Relaxed Nonlinear Vector Fitting for Calculation of Rational Approximation of Systems Defined by Input/Output Responses in the Frequency Domain

The so-called non-linear vector fitting (NL-VF) technique was recently introduced as a new method for rational function approximation in the frequency domain (FD). While the classical vector fitting (VF) fits a rational function to a given frequency response, NL-VF calculates the rational function approximation based on a set of input/output responses that characterize the system. The frequency responses can come from time domain (TD) responses that are transformed to the FD using the Numerical Laplace Transform (NLT), or it can be the set of frequency responses that result when characterizing non-linear systems in the FD, at a given operating point. This paper extends NL-VF to its relaxed version by replacing the scaling function used for pole relocation by a more relaxed constraint, following a similar approach as in the relaxed VF method. This paper shows that the relaxed NL-VF exhibits an improvement in both convergence and accuracy, as compared to its original formulation. The advantages are demonstrated for three examples of rational function approximation, 1) FD transfer function of a transmission line propagation function, 2) FD input/output variables of a system which includes a photovoltaic generator and a nonlinear reactor, and 3) TD measurements of an automatic voltage regulator response.