Mathematical and Simulation Modelling II. (E371081)

Katedra: | ústav přístrojové a řídící techniky (12110) | ||

Zkratka: | Schválen: | 13.01.2011 | |

Platí do: | ?? | Rozsah: | 2P+2C |

Semestr: | * | Kredity: | 5 |

Zakončení: | Z,ZK | Jazyk výuky: | EN |

Anotace

The course provides a basic knowledge on formulation and computer implementation of dynamical system models. It starts from theoretical issues of Laplace and Z transform in their application to describing the continuous and discrete linear systems respectively including the systems with distributed parameters. In the second part of the course particular emphasis is given on the skills in describing the dynamic processes in the state space approach in both linear and non-linear systems. A special part of the course is devoted to the system parameter optimization methods.

Osnova

A) Laplace and Z transform

1. The basic properties of the Laplace transforms

2. L transform solution of Cauchy problem in differential equations, inverse L transform

3. Convolution integral transform and transfer function models

4. Fourier transform, Bode diagram of the linear model

5. The basic properties of the Z transform

6. Sampled data linear system, discrete transfer function

7. Z transform solution of the difference equation, inverse Z transform

8. Conformal mapping of analytic function, argument increment rule

9. Discrete approximation of the continuous system by means of L and Z transform

B) State space model of dynamic system

10. The state space notion, state variables, state trajectory

11. Introduction methods of state variables, state equations

12. Steady state of the system, static characteristics, types of singular points

13. Characteristic function of the linear dynamic system, stability notion

14. Delay relations in the system model

C) Computer model

15. Methods of numerical solution of the state space equation

16. Sampling time assessment, stability of the numerical method

17. Explicit and implicit methods, predictor-corrector

18. Typical model nonlinearities, saturation

19. Simulation in Matlab Simulink

20. Optimization of model parameters, optimality criteria, basic methods of extremum search

1. The basic properties of the Laplace transforms

2. L transform solution of Cauchy problem in differential equations, inverse L transform

3. Convolution integral transform and transfer function models

4. Fourier transform, Bode diagram of the linear model

5. The basic properties of the Z transform

6. Sampled data linear system, discrete transfer function

7. Z transform solution of the difference equation, inverse Z transform

8. Conformal mapping of analytic function, argument increment rule

9. Discrete approximation of the continuous system by means of L and Z transform

B) State space model of dynamic system

10. The state space notion, state variables, state trajectory

11. Introduction methods of state variables, state equations

12. Steady state of the system, static characteristics, types of singular points

13. Characteristic function of the linear dynamic system, stability notion

14. Delay relations in the system model

C) Computer model

15. Methods of numerical solution of the state space equation

16. Sampling time assessment, stability of the numerical method

17. Explicit and implicit methods, predictor-corrector

18. Typical model nonlinearities, saturation

19. Simulation in Matlab Simulink

20. Optimization of model parameters, optimality criteria, basic methods of extremum search

Literatura

Ogata K.: System Dynamics. Prentice-Hall, Inc. Englewood Cliffs,, N. Jersey, 1978., Ogata K.: Modern Control Engineering. Prentice-Hall, Inc. Englewood Cliffs,, N. Jersey, 1990., Zítek P.: Mathematical and Simulation Models 1 and 2, CTU Praha, 2001 and 2004, In Czech