Course details

Control Theory 2

BPC-RR2 FEKT BPC-RR2 Acad. year 2023/2024 Summer semester 6 credits

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




Time span

  • 26 hrs lectures
  • 13 hrs exercises
  • 13 hrs pc labs




Learning objectives

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

Prerequisite knowledge and skills

The subject knowledge on the secondary school level is required. Knowledge of linear systems control (BPC-RR1) and systems modeling (BPC-MOD) is assumed.

Study literature

  • Slotine, J., Weiping, L.: Applied Nonlinear Control. Pearson Education, 1990.
  • Khalil, H.K.: Nonlinear Systems. Prentice Hall, 2001.
  • Gelb, A., Velde, W.: Multiple-input Describing Functions and Nonlinear System Design. McGraw-Hill, 1968.

Syllabus of lectures

1 Nonlinear systems description, basic nonlinearities, linearization.
2 Nonlinear systems state trajectories, equilibrium points.
3 State trajectory of the first and second order systems.
4 Phase trajectory, time computing using phase trajectory, limit cycle existence determination using index theorems.
5 Describing function method, harmonic balance method.
6 Nonlinear systems stability.
7 Nonlinear systems stability analysis using Lyapunov method.
8 Popovov's stability criterion, instability theorems. Nonlinear systems control using linear controllers, wind-up.
9 Nonlinear systems control - gain scheduling, exact feedback linearization.
10 Relay control systems, switched structure systems, time optimal relay control. Nonlinear systems solution existence.
11 Sliding mode control.
12 Identification of controlled plants parameters.
13 Summary.

Syllabus of numerical exercises

1 State trajectories, isoclines method, linearization.
2 Describing functions, harmonic balance method.
3 Lyapunov stability.
4 Popov stability criteria. Non-linear systems control – gain scheduling, feedback linearization.
5 Relay controllers.
6 Sliding mode control
7 Summary

Syllabus of computer exercises

1 State equations, discrete controllers
2 Non-linear systems state trajectories, limit cycles, equilibrium states
3 Harmonic balance method, measurement of parameters for Ziegler-Nichols method using relay feedback experiment
4 Wind-up, exercise on BLDC motor
5 Linear control of non-linear systems, gain scheduling, feedback linearization
6 Sliding mode control, relay approximation

Progress assessment

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
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.


Mon comp.lab even week T12/SD 2.105 13:0014:5022 3BIT xx Richter
Mon comp.lab odd week T12/SD 2.105 13:0014:5022 3BIT xx Richter
Mon comp.lab even week T12/SD 2.105 15:0016:5022 3BIT xx Richter
Mon comp.lab odd week T12/SD 2.105 15:0016:5022 3BIT xx Richter
Tue exam 2024-05-07 Aula profesora Braunera T12/SF 2.162 09:0012:00 První termín
Tue exercise even week T12/SD 1.48 09:0010:5022 3BIT xx Friml, Kozubík
Tue exercise even week T12/SD 1.48 12:0013:5022 3BIT xx Friml, Kozubík
Tue exercise even week T12/SD 1.48 14:0015:5024 3BIT xx Friml, Kozubík
Tue exercise even week T12/SD 1.48 16:0017:5022 3BIT xx Friml, Kozubík
Wed exam 2024-05-29 Aula profesora Braunera 09:0012:00 Třetí termín
Wed lecture lectures T12/SF 2.162 13:0014:5090 3BIT xx Václavek
Thu exam 2024-05-16 Aula profesora Braunera 09:0012:00 Druhý termín

Course inclusion in study plans

  • Programme BIT, 3rd year of study, Elective
  • Programme IT-BC-3, field BIT, 3rd year of study, Elective
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