Improved Pole Placement and Compaction of MIMO Vector Fitting Applied to System Identification

Abstract

In this work we address the modeling of multi-port subsystems with unknown inner dynamics by utilizing vector fitting to identify state-space models for performing eigenvalue-based analysis. Vector fitting is used to characterize frequency responses obtained from frequency domain analysis, for example, from Fourier transformation of time domain data. The intended use is for interconnection with other models in system stability analysis, where the use of compact state-space models is desirable. Typically, vector fitting of a multiple-input/multiple-output (mimo) system leads to a large state-space model where each column (input) is fitted by a common pole set using a predefined model order. An alternative vector fitting process based on a pole collapsing scheme is proposed which can find suitable poles for a more compact state-space model. Additionally, a method for simpler, more automated order determination is introduced. The use of the presented approach for obtaining a fully compacted model (without pole repetitions) is examined and compared against a previously proposed method based on singular value decomposition. Application to an example system representing a 2-level power electronic converter demonstrates that the proposed method gives a model with improved accuracy of eigenvalue identification and model compaction, while retaining the essential information in terms of system dynamic behavior.