A Singular Perturbation Approach for Modeling Differential-Algebraic Systems

Dynamic systems described by an implicit mixed set of Differential and Algebraic Equations (DAEs) are often encountered in control system modeling and analysis due to inherent constraints in the system. A key difficulty in control and simulation of DAE systems is that they are not expressed in an explicit state space representation. This paper describes a general approach based on singular perturbation analysis for adding fast dynamics to a system of DAEs so that they can be expressed in an explicit state space form. Conditions for asymptotic convergence and approximation methods are investigated. The approach is illustrated for a model of a two-phase flow heat exchanger.