Some Guidelines for Stiff Model Implementation with the Use of Discontinuities

Abstract

This paper studies continuous transients that are abstracted into discontinuous state changes, governed by the principle of conservation of the extensive state variable, e.g., the displacement, which holdsacross model configuration changes. This principle alleviates the modeling task by built-in bookkeeping of the simulation engine. If there is restitution of energy because of dominant storage effects, further conceptual investment is required to implement instantaneous state changes. These instantaneous changes are represented at the energy level, i.e., in the bond graph, in such a manner that the tool can handle them directly, and, consequently, enforce conservation constraints. This means that the model designer does not explicitly reset integrator values in the information model part, e.g., by using the action property of a finite state machine. It is shown how transients because of dominant storage effects and because of dominant dissipative effects may interact very differently with other fast continuous transients and how a priori and a posteriori switching values can be used to compute the correct values in case of a sequence of instantaneous changes.