Zero-Crossing Location and Detection Algorithms for Hybrid System Simulation

Computational models of embedded control systems often combine continuous-time with discrete-event behavior, mathematically representing hybrid dynamic systems. An essential element of numerical simulation of a hybrid dynamic system is the generation of discrete events from continuous variables that exceed thresholds. In particular, the occurrence of such an event has to be detected and the point in time where the threshold is first exceeded has to be located. This paper presents a number of problems that are encountered in event detection and location when using existing techniques. Solution strategies that balance efficiency and robustness are presented to address: (i) repeated detection of a zero-crossing event at consecutive time steps, (ii) masked zero-crossing events because of multiple zero-crossing functions, and (iii) chattering and Zeno behavior.