Interpolation-Based Modeling of MIMO LPV Systems

• Published in: IEEE transactions on control systems technology Vol. 19; no. 1; pp. 46 - 63
• Main Authors: De Caigny, Jan, Camino, Juan F, Swevers, Jan
• Format: Journal Article
• Language: English
• Published: New York IEEE 01-01-2011; The Institute of Electrical and Electronics Engineers, Inc. (IEEE)
• Subjects: Analytical models; Dynamical systems; Dynamics; Estimates; Gain scheduling control; Interpolation; Least squares method; linear parameter- varying (LPV) systems; Mathematical analysis; Mathematical model; Mathematical models; MIMO; multiple-in multiple-out (MIMO) systems; Numerical models; Optimization; Polynomials; Scheduling; state-space model interpolation; system identification
• ISSN: 1063-6536; 1558-0865
• DOI: 10.1109/TCST.2010.2078509

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 -motion system based on experimental data.