Modeling and Simulation of Event Systems

Many engineering problems are characterized by points of discontinuity in the first derivative of the phase variables. Such complicated discrete-continuous problems are called hybrid or event-continuous systems. The specification and computer analysis of the designated class of systems are illustrated by the common problem of a servo drive with the PWM controller. A mathematical model from the class of Cauchy problems with non-linear control logic is presented to resolve the task discussed. The designed model is performed in two stages: the mathematical model specification (modelling) and implementation (simulation). Two approaches to make a model specification are considered, the first one is the traditional structural technique, and the advanced method is based on the finite state machine paradigm. Structural and finite state software models are built in progressive simulation tools, such as Matlab, SimInTech, Ptolemy II and ISMA. Computer implementation of the software models of hybrid systems is performed using platform built-in libraries with numerical methods and algorithms for correct event detection. The results of computational experiments for transient processes of phase variables are qualitatively identical, that proves the adequacy of the models discussed. Quantitative errors, caused by using different integration techniques and event detection algorithms, are acceptable. The algorithm for asymptotic event detection, suggested by the Russian platform ISMA developers, is considered in detail. This technique demonstrates the best results by the one-sidedness criterion, which is explained by using the author’s algorithm for the integration step determining and the event function dynamics monitoring in the vicinity of the event limits.