Multivariable least squares frequency domain identification using polynomial matrix fraction descriptions

In this paper an approach is presented to estimate a linear multivariable model on the basis of (noisy) frequency domain data via a curve fitting procedure. The multivariable model is parametrized in either a left or a right polynomial matrix fraction description and the parameters are computed by using a two-norm minimization of a multivariable output error. Additionally, input-output or element-wise based multivariable frequency weightings can be specified to tune the curve fitting error in a flexible way. The procedure is demonstrated on experimental data obtained from a 3 input 3 output wafer stepper system.