Interpolation-Based Modeling of MIMO LPV Systems

Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)This paper presents State-space Model Interpolation of Local Estimates (SMILE), a technique to estimate linear parameter-varying (LPV) state-space models for multiple-input multiple-output (MIMO) systems whose dynamics depends on multiple time-varying parameters, called scheduling parameters. The SMILE technique is based on the interpolation of linear time-invariant models estimated for constant values of the scheduling parameters. As the linear time-invariant models can be either continuous- or discrete-time, both continuous-and discrete-time LPV models can be obtained. The underlying interpolation technique is formulated as a linear least-squares problem that can be efficiently solved. The proposed technique yields homogeneous polynomial LPV models in the multi-simplex that are numerically well-conditioned and therefore suitable for LPV control synthesis. The potential of the SMILE technique is demonstrated by computing a continuous- time interpolating LPV model for an analytic mass-spring-damper system and a discrete-time interpolating LPV model for a mechatronic XY-motion system based on experimental data.1914663Research Foundation-Flanders (FWO-Vlaanderen) [G.0446.06]K. U. Leuven-BOF Center-of-Excellence Optimization in Engineering [EF/05/006]Belgian Program on Interuniversity Poles of Attraction IAP [VI/4 DYSCO]K. U. Leuven [GOA/10/11]Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Coordenação de Aperfeiçoamento de Pessoal de Nível Superior (CAPES)Fundação de Amparo à Pesquisa do Estado de São Paulo (FAPESP)Research Foundation-Flanders (FWO-Vlaanderen) [G.0446.06]K. U. Leuven-BOF Center-of-Excellence Optimization in Engineering [EF/05/006]Belgian Program on Interuniversity Poles of Attraction IAP [VI/4 DYSCO]K. U. Leuven [GOA/10/11]FAPESP [Proc. 09/03304-5