Balancing Approach to Minimal Realization and Model Reduction of Stable Nonlinear Systems

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• 作者：Juergen Hahn and Thomas F. Edgar
• 刊名：Industrial & Engineering Chemistry Research
• 出版年：2002
• 出版时间：May 1, 2002
• 年：2002
• 卷：41
• 期：9
• 页码：2204 - 2212
• 全文大小：78K
• 年卷期：v.41,no.9(May 1, 2002)
• ISSN：1520-5045

文摘

This paper presents a computational approach to determine a reduced order model of a nonlinearsystem. The procedure is closely related to balanced model reduction and introduces the conceptof covariance matrices for local controllability and observability analysis of a nonlinear system.These covariance matrices are an extension of gramians of a linear system and are used todetermine unobservable and uncontrollable parts of the system for a given operating region.Additionally, an algorithm is introduced that eliminates these nonminimal parts of the modeland can further reduce the model, i.e., the number of state variables. This minimal realization/model reduction procedure is simple to implement and can be applied locally to any stable systemwithout making any assumptions about observability and controllability. Examples are presentedto demonstrate the procedure. When the algorithm is applied to linear systems, it reduces towell-known techniques for minimal realization and balanced model reduction.