Multivariable frequency domain identification using IV-based linear regression

Identification of output error models from frequency domain data generally results in a non-convex optimization problem. A well-known method to approach the output error minimum by iterative linear regression steps was formulated by Sanathanan and Koerner. A disadvantage of this approach is that in general convergence of the iterations only implies optimality under restrictive conditions. In the literature, an alternative iterative linear regression procedure is available, which ensures optimality upon convergence, also in case of undermodeling. This algorithm is known for time-domain identification as the Simplified Refined Instrumental Variable method (SRIV), and was recently formulated for frequency domain identification of SISO output error models. Here we generalize this formulation to MIMO identification of models in matrix fraction description. The effectiveness of the approach is demonstrated by its application to estimation of a parametric model of the multivariable dynamics of a spindle with Active Magnetic Bearings.