Modelling of Simplified Dynamical Systems

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 Routhtable 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.