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Model and controller reduction applied to structural control using passivity theory
Author(s) -
Gildin E.,
Antoulas A. C.,
Sorensen D.,
Bishop R. H.
Publication year - 2009
Publication title -
structural control and health monitoring
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.587
H-Index - 62
eISSN - 1545-2263
pISSN - 1545-2255
DOI - 10.1002/stc.257
Subject(s) - passivity , reduction (mathematics) , model order reduction , controller (irrigation) , control theory (sociology) , krylov subspace , benchmark (surveying) , stability (learning theory) , projection (relational algebra) , modal , computer science , subspace topology , dimensionality reduction , mathematical optimization , mathematics , control (management) , engineering , algorithm , iterative method , artificial intelligence , agronomy , chemistry , geometry , geodesy , machine learning , geography , polymer chemistry , electrical engineering , biology
In this paper, model and controller reduction problems for the large‐scale control of building models are analyzed. First, the model reduction problem is posed in a projection framework, and some techniques are shown, such as modal reduction, balanced truncation, and moment matching by Krylov subspace, to obtain reduced‐order models. Based on those techniques, reduced‐order controllers are obtained from the large‐scale building models. However, there is the lack of closed‐loop stability guarantees using the above methods. In order to overcome this issue, it is proposed to use the so‐called passivity preserving model reduction, where one performs reduction based on the spectral zeros of the system and passive controller design. It is shown from the results of some simulations applied to the second generation of benchmark building control problem that the proposed algorithm indeed guarantees closed‐loop stability and offers good performance. Copyright © 2008 John Wiley & Sons, Ltd.