CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2023/2024

# Mathematical and Simulation Modelling II

The course is not on the list Without time-table
Code Completion Credits Range Language
2371081 Z,ZK 5 2P+2C Czech
Garant předmětu:
Lecturer:
Tutor:
Supervisor:
Department of Instrumentation and Control Engineering
Synopsis:

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.

Requirements:
Syllabus of lectures:

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

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

Syllabus of tutorials:
Study Objective:

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.

Study materials:

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

Note:
Further information:
No time-table has been prepared for this course
The course is a part of the following study plans:
Data valid to 2024-08-09
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