Interpolating model identification for SISO linear parameter-varying systems

• Published in: Mechanical systems and signal processing Vol. 23; no. 8; pp. 2395 - 2417
• Main Authors: De Caigny, Jan, Camino, Juan F., Swevers, Jan
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01-11-2009; Elsevier
• Subjects: Applied sciences; Computer science; control theory; systems; Control system synthesis; Control theory. Systems; Exact sciences and technology; Fundamental areas of phenomenology (including applications); Linear parameter-varying systems; Measurement and testing methods; Modelling and identification; Physics; Solid mechanics; State-space model interpolation; Structural and continuum mechanics; System identification; Linear parameter-varying systems; State-space model interpolation; System identification; Linear interpolation; Least squares problem; Control synthesis; Linear parameter varying system; State space; Scheduling; Non linear programming; State space method; Linear control; Modeling; Operating conditions; Time varying system; Linear time invariant system; Model matching; Well conditioned; SISO system; Electromechanical system
• ISSN: 0888-3270; 1096-1216
• DOI: 10.1016/j.ymssp.2009.04.007

This paper presents a new method to estimate linear parameter-varying (LPV) state-space models for single-input single-output systems whose dynamics depend on one or more time-varying parameters, called scheduling parameters. The method is based on the interpolation of linear time-invariant models that are identified for fixed operating conditions of the system, that is, for constant values of the scheduling parameters. The proposed method can account for multiple scheduling parameters and yields either a polynomial or an affine LPV model that is numerically well-conditioned and therefore suitable for LPV control synthesis. The underlying interpolation technique is formulated as a nonlinear least-squares optimization problem that can be solved efficiently by standard solvers. The new interpolation method is applied to an electromechanical system that depends on two scheduling parameters. The numerical results are compared to existing techniques in the literature, demonstrating the potential and advantages of the proposed method.