Parametric system identification on logarithmic frequency response data

Gradient search methods that fit the parameters of a user-defined transfer function to experimental logarithmic frequency response data are presented. The methods match a model based on physically significant parameters, including natural frequencies of poles and zeros and damping ratios of complex poles and zeros. The algorithms construct and utilize their own analytical gradient descent functions, based on the desired model. One method attempts to fit both log magnitude and phase, while another identifies a minimum phase transfer function model from only log magnitude frequency response data. The log magnitude algorithm is shown to be superior to traditional methods using nonlogarithmic frequency response data, including those used in commercially available frequency response analyzers. The algorithms are shown to perform well, especially for systems with lightly-damped dynamics