Sliding Mode Model Semantics and Simulation for Hybrid Systems

Abstract

We describe model semantics and develop a simulation algorithm for characterizing a class of dynamic physical systems operating in the so-called sliding regimes. Complex continuous system behavior combines effects that occur at multiple temporal and spatial scales. Behavior generation is simplified by creating system models that employ time scale and parameter abstraction techniques. The resultant hybrid systems possess discrete and continuous behaviors, which manifest as piecewise continuous behaviors interspersed with discontinuous changes between the continuous operating modes. Mode transitions are induced by internal state changes and external control signals. Sometimes hybrid systems exhibit chattering behaviors at the discontinuous transition boundaries. This presents computational challenges to conventional numerical simulation methods. We develop an efficient, adaptive algorithm for simulating this class of systems, based on a careful analysis of the model semantics at the discontinuous boundaries. Simulation results show that the algorithm is more efficient and accurate than conventional integration methods for sliding-mode systems.