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.

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


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


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

ŠOLC, F.; VÁCLAVEK, P.; VAVŘÍN, P. Řízení a regulace II. Brno: VUT, 2004. s. 1 ( s.) (CS)
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)
Khalil, H.K.: Nonlinear Systems. Prentice Hall, 1996. (EN)
Gelb, A., Velde, W.: Multiple-input Describing Functions and Nonlinear System Design. McGraw-Hill, 1968. (EN)

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

Language of instruction


Work placements

Not applicable.

Course curriculum

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.


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.

Classification of course in study plans

  • Programme EEKR-B Bachelor's

    branch B-AMT , 3. year of study, winter semester, 6 credits, compulsory

  • Programme EEKR-CZV lifelong learning

    branch ET-CZV , 1. year of study, winter semester, 6 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer

Fundamentals seminar

10 hours, compulsory

Teacher / Lecturer

Exercise in computer lab

10 hours, compulsory

Teacher / Lecturer

Laboratory exercise

6 hours, compulsory

Teacher / Lecturer