Course detail

Theory of Dynamic Systems

FEKT-MPA-TDSAcad. year: 2022/2023

System approach for solving technical problems. Cybernetics and system science .I/O and state space approach to the analysis and design of dynamic systems. Continuous,discrete, linear, non linear,time constant and time variable systems. Controlability and observability. State observers. Deterministic and stochastic systems.

Language of instruction

English

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Ing. Petr Blaha, Ph.D.

Department

Department of Control and Instrumentation (UAMT)

Offered to foreign students

Of all faculties

Learning outcomes of the course unit

After passing the course, the student is able to:
- demonstrate and explain the difference between state space and input output description of the system
- explain the concept of causality, realizability, reachability, controlability, observability and reconstructability of the system
- identify and approximate basic types of dynamic systems and discretize the system
- apply the principles of block algebra and Mason’s gain rule for the evaluation of the system’s transfer function
- design the state observer and state feedback

Prerequisites

The subject knowledge on the Bachelor´s degree level is requested.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods depend on the type of course unit as specified in the article 7 of BUT Rules for Studies and Examinations. Materials for lectures and exercises are available for students from web pages of the course. Students have to write a single project/assignment during the course.

Assesment methods and criteria linked to learning outcomes

70% final written exam
30% from activities in numerical examples

Course curriculum

1. Dynamic systems - definition and subdivision.
2. Different types of system description: input-output, transfer function, frequency response, polynomials.
3. Modeling of dynamical systems in MATLAB Simulink.
4. Stability of linear and nonlinear systems.
5. State space description, state equations, their solution.
6. Model realization: serial, parallel, direct programming. Canonical forms.
7. Controllability, reachability, observability, reconstruct-ability of systems.
8. Block algebra. Masons’s gain rule for transfer function computation.
9. State feedback controller.
10. State observers.
11. Methods of continuous time system discretization.
12. Stability of interval polynomials.
13. Reserve, review.

Work placements

Not applicable.

Aims

The aim of the course is to introduce general system theory and its application to dynamic systems and systemic approach towards control tasks solution.

Specification of controlled education, way of implementation and compensation for absences

The content and forms of instruction in the evaluated course are specified by a regulation issued by the lecturer responsible for the course and updated for every academic year.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Ogata, K.: Modern Control Engineering, Fifth edition. Prentice Hall, 2010, ISBN 10: 0-13-615673-8. (EN)

Recommended reading

Not applicable.

eLearning

eLearning: currently opened course

Classification of course in study plans

  • Programme MPA-CAN Master's, any year of study, winter semester, elective
  • Programme MPAD-CAN Master's, any year of study, winter semester, elective
  • Programme MPA-SAP Master's, any year of study, winter semester, elective

Type of course unit

 

Lecture

39 hours, compulsory

Teacher / Lecturer

doc. Ing. Petr Blaha, Ph.D.

Syllabus

1. Dynamic systems - definition and subdivision.
2. Different types of system description: input-output, transfer function, frequency response, polynomials.
3. Modeling of dynamical systems in MATLAB Simulink.
4. Stability of linear and nonlinear systems.
5. State space description, state equations, their solution.
6. Model realization: serial, parallel, direct programming. Canonical forms.
7. Controllability, reachability, observability, reconstruct-ability of systems.
8. Block algebra. Masons’s gain rule for transfer function computation.
9. State feedback controller.
10. State observers.
11. Methods of continuous time system discretization.
12. Stability of interval polynomials.
13. Reserve, review.

Fundamentals seminar

14 hours, compulsory

Teacher / Lecturer

Ing. Matúš Kozovský, Ph.D.

Syllabus

1. Different descriptions of dynamic systems, Conversion between various descriptions.
2.Designing of the input function generators.
3. Controlability, reachability, observability and reconstructability of system.
4. Reachability index, minimal realization of the system
5. Conversion of block diagram to signal flow graph. Utilization of Mason’s gain rule.
6. Determination of observability index for the system with two inputs.
7. Summary, work on the project.

Exercise in computer lab

12 hours, compulsory

Teacher / Lecturer

Ing. Matúš Kozovský, Ph.D.

Syllabus

1. Introduction to MATLAB. Work with vectors and matrixes. Creating custom functions. Basic script programming.
2. Introduction to MATLAB Simulink. Definition of systems using Control toolbox commands. System analysis (impulse, step, freq, freqz, pzmap, ....)
3. Modelling of the mechanical systems in Matlab Simulink. Nyquist stability criterion.
4. Canonical forms of state space description implementation in MATLAB Simulink.
5. State feedback design, implementation of state controller in Simulink environment.
6. Design and implementation of state observers. Project work.

eLearning

eLearning: currently opened course