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Stability analysis of digital repetitive control systems under time-varying sampling period

Stability analysis of digital repetitive control systems under time-varying sampling period

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Repetitive control is an internal model principle-based technique for tracking periodic references and/or rejecting periodic disturbances. Digital repetitive controllers are usually designed assuming a fixed frequency for signals to be tracked/rejected, its main drawback being a dramatic performance decay when this frequency varies. A common approach to overcome this problem consists of an adaptive change of the sampling time according to the reference/disturbance period variation. Such a structural change may indeed compromise closed-loop stability. Nevertheless, no formal stability proofs are reported in the literature. This study addresses the stability analysis of a digital repetitive control system operating under time-varying sampling period. The procedure adapts the robust control approach introduced by Fujioka and Suh, which treats the time-varying parts of the system description as norm-bounded uncertainties, to the special features of digital repetitive control systems. This results in a conservatism reduction leading to an improvement in the obtained stability intervals. The proposed technique is also applicable to a more general class of systems incorporating a discrete-time dynamic controller. The article is completed with the application of the method to two standard examples in the repetitive control literature. Experimental results confirm the theoretical predictions.

References

    1. 1)
      • Hillerström, G., Walgama, K.: `Repetitive control theory and applications – a survey', Proc. 13th IFAC World Congress, 1996, D, p. 1–6.
    2. 2)
    3. 3)
    4. 4)
    5. 5)
      • Zhou, K., Wang, D., Xu, G.: `Repetitive controlled three-phase reversible PWM rectifier', Proc. American Control Conf., 2000, p. 125–129.
    6. 6)
    7. 7)
    8. 8)
    9. 9)
    10. 10)
    11. 11)
      • Costa-Castelló, R., Malo, S., Griñó, R.: `High performance repetitive control of an active filter under varying network frequency', Proc. 17th IFAC World Congress, 2008, p. 3344–3349.
    12. 12)
    13. 13)
      • G. Hillerström . (1994) On repetitive control.
    14. 14)
    15. 15)
    16. 16)
    17. 17)
    18. 18)
      • Naghshtabrizi, P., Hespanha, J.P., Teel, A.R.: `On the robust stability and stabilization of sampled-data systems: a hybrid system approach', Proc. 45th IEEE Conf. on Decision and Control, 2006, p. 4873–4878.
    19. 19)
      • Fujioka, H.: `Stability analysis for a class of networked-embedded control systems: a discrete-time approach', Proc. American Control Conf., 2008, p. 4997–5002.
    20. 20)
    21. 21)
    22. 22)
    23. 23)
      • Inoue, T., Nakano, M., Kubo, T., Matsumoto, S., Baba, H.: `High accuracy control of a proton synchroton magnet power supply', Proc. Eighth IFAC World Congress, 1981, p. 216–220.
    24. 24)
      • W.J. Rugh . (1996) Linear system theory.
    25. 25)
      • Ramos, G.A., Olm, J.M., Costa-Castelló, R.: `Non-uniform sampling in digital repetitive control systems: an LMI stability analysis', Technical Report n IOC-DT-P-2009-01, 2009, available at: http://hdl.handle.net/2117/2651.
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