Interpolated Modeling of LPV Systems Based on Observability and Controllability

Abstract This paper presents a State-space Model Interpolation of Local Estimates (SMILE) technique to compute linear parameter-varying (LPV) models for parameter-dependent systems through the interpolation of a set of linear time-invariant (LTI) state-space models obtained for fixed operating conditions. Since the state-space representation of LTI models is not unique, a suitable coherent representation needs to be computed for the local LTI models such that they can be interpolated. In this work, this coherent representation is computed based on observability and controllability properties. It is shown that compared with the state of the art in the literature, this new method has three strong appeals: it is general, fully automatic and results in numerically well-conditioned LPV models. An example demonstrates the potential of the new SMILE technique.

[1]  Javad Mohammadpour,et al.  Control of linear parameter varying systems with applications , 2012 .

[2]  Marco Lovera,et al.  Guest Editorial Special Issue on Applied LPV Modeling and Identification , 2011 .

[3]  Jan Swevers,et al.  Identification of Interpolating Affine LPV Models for Mechatronic Systems with one Varying Parameter , 2008, Eur. J. Control.

[4]  Jan Swevers,et al.  Interpolating model identification for SISO linear parameter-varying systems , 2009 .

[5]  Jeremy Hoyt Yung.  Gain scheduling for geometrically nonlinear flexible space structures , 2001 .

[6]  L. Silverman,et al.  Controllability and Observability in Time-Variable Linear Systems , 1967 .

[7]  Okko H. Bosgra,et al.  LPV control for a wafer stage: beyond the theoretical solution , 2005 .

[8]  Jan Swevers,et al.  Interpolation-Based Modeling of MIMO LPV Systems , 2011, IEEE Transactions on Control Systems Technology.

[9]  R. van de Molengraft,et al.  Experimental modelling and LPV control of a motion system , 2003, Proceedings of the 2003 American Control Conference, 2003..

[10]  C. Paige.  Properties of numerical algorithms related to computing controllability , 1981 .

[11]  Stephen P. Boyd,et al.  Convex Optimization , 2004, Algorithms and Theory of Computation Handbook.

[12]  M. Lovera,et al.  Identification for gain-scheduling: a balanced subspace approach , 2007, 2007 American Control Conference.

[13]  Roland Toth,et al.  Modeling and Identification of Linear Parameter-Varying Systems , 2010 .