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Analyzing Discontinuities in Physical System Models

Pieter J. Mosterman - Gautam Biswas
Center for Intelligent Systems
Box 1679, Sta B
Vanderbilt University
Nashville, Tennessee 37235
pjm, biswas@vuse.vanderbilt.edu

Abstract:

Physical systems are by nature continuous. Perceived discontinuities in system models are in reality nonlinear behaviors that are linearized to reduce computational complexity and prevent stiffness in system analysis and behavior generation. Discontinuities arise primarily from component parameter simplification and time-scale abstraction. Discontinuities in models are handled by introducing idealized switching elements controlled by finite state automata to bond graph models. In this paper, we make a systematic study of the nature and effects of discontinuities in physical system models, and present an algorithm that generates consistent and correct behaviors from hybrid models. A primary contribution of this paper is the characterization of discontinuous changes, and a systematic method for validating system models and behavior generation algorithms.

• 1 Introduction
• 2 The Hybrid Modeling Scheme
  • 2.1 Controlled Junctions
  • 2.2 Mode Switching in the Hybrid Model
• 3 Analyzing Model Discontinuities
  • 3.1 The Nature and Effects of Discontinuities
  • 3.2 Evolution of System Behavior: Invariance of State
  • 3.3 The Initial Value Problem
  • 3.4 Analyzing Correctness of System Models
    • Source-Buffer Dependency
    • Buffer-Buffer Dependency
• 4 Conclusions and Discussion
• References
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