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Authors
De Caigny, J.; Camino, J. F.; Paijmans, B.; Swevers, J.

Digital Object Identifier (DOI)
10.3182/20071017-3-BR-2923.00015

Page Numbers:
88-93

Index Terms
active noise control,time varying system,parametric variation,discrete-time

Abstract
This work investigates an application of interpolating gain-scheduling control for a structural acoustic problem. The dynamics of the system under consideration are highly sensitive to variation in the temperature. Therefore, linear time invariant H2 output feedback controllers are designed for different temperature conditions. Afterwards, these controllers are interpolated to provide a global discrete-time linear parametervarying controller. The closed-loop stability is a posteriori guaranteed using recent less conservative analyses that consider bounds on the rate of variation of the temperature.

References

[1] Amato, F., M. Mattei and A. Pironti (2005). Gain
    scheduled control for discrete-time systems depending
     on bounded rate parameters. Int. J. Robust
     Nonlinear Control 15, 473-494.
[2] Aouf, N., D. G. Bates, I. Postlethwaite and B. Boulet
    (2002). Scheduling schemes for an integrated
    flight and propulsion control system. Control Engineering
     Practice 10(1), 685-696.
[3] Apkarian, P., P. C. Pellanda and H. D. Tuan (2000).
    Mixed H2/H∞ multi-channel linear parametervarying
     control in discrete time. Systems & Control
     Letters 41, 333-346.
[4] Daafouz, J. and J. Bernussou (2001). Parameter dependent
     Lyapunov functions for discrete time
    systems with time varying parametric uncertainties.
     Systems & Control Letters 43(5), 355-359.
[5] Donadon, L. V., D. A. Siviero, J. F. Camino and
    J. R. F. Arruda (2006). Comparing a filtered-X
    LMS and an H2 controller for the attenuation of
    the sound radiated by a panel. In: Proc. of the
    ISMA. Leuven. (cdrom).
[6] Doyle, J. C. (1987). Guaranteed margins for LQG regulators.
     IEEE Trans. Automat. Contr. 23(4), 756-
    757.
[7] Haddad, W.M. and V. Kapila (1996). Robust stabilization
     for discrete-time systems with slowly time-varying
     uncertainty. J. Franklin Inst. 333(1), 71-
    84.
[8] Leith, D. J. and W. E. Leithead (2002). Survey of gain-scheduling
     analysis and design. Int. J. Control
    73(11), 1001-1025.
[9] Nichols, R. A., R. T. Reichert and W. J. Rugh (1993).
    Gain scheduling for H-infinity controllers: A
    flight control example. IEEE Trans. Contr. Syst.
    Technol. 1(2), 69-79.
[10] Paijmans, B., W. Symens, H. Van Brussel and J. Swevers
      (2006). Gain-scheduling control for mechatronic
      systems with position dependent dynamics.
      In: Proc. of the ISMA. Leuven. (cdrom).
[11] Rugh, W. J. and J. S. Shamma (2000). Research on
     gain scheduling. Automatica 36(10), 1401-1425.
[12] Wassink, M. G., M. V. de Wal, C. Scherer and
     O. Bosgra (2005). LPV control for a wafer stage:
     beyond the theoretical solution. Control Engineering
      Practice 13(2), 231-245.
[13] Xie, L., S. Shishkin and M. Fu (1997). Piecewise
     Lyapunov functions for robust stability of linear
     time-varying systems. Systems & Control Letters
     31(3), 165-171.