Implicit Modeling and Simulation of Discontinuities in Physical System Models

Abstract

The design of continuous models of physical systems is often most convenient, less error prone, and intuitive with declarative noncausal constraints that allow an implicit formulation. Discontinuous changes in continuous variables, however, are in general still modeled by explicit reinitialization constructs. This paper shows that it is beneficial to model discontinuous changes implicitly as well by changing sets of algebraic constraints. It also shows that the computation of explicit changes can be automated based on deriving the Kronecker canonical form. An approach that is numerically more stable is presented for index 1 systems based on deriving a pseudo Kronecker canonical form.