Continuous System Simulation and Control

ERNESTO KOFMAN; FRANÇOIS CELLIER; GUSTAVO MIGONI

Discrete Event Simulation and Modeling: Theory and Applications

CRC Press

Lugar: Boca Raton, Florida; Año: 2010;

Continuous systems are usually represented by sets of ordinary and  algebraic differential equations that must be discretized in order  to be simulated. Conventional numerical integration methods perform  the discretization based on time slicing principles, and the  simulation models result of discrete time type. However, there is a  new family of numerical integration methods that replaces time  slicing by state quantization, and the resulting discretized systems  are of discrete event type within the DEVS formalism framework.  These new algorithms are called Quantized State System (QSS) methods  and exhibit many advantages: unconditional stability, efficient  discontinuity handling, intrinsic error control, sparsity  exploitation, explicit stiffness treatment, geometric properties,  etc. The QSS methods also provide a formal way to approximate  continuous systems by DEVS models, allowing to simulate hybrid  systems under a unified formalism on standard DEVS simulation  software tools.  This chapter introduces the QSS methods, discusses their theoretical  properties, practical advantages, drawbacks, and shows some examples  that illustrate their main features. The chapter concludes showing  the application of the QSS methods to the emulation of continuous  feedback controllers. This application provides a systematic  methodology for the synthesis of DEVS-based digital controllers for  continuous systems.