Chattering avoidance in hybrid simulation models: a modular approach based on the HyFlow formalism

The possibility that a hybrid simulation model can change its state infinitely often in a finite time interval impacts negatively, or even disables, the ability to simulate some hybrid systems. This behavior also known as chattering occurs in models that can switch continuously between different modes of operation. In this paper we provide two solutions to different kinds of chattering behavior. One solution is based on model discretization and on sliding mode control, enabling the elimination of chattering in linear systems with relay components. Another approach is based on dynamic topology models. This solution helps eliminate chattering in models that must be prevented to change their operation mode. We provide examples for these approaches and we show that chattering is avoided enabling an efficient simulation of hybrid systems. Solutions are described in HyFlow, a formalism supporting the definition and the interoperability of modular hybrid components.