Interpolation-Based Modeling of MIMO LPV Systems

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 SM...

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Bibliographic Details
Published in:IEEE transactions on control systems technology 2011-01, Vol.19 (1), p.46-63
Main Authors: De Caigny, Jan, Camino, Juan F, Swevers, Jan
Format: Article
Language:English
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
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Summary: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.
ISSN:1063-6536
1558-0865
DOI:10.1109/TCST.2010.2078509