Continuous System Simulation and Control
Abstract
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.
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Last modified: January 20, 2011 -- © François Cellier