Modelling of Simplified Dynamical Systems

By: Edward Layer

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Hardcover | 12 September 2002

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180 Pages

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22.86 x 15.88 x 1.27

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Problems involving synthesis of mathematical models of various physical systems, making use of these models in practice and verifying them qualitatively has - come an especially important area of research since more and more physical - periments are being replaced by computer simulations. Such simulations should make it possible to carry out a comprehensive analysis of the various properties of the system being modelled. Most importantly its dynamic properties can be - dressed in a situation where this would be difficult or even impossible to achieve through a direct physical experiment. To carry out a simulation of a real, phy- cally existing system it is necessary to have its mathematical description; the s- tem being described mathematically by equations, which include certain variables, their derivatives and integrals. If a single independent variable is sufficient in - der to describe the system, then derivatives and integrals with respect to only that variable will appear in the equations. Differentiation of the equation allows the integrals to be eliminated and produces an equation which includes derivatives with respect to only one independent variable i. e. an ordinary differential equation. In practice, most physical systems can be described with sufficient accuracy by linear differential equations with time invariant coefficients. Chapter 2 is devoted to the description of models by such equations, with time as the independent va- able.

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Non-Fiction Engineering & Technology Technology in General Engineering in General Mathematics Applied Mathematics Mathematical Modelling Mechanical Engineering & Materials Mechanical Engineering Science Physics Industrial Chemistry & Manufacturing Technologies

Reference, Information & Interdisciplinary Subjects Research & Information Information theory Cybernetics & Systems Theory

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Paperback

Published: 5th November 2012

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Introduction	p. 1
Mathematical Models	p. 3
Differential equaions	p. 3
Transfer function	p. 7
State equations	p. 8
Models of standards	p. 16
Examples	p. 22
System Parameters	p. 37
Overshoot	p. 37
Damping factor	p. 38
Half-time	p. 39
Equivalent time delay	p. 39
Time constants	p. 40
Resonance angular frequency	p. 41
Model Synthesis	p. 43
Algebraic polynomials	p. 43
The least squares method	p. 45
Cubic splines	p. 47
Square of frequency response method	p. 51
The Maclaurin series method	p. 53
Multi-inertial models	p. 56
Weighted means method	p. 61
Smoothing functions	p. 66
Kalman filter	p. 68
Examples	p. 70
Simplification of Models	p. 84
The least-squares approximation	p. 85
The Rao-Lamba method	p. 92
Criterion of consistency of model response derivatives at the origin	p. 93
Reduction of state matrix order with selected eigenvalues retained	p. 94
Simpliicaion of models using the Routh table coefficients	p. 99
Simplification of models by means of Routh table and Schwarz matrix	p. 100
Simplificaion of models by comparison of characteristic equation coefficients	p. 106
Examples	p. 107
Maximum Mapping Errors	p. 124
Input signals with one constraint	p. 125
Input signals with two constraints	p. 134
Examples	p. 138
Signals Maximising the Integral-Square-Error in the Process of Models Optimisation	p. 143
Opimisation of models in the case of the high value of primary mapping error. Optimisaion of Butterworth filters	p. 144
Examples	p. 145
Opimisation of models in the case of the small value of primary mapping error	p. 159
Examples	p. 159
References	p. 165
Index	p. 169
Table of Contents provided by Publisher. All Rights Reserved.

Modelling of Simplified Dynamical Systems

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