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Modelling of Simplified Dynamical Systems

Autor Edward Layer
en Limba Engleză Hardback – 12 sep 2002
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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Specificații

ISBN-13: 9783540437628
ISBN-10: 3540437622
Pagini: 180
Ilustrații: VI, 171 p.
Dimensiuni: 155 x 235 x 15 mm
Greutate: 0.43 kg
Ediția:2002
Editura: Springer Berlin, Heidelberg
Colecția Springer
Locul publicării:Berlin, Heidelberg, Germany

Public țintă

Research

Cuprins

1. Introduction.- 2. Mathematical Models.- 2.1. Differential equations.- 2.2. Transfer function.- 2.3. State equations.- 2.4. Models of standards.- 2.5. Examples.- 3. System Parameters.- 3.1. Overshoot.- 3.2. Damping factor.- 3.3. Half-time.- 3.4. Equivalent time delay.- 3.5. Time constants.- 3.6. Resonance angular frequency.- 4. Model Synthesis.- 4.1. Algebraic polynomials.- 4.2. The least squares method.- 4.3. Cubic splines.- 4.4. Square of frequency response method.- 4.5. The Maclaurin series method.- 4.6. Multi-inertial models.- 4.7. Weighted means method.- 4.8. Smoothing functions.- 4.9. Kalman filter.- 4.10. Examples.- 5. Simplification Of Models.- 5.1. The least-squares approximation.- 5.2. The Rao-Lamba method.- 5.3. Criterion of consistency of model response derivatives at the origin.- 5.4. Reduction of state matrix order with selected eigenvalues retained.- 5.5. Simplification of models using the Routh table coefficients.- 5.6. Simplification of models by means of Routh table and Schwarz matrix.- 5.7. Simplification of models by comparison of characteristic equation coefficients.- 5.8. Examples.- 6. Maximum Mapping Errors.- 6.1. Input signals with one constraint.- 6.2. Input signals with two constraints.- 6.3. Examples.- 7. Signals Maximising The Integral-Square-Error In The Process Of Models Optimisation.- 7.1. Optimisation of models in the case of the high value of primary mapping error. Optimisation of Butterworth filters.- 7.2. Examples.- 7.3. Optimisation of models in the case of the small value of primary mapping error.- 7.4. Examples.- References.

Textul de pe ultima copertă

This book is addressed to scientists, engineers and student of engineering departments, who make use of modelling and computer simulation. Since more and more physical experiments are being replaced by computer simulations the use of mathematical models of various engineering systems has become an especially important area of research. The book is devoted to selected problems of various engineering domains, such as control, electrical engineering or electrical metrology. They are based on different mathematical fields such as matrix theory, differential equations, function approximation with applications in dynamic modelling, methods of simplifying high-order models determining mapping errors of simplified models, their optimization and the synthesis of suitable input signals. The book is easy to read and understand because all the needed mathematical transformations and formula are derived and explained by means of the examples enclosed.

Caracteristici

Dynamic Modelling for Engineers Simplification and Synthesis of Dynamic Models for Practical Use with a lot of Examples Includes supplementary material: sn.pub/extras