Multivariable State-Space Identification in the Delta and Shift Operators: Algorithms and Experimental Results

This paper develops algorithms for multivariable state-space identification which can be used to estimate models in any operator of interest i.e., delta-rule, shift, Laplace s, etc. The approach is based on the State-Space from Frequency Data (SSFD) algorithm which was designed specifically to eliminate distortions from windowing effects. An important aspect of the approach is the use of overparametrization. A theoretical result is proved which demonstrates that the extra dynamics introduced from overparametrizing in the shift operator are stable, while the extra dynamics introduced from overparametrizing in the Laplace s and delta operators are generically unstable. This leads to certain modifications of the Laplace and delta operators to ensure stability under overparametrization. The usefulness of the identification algorithm is demonstrated on data taken from a 4-input/3-output flexible structure experiment, resulting in an identified state-space model with 100 states accurate over a 100 Hertz bandwidth.