CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2024/2025

# Mathematical Simulation Models

Code Completion Credits Range Language
2371097 Z,ZK 6 3P+2C Czech
Garant předmětu:
Tomáš Vyhlídal
Lecturer:
Tomáš Vyhlídal
Tutor:
Jaroslav Bušek, Goran Simeunovič, Pavel Skopec, Tomáš Vyhlídal
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. A particular emphasis is given on the skills in describing the dynamic processes in the state space approach in both linear and non-linear systems.

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

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

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

Syllabus of tutorials:
Study Objective:

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, 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, 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

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.: Matematicke a simulační modely 1 a 2, ČVUT Praha, 2004.

Note:
Time-table for winter semester 2024/2025:
 06:00–08:0008:00–10:0010:00–12:0012:00–14:0014:00–16:0016:00–18:0018:00–20:0020:00–22:0022:00–24:00 roomT4:C1-308Vyhlídal T.09:00–11:30(lecture parallel1)DejviceLaboratoř 12110.3 - 308roomT4:C1-308Bušek J.12:30–14:00(parallel nr.1)DejviceLaboratoř 12110.3 - 308
Time-table for summer semester 2024/2025:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2024-09-10
Aktualizace výše uvedených informací naleznete na adrese https://bilakniha.cvut.cz/en/predmet3053806.html