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CZECH TECHNICAL UNIVERSITY IN PRAGUE
STUDY PLANS
2019/2020

Mathematical Simulation Models

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Code Completion Credits Range Language
E371097 Z,ZK 6 3P+2C English
Lecturer:
Tomáš Vyhlídal (guarantor), Goran Simeunovič
Tutor:
Tomáš Vyhlídal (guarantor), Jaroslav Bušek, Goran Simeunovič
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 2019/2020:
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
Mon
roomT4:C1-308
Vyhlídal T.
09:00–11:30
(lecture parallel1)
Dejvice
Laboratoř 12110.3 - 308
roomT4:A1-207
Bušek J.
12:30–14:00
(lecture parallel1
parallel nr.1)

Dejvice
Poč. učebna 207
Tue
Fri
Thu
Fri
Time-table for summer semester 2019/2020:
Time-table is not available yet
The course is a part of the following study plans:
Data valid to 2020-08-12
For updated information see http://bilakniha.cvut.cz/en/predmet3527206.html