Frequency domain identification for undergraduates

A method to synthesize a transfer function from experimentally obtained gain and phase data is presented. The least squares technique discussed minimizes the error between the inverse transfer function and the inverse of the experimental frequency response data. The relevant formulas are derived in a straightforward manner so that undergraduate students can follow the development. The inverse formulation appears to give a better fit to the data than the previous approaches. This is most likely due to the fact that the technique biases the error with the numerator rather than the denominator of the derived transfer function. There is, however, no guarantee that a minimum phase transfer function will result from this technique. The user of this technique must preselect the numerator and denominator orders. The formulation assumes that there are no zeros at the origin. A modification to the basic scheme is presented for this case