the effects of a periodic disturbance. The ILC literature has many contributions developing what are called higher order ILC laws, where the control action in the current repetition is a function of the errors observed in multiple previous runs. It is the purpose of this paper to develop the higher order repetitive control, and in particular to develop the relevant theory of stability. It is proved that the simple frequency response based sufficient condition for convergence in first order RC, is also a sufficient condition for convergence in higher order RC, and it is independent of the order chosen. Furthermore, this condition is very close to being a necessary condition for stability. The result is that the typical design process in the frequency domain for first order RC can now be directly extended to the design of higher order RC as well.

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Author information

Authors and Affiliations

  1. Columbia University, New York, NY, 10027, USA

    Sang June Oh & Richard W. Longman

Authors
  1. Sang June Oh
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  2. Richard W. Longman
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Editor information

Editors and Affiliations

  1. Interdisziplinäres Zentrum für Wissenschaftliches Rechnen (IWR), Universität Heidelberg, Im Neuenheimer Feld 368, 69120, Heidelberg, Germany

    Hans Georg Bock  & Ekaterina Kostina  & 

  2. Institute of Mathematics, Vietnamese Academy of Science and Technology (VAST), 18 Hoang Quoc Viet Road, 10307, Hanoi, Vietnam

    Hoang Xuan Phu

  3. Institut für Angewandte Mathematik, Universität Heidelberg, Im Neuenheimer Feld 294, 68120, Heidelberg, Germany

    Rolf Rannacher

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© 2005 Springer-Verlag Berlin Heidelberg

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Oh, S.J., Longman, R.W. (2005). Stability of Higher Order Repetitive Control. In: Bock, H.G., Phu, H.X., Kostina, E., Rannacher, R. (eds) Modeling, Simulation and Optimization of Complex Processes. Springer, Berlin, Heidelberg. https://doi.org/10.1007/3-540-27170-8_29

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