Course detail

Control Theory II

FSI-VA2Acad. year: 2010/2011

The primary aim of the course is to deepen the knowledge of
control theory (State-Space Representation of Dynamic System. Analysis and Design Methods for Nonlinear Systems.)
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 Systems.
The second part of the course presents nonlinear control systems.
Phase plane method. Stability analysis of Nonlinear Control Systems.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

prof. RNDr. Ing. Miloš Šeda, Ph.D.

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

...Fundamental concepts of the methods used in the analysis and design of linear continuous feedback control systems. Essential principles of automatic control, logical control and PLC systems. The differential equations of control systems, transient response, frequency analysis, stability of systems.

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.

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

...Goals of the course: 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)

Recommended reading

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)

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

doc. Ing. Ivan Švarc, CSc.

Syllabus

Week 1: State-Space Representation of a Dynamic System. Introduction
Week 2: The State Variables of a Dynamic System
Week 3: The State Differential Equation. Signal-Flow Graph State Models
Week 4: The Transfer Function from the State Equation
Week 5: Relationship between State Equations and Differential Equations
Week 6: Solving the Time-Invariant State Equation
Week 7: State Equations of Linear Discrete Systems
Week 8: Analysis and Design Methods for Nonlinear Systems. Introduction
Week 9: Typical nonlinearities. The general approach to analysis
Week 10: Phase plane method
Week 11: Stability analysis of Nonlinear Control Systems
Week 12: Lyapunov Stability.
Week 13: Method of Linearization, Lyapunov Direct Method, Popov Criterion

Exercise

14 hod., compulsory

Teacher / Lecturer

Ing. Olga Davidová, Ph.D.

Syllabus

Seminars to the previous lecture:
--------------------------------------
Week 1: Introduction
Week 3: State-Space Representation of Dynamic System (The State Variables, The State Differential Equation,
..............................Signal-Flow Graph State Models)
Week 5: State-Space Representation of Dynamic System (The Transfer Function from the State Equation,
..............................Relationship between State Equations and Differential Equations)
Week 7: State-Space Representation of Dynamic System, Solving the Time-Invariant State Equation,
...............State Equations of Linear Discrete Systems)
Week 9: Nonlinear Systems (Analysis and Design Methods for Nonlinear Systems, Typical nonlinearities)
Week 11: Nonlinear Systems (Phase plane method, Stability analysis of Nonlinear Control Systems,
...............Lyapunov Stability)
Week 13: Nonlinear Systems (Method of Linearization, Lyapunov Direct Method, Popov Criterion)

Computer-assisted exercise

12 hod., compulsory

Teacher / Lecturer

Ing. Olga Davidová, Ph.D.

Syllabus

Seminars in the laboratory:
-------------------------------
Week 2: Analysis of State Variable Models Using Matlab
Week 4: Simulation of State Variable Equations for a Spacecraft
Week 6: Simulation of Linear Discrete Systems in the State-Space
Week 8: Simulation of Nonlinear Systems Using Matlab
Week 10: Simulation of Nonlinear Systems Using the Phase Plane)
Week 12: Simulation of Stability of Nonlinear Control Systems