Mathematical Simulation Models
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, 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 nonlinear 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, predictorcorrector
 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, predictorcorrector
 Study materials:

Ogata K.: System Dynamics. PrenticeHall, Inc. Englewood Cliffs,, N. Jersey, 1978.
Ogata K.: Modern Control Engineering. PrenticeHall, Inc. Englewood Cliffs, N. Jersey, 1990.
Zítek P.: Matematicke a simulační modely 1 a 2, ČVUT Praha, 2004.
 Note:
 Timetable for winter semester 2021/2022:

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 Fri Thu Fri  Timetable for summer semester 2021/2022:
 Timetable is not available yet
 The course is a part of the following study plans: