Transfer Function Estimation in System Identification Toolbox via Vector Fitting

Abstract

This paper considers black-and grey-box continuous-time transfer function estimation from frequency response measurements. The first contribution is a bilinear mapping of the original problem from the imaginary axis onto the unit disk. This improves the numerics of the underlying Sanathanan-Koerner iterations and the more recent instrumental-variable iterations. Orthonormal rational basis functions on the unit disk are utilized. Each iteration step necessitates a minimal state-space realization with these basis functions. One such derivation is the second contribution. System identification with these basis functions yield zero-pole-gain models. The third contribution is an efficient method to express transfer function coefficient constraints in terms of the orthonormal rational basis functions. This allows for estimating transfer function models with arbitrary relative degrees (including improper models), along with other fixed and bounded parameter values. The algorithm is implemented in the tfest function in System Identification Toolbox (Release 2016b, for use with MATLAB) for frequency domain data. Two examples are presented to demonstrate the algorithm performance.

Digital synthesis of multistage etalons based upon unequal cavity lengths

“…During the processing, we take 15 FSRs of the given transmission profile and apply a digital bandpass filter with PR of -40dB to the central peak in Matlab. After generating the desired transmission profile, t d , we use tfest method in Matlab [8] to estimate its z-domain transfer function, T est (z). While estimating the transfer function we keep on increasing the number of poles until the maximum percentage fit and minimum mean square error(MSE) are achieved as shown in Fig.…”

“…2. Starting from a desired transmission response (T d ), we use discrete system identification via vector fitting [8] to estimate its transfer function T est (z) in the z-domain. The obtained T est (z) is generally a higher order function with typically more than 100 poles and zeros.…”

“…Our design process starts with a given transmission profile. We then estimate a z-domain transfer function from the given transmission response by using a vector fitting technique [8]. With our developed algorithm, we then map the estimated transfer function to an FPE system with a desired number of reflectors and given reflectivities.…”

Multilayer thermal object identification in frequency domain using IR thermography and vector fitting

“…F I G 4 Foster thermal network of a multilayer structure where τ fi = R fi C fi and R fi are the thermal time constants and thermal resistances of the Foster network. According to the VF method, 12,13,[22][23][24][25] if one knows the thermal impedance Z th (s), typically in the form of complex element vector, it is possible to introduce two additional functions σ(s) and p(s):…”

“…One of the latest approaches for dynamic system identification is vector fitting (VF), originally developed and used in electronic and electrical engineering. 12,13,[22][23][24][25] In this paper, a new approach is proposed using the VF algorithm for inverse heat conduction problem for multilayers thermal objects. From the temperature response of a thermal multilayer object obtained from an infrared (IR) measurement, the thermal parameters in each layer are approximated.…”