An application of interpolating gain-scheduling control
System, Structure and Control, Volume # 3 | Part# 1
De Caigny, J.; Camino, J. F.; Paijmans, B.; Swevers, J.
Digital Object Identifier (DOI)
active noise control,time varying system,parametric variation,discrete-time
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.
 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.  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.  Apkarian, P., P. C. Pellanda and H. D. Tuan (2000). Mixed H
2/H ∞multi-channel linear parametervarying control in discrete time. Systems & Control Letters 41, 333-346.  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.  Donadon, L. V., D. A. Siviero, J. F. Camino and J. R. F. Arruda (2006). Comparing a filtered-X LMS and an H 2controller for the attenuation of the sound radiated by a panel. In: Proc. of the ISMA. Leuven. (cdrom).  Doyle, J. C. (1987). Guaranteed margins for LQG regulators. IEEE Trans. Automat. Contr. 23(4), 756- 757.  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.  Leith, D. J. and W. E. Leithead (2002). Survey of gain-scheduling analysis and design. Int. J. Control 73(11), 1001-1025.  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.  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).  Rugh, W. J. and J. S. Shamma (2000). Research on gain scheduling. Automatica 36(10), 1401-1425.  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.  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.