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Modelling of Simplified Dynamical Systems - Edward Layer

Modelling of Simplified Dynamical Systems

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Published: 12th September 2002
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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.

Introductionp. 1
Mathematical Modelsp. 3
Differential equaionsp. 3
Transfer functionp. 7
State equationsp. 8
Models of standardsp. 16
Examplesp. 22
System Parametersp. 37
Overshootp. 37
Damping factorp. 38
Half-timep. 39
Equivalent time delayp. 39
Time constantsp. 40
Resonance angular frequencyp. 41
Model Synthesisp. 43
Algebraic polynomialsp. 43
The least squares methodp. 45
Cubic splinesp. 47
Square of frequency response methodp. 51
The Maclaurin series methodp. 53
Multi-inertial modelsp. 56
Weighted means methodp. 61
Smoothing functionsp. 66
Kalman filterp. 68
Examplesp. 70
Simplification of Modelsp. 84
The least-squares approximationp. 85
The Rao-Lamba methodp. 92
Criterion of consistency of model response derivatives at the originp. 93
Reduction of state matrix order with selected eigenvalues retainedp. 94
Simpliicaion of models using the Routh table coefficientsp. 99
Simplification of models by means of Routh table and Schwarz matrixp. 100
Simplificaion of models by comparison of characteristic equation coefficientsp. 106
Examplesp. 107
Maximum Mapping Errorsp. 124
Input signals with one constraintp. 125
Input signals with two constraintsp. 134
Examplesp. 138
Signals Maximising the Integral-Square-Error in the Process of Models Optimisationp. 143
Opimisation of models in the case of the high value of primary mapping error. Optimisaion of Butterworth filtersp. 144
Examplesp. 145
Opimisation of models in the case of the small value of primary mapping errorp. 159
Examplesp. 159
Referencesp. 165
Indexp. 169
Table of Contents provided by Publisher. All Rights Reserved.

ISBN: 9783540437628
ISBN-10: 3540437622
Audience: Professional
Format: Hardcover
Language: English
Number Of Pages: 171
Published: 12th September 2002
Publisher: Springer-Verlag Berlin and Heidelberg Gmbh & Co. Kg
Country of Publication: DE
Dimensions (cm): 23.5 x 15.5  x 1.27
Weight (kg): 0.95