ISBN: 3540437622
TITLE: Modelling of Simplified Dynamical Systems
AUTHOR: Layer
TOC:

1. INTRODUCTION 1
2. MATHEMATICAL MODELS 3
2.1. Differential equations 3
2.2. Transfer function 7
2.3. State equations 8
2.4. Models of standards 16
2.5. Examples 22
3. SYSTEM PARAMETERS 37
3.1. Overshoot 37
3.2. Damping factor 38
3.3. Half-time 39
3.4. Equivalent time delay 39
3.5. Time constants 40
3.6. Resonance angular frequency 41
4. MODEL SYNTHESIS 43
4.1. Algebraic polynomials 43
4.2. The least squares method 45
4.3. Cubic splines 47
4.4. Square of frequency response method 51
4.5. The Maclaurin series method 53
4.6. Multi-inertial models 56
4.7. Weighted means method 61
4.8. Smoothing functions 66
4.9. Kalman filter 68
4.10. Examples 70
5. SIMPLIFICATION OF MODELS 84
5.1. The least-squares approximation 85
5.2. The Rao-Lamba method 92
5.3. Criterion of consistency of model response derivatives at the origin 93
5.4. Reduction of state matrix order with selected eigenvalues retained 94
5.5. Simplification of models using the Routh table coefficients 99
5.6. Simplification of models by means of Routh table and Schwarz matrix 100
5.7. Simplification of models by comparison of characteristic equation coefficients 106
5.8. Examples 107
6. MAXIMUM MAPPING ERRORS 124
6.1. Input signals with one constraint 125
6.2. Input signals with two constraints 134
6.3. Examples 138
7. SIGNALS MAXIMISING THE INTEGRAL-SQUARE-ERROR IN THE PROCESS OF MODELS OPTIMISATION 143
7.1. Optimisation of models in the case of the high value of primary mapping error. Optimisation of Butterworth filters 144
7.2. Examples 145
7.3. Optimisation of models in the case of the small value of primary mapping error 159
7.4. Examples 159
REFERENCES 165
INDEX 169
END
