Mathematical Simulation Models

Course guarantor:

Tomáš Vyhlídal

Lecturer:

Tomáš Vyhlídal

Tutor:

Jaroslav Bušek, Pavel Skopec, Tomáš Vyhlídal, Can Yuksel

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
Mon
Tue	roomT4:C1-308 Vyhlídal T. 09:00–11:30 (lecture parallel1) Dejvice roomT4:C1-308 Yuksel C. 12:30–14:00 (lecture parallel1 parallel nr.1) Dejvice
Wed
Thu
Fri

Time-table for summer semester 2024/2025:

Time-table is not available yet

The course is a part of the following study plans: