Course detail

Control Theory II

FSI-VA2Acad. year: 2014/2015

The first part of the course presents the state variable description of linear systems. The State differential equation. Relationship between state equations and differential equations. State equations of linear discrete dystems.
The second part of the course presents nonlinear control systems.
Phase plane method. Stability analysis of nonlinear nontrol nystems.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

prof. RNDr. Ing. Tomáš Březina, CSc.

Department

Institute of Automation and Computer Science (ÚAI)

Learning outcomes of the course unit

Analysis and design of nonlinear feedback control systems. Students will obtain the basic knowledge of automation, description and classification of nonlinear control systems, determination of their characteristics. Students will be able to solve problems of stability of control systems. They will obtain the knowledge of state-space representation of system.

Prerequisites

Completion of the course Control Theory I.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

In order to be awarded the course-unit credit students must prove 100% active participation in laboratory exercises and elaborate a paper on the presented themes. The exam is written and oral. In the written part a student compiles two main themes which were presented during the lectures and solves three examples. The oral part of the exam will contain discussion of tasks and possible supplementary questions.

Course curriculum

Not applicable.

Work placements

Not applicable.

Aims

The aim of the course is to formulate and establish basic conceptions of automatic control. State-space representation of dynamic system and analysis and design methods for nonlinear systems are presented.

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

Attendance and activity at the seminars are required. One absence can be compensated for by attending a seminar with another group in the same week, or by elaboration of substitute tasks. Longer absence can be compensated for by the elaboration of compensatory tasks assigned by the tutor.

Recommended optional programme components

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

Schwarzenbach,J.-Gill,F.K.:System Modelling and Control, Butterworth-Heinemann, Oxford 2002, ISBN 0 340 54379 5 (EN)
Dorf, R.C. and Bishop, R.H.: Modern Control Systems. Addison-Wesley, New York, 2010. (EN)
Ogata, K.: Modern Control Engineering. Prentice-Hall, New Jersey, 2009. (EN)

Recommended literature

Švarc, I., Matoušek, R., Šeda, M., Vítečková, M.: Automatizace-Automatické řízení, skriptum VUT FSI v Brně, CERM 2011. (CS)
Švarc,I.:Teorie automatického řízení, podpory FSI, www stránky 2003 (CS)
Donald E. Kirk: Optimal Control Theory: An Introduction. Dover Publications, 2004. ISBN-10: 0486434842. (EN)
Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. ISBN-10: 0486442780. (EN)

Classification of course in study plans

  • Programme N2301-2 Master's

    branch M-AIŘ , 1 year of study, summer semester, compulsory
    branch M-AIŘ , 1 year of study, summer semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. RNDr. Ing. Tomáš Březina, CSc.

Syllabus

1. Description of systems in state space, continuous and discrete form
2. Methods of identification of systems
3: Transformations of state model
4. State feedback control
5. Design of state controller with error compensation
6. Design of state controller with observer
7. Generalisation of design of state control, suitable structures for state space control
8. Description of nonlinear system, typical nonlinearities
9. Method of state plane
10. Linearisation method
11. Verification of linearised model
12. Introduction to robust control
13. Synthesis of regulation circuit with robust controller

Computer-assisted exercise

26 hod., compulsory

Teacher / Lecturer

Ing. Jiří Kovář, Ph.D.

Syllabus

Seminars in computer labs:
1. Solving MIMO and MISO LTI systems, state description
2. Identification of system from measured data (ARX, ARMAX)
3. Transformations of models of systems
4. Synthesis in state space, state controller
5. State controller with error compensation
6. State controller with observer
7. State controller with observer and error compensation
8. Modelling of system nonlinearities
9. Application of state plane
10. Linearisation of system models
11. Assessment of behaviour of linearised model
12. Synthesis of circuit with linearised system model
13. Course-unit credit awarding.