Modelling of Simplified Dynamical Systems

ISBN-13: 9783642628566 / Angielski / Miękka / 2012 / 171 str.

Edward Layer

Opis

This book is addressed to scientists, engineers and students 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.

Spis treści

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.

Blurb

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.