Course detail

Control Theory 2

FEKT-BRR2Acad. year: 2015/2016

Analysis and synthesis of advanced control systems, especially nonlinear, is discussed in this course. Basic methods for nonlinear systems stability analysis, state trajectory behaviour evaluation and nonlinear control design are presented. Methods for robust control design and system parameters estimation are also described.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

prof. Ing. Pavel Václavek, Ph.D.

Department

Department of Control and Instrumentation (UAMT)

Learning outcomes of the course unit

Student can:
- analyse nonlinear systems behaviour
- design nonlinear control systems
- analyse stability of nonlinear dynamical systems
- design control algorithms based on linearisation techniques
- design control structures based on relay control and sliding mode control

Prerequisites

The subject knowledge on the secondary school level is required. Knowledge of linear systems control (BRR1) and systems modeling (BMOD) is assumed.

Co-requisites

Not applicable.

Planned learning activities and teaching methods

Teaching methods include lectures, exercises and computer laboratories. Knowledge is verified using tests at exercises. Students have to write three assignments during the course.

Assesment methods and criteria linked to learning outcomes

70 points written exam
30 points projects and tests done on seminars
Conditions for awarding the course-unit credit:
1. Active participation in exercises
2. Minimum of 10 points awarded for tests at exercises

Course curriculum

Introduction.
Nonlinear systems description, basic nonlinearities, linearization.
Nonlinear systems state trajectories, equilibrium points, state trajectory of the first and second order systems.
Phase trajectory, time computing using phase trajectory, limit cykle existence determination using index theorems.
Describing function method, harmonic balance method.
Nonlinear systems stability.
Nonlinear systems stability analysis using Lyapunov method.
Popovov's stability criterion, instability theorems. Nonlinear systems control using linear controllers, wind-up.
Nonlinear systems control - gain scheduling, exact feedback linearization.
Relay control systems, switched structure systems, time optimal relay control. Nonlinear systems solution existence.
Sliding mode control.
Robust control.
Identification of controlled plants parameters.

Work placements

Not applicable.

Aims

Linear system control knowledge improvement. Learning of basic methods of nonlinear systems analysis and synthesis. Nonlinear systems control design, linearization, exact linearization, robust control.

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

ŠOLC, F.; VÁCLAVEK, P.; VAVŘÍN, P. Řízení a regulace II. Brno: VUT, 2004. s. 1 ( s.) (CS)

Recommended reading

Kotek, Kubík,:Teorie automatického řízení II. (CS)
Razím, M., Štecha, J.: Nelineární systémy, ČVUT 1997 (CS)
Slotine, J., Weiping, L.: Applied Nonlinear Control. Pearson Education, 1990. (EN)

Classification of course in study plans

  • Programme EECC Bc. Bachelor's

    branch B-AMT , 3 year of study, winter semester, compulsory

  • Programme EEKR-CZV lifelong learning

    branch EE-FLE , 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

prof. Ing. Pavel Václavek, Ph.D.

Syllabus

Introduction.
Nonlinear systems description, basic nonlinearities, linearization.
Nonlinear systems state trajectories, equilibrium points, state trajectory of the first and second order systems.
Phase trajectory, time computing using phase trajectory, limit cykle existence determination using index theorems.
Describing function method, harmonic balance method.
Nonlinear systems stability.
Nonlinear systems stability analysis using Lyapunov method.
Popovov's stability criterion, instability theorems. Nonlinear systems control using linear controllers, wind-up.
Nonlinear systems control - gain scheduling, exact feedback linearization.
Relay control systems, switched structure systems, time optimal relay control. Nonlinear systems solution existence.
Sliding mode control.
Robust control.
Identification of controlled plants parameters.

Fundamentals seminar

10 hod., compulsory

Teacher / Lecturer

Ing. Libor Veselý, Ph.D.

Syllabus

Excercise in previous knowledge.
Linearization, equilibrium points.
Harmonic balance method
Nonlinear systems stability analysis.
Exact feedback linearization.

Exercise in computer lab

10 hod., compulsory

Teacher / Lecturer

Ing. Lukáš Otava, Ph.D.
Ing. Miloslav Richter, Ph.D.

Syllabus

Discrete time controller design.
Phase portrait contruction and its verification using simulation.
Equilibrium points and limit cycles stability.
Sliding mode control design and its testing on simulation examples.
Controlled plants parameters estimation in Matlab environment.

Laboratory exercise

6 hod., compulsory

Teacher / Lecturer

prof. Ing. Pavel Václavek, Ph.D.

Syllabus

Sliding mode control design for the plant with uncertainties.
Gain scheduling controlled design.
Linear controller design for nonlinear plant control using exact feedback linearization.