Numerical Simulation of Distributed Dynamic Systems using Hybrid Tools of Intelligent Computing

Numerical Simulation of Distributed Dynamic Systems using Hybrid Tools of Intelligent Computing

Fethi H. Bellamine (University of Waterloo, Canada & National Institute of Applied Sciences and Technologies, Tunisia) and Aymen Gdouda (National Institute of Applied Sciences and Technologies, Tunisia)
DOI: 10.4018/978-1-4666-3922-5.ch018

Abstract

Developing fast and accurate numerical simulation models for predicting, controlling, designing, and optimizing the behavior of distributed dynamic systems is of interest to many researchers in various fields of science and engineering. These systems are described by a set of differential equations with homogenous or mixed boundary constraints. Examples of such systems are found, for example, in many networked industrial systems. The purpose of the present work is to review techniques of hybrid soft computing along with generalized scaling analysis for the solution of a set of differential equations characterizing distributed dynamic systems. The authors also review reduction techniques. This paves the way to control synthesis of real-time robust realizable controllers.
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Background

An input-output process model is a set of equations to predict the future outputs of a system based on input data. The model should closely represent the relationships between inputs, outputs, and system variables to reduce the error caused by plant-model mismatch. Distributed dynamic systems are often represented by partial differential equations. For example, a large number of processes in different industries are distributed in nature, thus a significant number of modeling, control, and optimization applications arise for these types of systems. The state variables depend on at least two independent variables (i.e. time and space). For example, a tubular reactor may be modeled by a second order partial differential equation describing the change in axial position in the reactor and in time. Partial differential equations can be discretized so the system is represented by ordinary differential equations at separate discrete spatial points, which can then be used to synthesize a model-based control.

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