Numerically robust frequency domain identification of multivariable systems

Frequency domain methods are known to suffer from a poor numerical conditioning when the frequency span and/or the model order become large (more than 2 decades and an order more than 20). This numerical problem ruins both the modeling performance and the model order selection capability. This paper presents a modeling approach that leads to (almost) optimal numerical conditioning of the normal equations (condition number = 1). The key idea is to expand the numerator and denominator of the transfer function model in a vector orthogonal basis. The theory is illustrated on a real measurement example.

[1]  Joe Brewer,et al.  Kronecker products and matrix calculus in system theory , 1978 .

[2]  J. Schoukens,et al.  Identification of linear systems in the presence of nonlinear distortions. A frequency domain approach. I. Non-parametric identification , 1995, Proceedings of 1995 34th IEEE Conference on Decision and Control.

[3]  Thomas Kailath,et al.  Linear Systems , 1980 .

[4]  Gene H. Golub,et al.  Matrix computations (3rd ed.) , 1996 .

[5]  P. Guillaume,et al.  Application of a Fast-Stabilizing Frequency Domain Parameter Estimation Method , 2001 .

[6]  J. Schoukens,et al.  Parametric and nonparametric identification of linear systems in the presence of nonlinear distortions-a frequency domain approach , 1998, IEEE Trans. Autom. Control..

[7]  Adhemar Bultheel,et al.  A parallel algorithm for discrete least squares rational approximation , 1992 .

[8]  C. Sanathanan,et al.  Transfer function synthesis as a ratio of two complex polynomials , 1963 .

[9]  Yves Rolain,et al.  Best conditioned parametric identification of transfer function models in the frequency domain , 1995, IEEE Trans. Autom. Control..

[10]  Yves Rolain,et al.  Analyses, development and applications of TLS algorithms in frequency domain system identification , 1997 .

[11]  Adhemar Bultheel,et al.  Discrete linearized least-squares rational approximation on the unit circle , 1993 .

[12]  J. Schoukens,et al.  Robust rational approximation for identification , 2001, Proceedings of the 40th IEEE Conference on Decision and Control (Cat. No.01CH37228).

[13]  Gene H. Golub,et al.  Matrix computations , 1983 .

[14]  Gerd Vandersteen,et al.  Frequency-domain system identification using non-parametric noise models estimated from a small number of data sets , 1997, Autom..