Modelling of Simplified Dynamical Systems

2002
ISBN: 978-3-540-43762-8
Verlag: Springer Berlin Heidelberg

Buch, Englisch, 171 Seiten, Format (B × H): 160 mm x 241 mm, Gewicht: 442 g

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.

Zielgruppe

Research

Autoren/Hrsg.

Layer, Edward

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Numerische Mathematik
• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Angewandte Mathematik, Mathematische Modelle
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Naturwissenschaften Physik Physik Allgemein Theoretische Physik, Mathematische Physik, Computerphysik
• Technische Wissenschaften Technik Allgemein Computeranwendungen in der Technik
• Technische Wissenschaften Technik Allgemein Technik: Allgemeines
• Mathematik | Informatik EDV | Informatik Angewandte Informatik Computeranwendungen in Wissenschaft & Technologie
• Technische Wissenschaften Maschinenbau | Werkstoffkunde Technische Mechanik | Werkstoffkunde Statik, Dynamik, Kinetik, Kinematik
• Mathematik | Informatik EDV | Informatik Professionelle Anwendung Computer-Aided Design (CAD)

Inhaltsverzeichnis

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.