Mathematical and Simulation Modelling II.
Code  Completion  Credits  Range  Language 

E371081  Z,ZK  5  2P+2C  English 
 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 nonlinear 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, predictorcorrector
18. Typical model nonlinearities, saturation
19. Simulation in Matlab Simulink
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 nonlinear systems. A special part of the course is devoted to the system parameter optimization methods.
 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.: Mathematical and Simulation Models 1 and 2, CTU Praha, 2001 and 2004, In Czech
 Note:
 Further information:
 No timetable has been prepared for this course
 The course is a part of the following study plans: