ISSN:
1531-5878
Keywords:
Rational approximation
;
rational fitting
;
state equations
;
transfer function
;
transmission lines
;
poles
;
residues
Source:
Springer Online Journal Archives 1860-2000
Topics:
Electrical Engineering, Measurement and Control Technology
Notes:
Abstract Often the information available for a state equation description in the form $$\dot x = Ax + Bu$$ ,y=Cx+Du is via a transfer function matrixH(s) obtained by measurements or complicated computations for frequenciess=jω. ThusH(s) is nonrational or rational of high order. Its state equation approximation means obtainingA, B, C, D in the rational transfer matrixC(sI-A) −1 B+D≈H(s). This approximation problem is difficult because it is nonlinear and often ill conditioned. This paper describes a methodology for fitting the columnsh(s) ofH(s) by two linear procedures. First θ(s)h(s) is fitted with a set of prescribed poles, where θ(s) is an unknown rational function with the same poles as θ(s)h(s). Then the poles forh(s) are calculated as the zeros of θ(s). With the poles known, the unknown residues and constant terms are calculated forh(s). If necessary, the procedure is repeated with the new poles taken as prescribed poles. The procedure is accurate and robust, and uses only standard numerical linear algebra computations. Illustrative examples for the application of vector fitting are given for a power transformer, a transmission line, and a network of transmission lines.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF01271288
Permalink
