Identification Of Mimo Lpv Models Based On Interpolation

This paper presents SMILE (State-space Model Interpolation of Local Estimates), a new technique to estimate linear parameter varying state-space models for multiple-input multiple-output systems whose dynamics depends on a single varying parameter, called the scheduling parameter. The SMILE technique is based on the interpolation of linear time-invariant models that are valid for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The methodology yields affine LPV models that are numerically well-conditioned and therefore suitable for LPV control synthesis procedures. The underlying interpolation technique is formulated as a nonlinear least-squares optimization problem that can be efficiently solved by standard solvers. Application of the proposed methodology to a vibroacoustic setup, whose dynamics are highly sensitive to the ambient temperature, clearly demonstrates the potential of the SMILE technique. © 2008 by the Katholieke Universiteit Leuven Department of Mechanical Engineering All rights reserved.526312644Leith, D.J., Leithead, W.E., Survey of gain-scheduling analysis and design (2000) Int. J. Control, 73 (11), pp. 1001-1025Rugh, W.J., Shamma, J.S., Research on gain scheduling (2000) Automatica, 36 (10), pp. 1401-1425Shamma, J.S., Athans, M., Guaranteed properties of gain scheduled control for linear parametervarying plants (1991) Automatica, 27 (3), pp. 559-564De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D., Swevers, J., Gain scheduled H2- control of discrete-time polytopic time varying systems (2008) Congresso Brasileiro De Automática, , Juiz de Fora, Brazil, Sept, (To appear)De Caigny, J., Camino, J.F., Oliveira, R.C.L.F., Peres, P.L.D., Swevers, J., Gain scheduled H∞- control of discrete-time polytopic time varying systems (2008) Proc. 47th IEEE Conf. Decision Control, , Cancun, Mexico, Dec, (To appear)Nemani, M., Ravikanth, R., Bamieh, B.A., Identification of linear parametrically varying systems (1995) Proc. 34th IEEE Conf. Decision Control, pp. 2990-2995. , (New Orleans, LA, USA), DecLee, L.H., Poolla, K., Identification of linear parameter-varying systems using nonlinear programming (1999) J. Dyn. Syst. Meas. Contr, 121 (1), pp. 71-78Bamieh, B., Giarre, L., Identification of linear parameter varying models (2002) Int. J. Robust Nonlinear Control, 12 (9), pp. 841-853Verdult, V., Verhaegen, M., Kernel methods for subspace identification of multivariable LPV and bilinear systems (2005) Automatica, 41 (9), pp. 1557-1565Felici, F., van Wingerden, J.W., Verhaegen, M., Subspace identification of MIMO LPV systems using a periodic scheduling sequence (2007) Automatica, 43 (10), pp. 1684-1697Steinbuch, M., van de Molengraft, R., der Voort, A., Experimental modelling and LPV control of a motion system (2003) Proc. 2003 Amer. Control Conf, pp. 1374-1379. , (Denver, CO, USA)Wassink, M.G., de Wal, M.V., Scherer, C., Bosgra, O., LPV control for a wafer stage: Beyond the theoretical solution (2005) Control Engineering Practice, 13 (2), pp. 231-245Lovera, M., Mercere, G., Identification for gain-scheduling: A balanced subspace approach (2007) Proc. 2007 Amer. Control Conf, pp. 858-863. , (New York, NY, USA) JulyPaijmans, B., Symens, W., Brussel, H.V., Swevers, J., Experimental identification of affine LPV models for mechatronic systems with one varying parameter (2008) European Journal of Control, 14 (1)De Caigny, J., Camino, J.F., Swevers, J., Interpolating model identification for SISO linear parameter varying systems (2008) Mechanical Systems and Signal Processing, , SubmittedBalas, G.J., Linear, parameter-varying control and its application to a turbofan engine (2002) Int. J. Robust Nonlinear Control, 12, pp. 763-796Shamma, J.S., Athans, M., Gain scheduling: Potential hazards and possible remedies (1992) IEEE Control Syst. Mag, 12 (3), pp. 101-107Emami-Naeini, A., Van Dooren, P., Computation of zeros of linear multivariable systems (1982) Automatica, 18 (4), pp. 415-430Kailath, T., (1980) Linear Systems, , Upper Saddle River, NJ, USA: Prentice-HallMoré, J.J., (1978) The Levenberg-marquardt Algorithm: Implementation and Theory, pp. 105-116. , in Numerical Analysis (G. A. Watson, ed.), vol. 630 of Lecture Notes in Mathematics, Springer Berlin/HeidelbergDonadon, L.V., Siviero, D.A., Camino, J.F., Arruda, J.R.F., Comparing a filtered-X LMS and an H2 controller for the attenuation of the sound radiated by a panel (2006) Proc. ISMA, , (Leuven, Belgium), SeptLaub, A., Heath, M., Paige, C., Ward, R., Computation of system balancing transformations and other applications of simultaneous diagonalization algorithms (1987) IEEE Trans. Autom. Control, 32 (2), pp. 115-12