Towards Procedures for Systematically Deriving Hybrid Models of Complex Systems
In many cases, complex system behaviors are naturally modeled as nonlinear differential equations. However, these equations are often hard to analyze because of “stiffness” in their numerical behavior and the difficulty in generating and interpreting higher order phenomena. Engineers often reduce model complexity by transforming the nonlinear systems to piecewise linear models about operating points. Each operating point corresponds to a mode of operation, and a discrete event switching structure is added to implement the mode transitions during behavior generation. This paper presents a methodology for systematically deriving mixed continuous and discrete, i.e., hybrid models from a nonlinear ODE system model. A complete switching specification and state vector update function is derived by combining piecewise linearization with singular perturbation approaches and transient analysis. The model derivation procedure is then cast into the phase space transition ontology that we developed in earlier work. This provides a systematic mechanism for characterizing discrete transition models that result from model simplification techniques. Overall, this is a first step towards automated model reduction and simplification of complex high order nonlinear systems.
KeywordsHybrid Model Control Valve Mode Transition Switching Condition Hydraulic Actuator
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- 1.Rajeev Alur, Costas Courcoubetis, Thomas A. Henzinger, and Pei-Hsin Ho. Hybrid automata: An algorithmic approach to the specification and verification of hybrid systems. In R.L. Grossman, A. Nerode, A.P. Ravn, and H. Rischel, editors, Lecture Notes in Computer Science, volume 736, pages 209–229. Springer-Verlag, 1993.Google Scholar
- 2.James Demmel and Bo Kågström. Stably computing the Kronecker structure and reducing subspaces of singular pencils A − λB for uncertain data. In J. Cullum and R. A. Willoughby, editors, Large Scale Eigenvalue Problems. Elsevier Science Publishers B.V. (North-Holland), 1986.Google Scholar
- 4.Pieter J. Mosterman. State Space Projection onto Linear DAE Manifolds Using Conservation Principles. Technical Report #R262-98, Institute of Robotics and System Dynamics, DLR Oberpfaffenhofen, P.O. Box 1116, D-82230 Wessling, Germany, 1998.Google Scholar
- 5.Pieter J. Mosterman and Gautam Biswas. Building Hybrid Observers for Complex Dynamic Systems using Model Abstractions. In Frits W. Vaandrager and Jan H. van Schuppen, editors, Hybrid Systems: Computation and Control, pages 178–192, 1999. Lecture Notes in Computer Science; Vol. 1569.CrossRefGoogle Scholar
- 6.Pieter J. Mosterman, Feng Zhao, and Gautam Biswas. An Ontology for Transitions in Physical Dynamic Systems. In AAAI98, July 1998.Google Scholar
- 8.Andreas Varga. On modal techniques for model reduction. Technical Report TR R136-93, Institute of Robotics and System Dynamics, DLR Oberpfaffenhofen, P.O. Box 1116, D-82230 Wessling, Germany, 1993.Google Scholar