Identification of parametric models in the frequency-domain through the subspace framework under LMI constraints

Abstract

In this paper, an algorithm to identify parametric systems with an affine (or polynomial) parameter dependence through the subspace framework is proposed. It stands as an extension of the standard subspace-based algorithm which is well established in the linear time invariant (LTI) case. The formulation is close to the LTI identification scheme and simply involves frequency-domain data obtained at different operating points (the parameters are frozen during each experiment). The proposed algorithm allows to identify directly a parameter-dependent model instead of interpolating multiple local models as in traditional local approaches. Another contribution is that it is possible to impose the poles location through linear matrix inequalities (LMI) constraints, extending what has been done in the LTI case. This technique is applied to a numerical example and to real industrial frequency-domain data originating from an open-channel flow simulation for hydroelectricity production.

Keywords:

• LMIs
• identification
• linear systems
• subspace
• parametric model

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1 Here, parameters can be the geometrical coefficients of a system.

2 Affine forms are considered for simplicity, but polynomial extensions are straightforwardly derived.