Cascade structural model approximation of identified state space models

General black-box system identification techniques such as subspace system identification and FIR/ARX least squares system identification are commonly used to identify multi-input multi-output models from experimental data. However, in many applications there are a priori given structural information. Here the focus is on linear dynamical systems with a cascade structure, and with one input signal and two output signals. Models of such systems are important in e.g. cascade control applications. It is possible to incorporate such a structure in a prediction error method, which, however, is based on rather advanced numerical non-convex optimization techniques to calculate the corresponding structured model estimate. We will instead study how to use model approximation techniques to approximate a general black-box estimate with a structured model. This will avoid the use of numerical optimization and works well with e.g. subspace system identification, which is a standard method in process industry where cascade systems are very common. The problems of cascade structural model approximation and model reduction are rather non-standard, and we will study several new methods. The basic idea is to first find a higher order but structured model approximation using standard Hâ\u88\u9e model matching techniques, and then in a second step use so-called structured balanced model reduction to find lower order structured approximation. Structured balanced model reduction is a rather new approach, with powerful model order selection tools and error bound results. The results of the corresponding two step model approximation approach seem promising, as illustrated by a simple numerical example.© 2008 IEEE. Personal use of this material is permitted. Permission from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertising or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works. QC 20110120