352-0553/02 – Nonlinear Control (NŘ)

Gurantor departmentDepartment of Control Systems and InstrumentationCredits5
Subject guarantordoc. Ing. Renata Wagnerová, Ph.D.Subject version guarantordoc. Ing. Renata Wagnerová, Ph.D.
Study levelundergraduate or graduateRequirementCompulsory
Study languageCzech
Year of introduction2020/2021Year of cancellation
Intended for the facultiesFSIntended for study typesFollow-up Master
Instruction secured by
LoginNameTuitorTeacher giving lectures
CEL0034 Ing. Pavel Čelovský
WAG52 doc. Ing. Renata Wagnerová, Ph.D.
Extent of instruction for forms of study
Form of studyWay of compl.Extent
Full-time Credit and Examination 3+2
Part-time Credit and Examination 10+4

Subject aims expressed by acquired skills and competences

The main objective of the subject “Nonlinear Control” is acquainting students with the basic and the advanced methods which are used in the theory of the nonlinear automatic control. These methods are e.g.: the describing function method and its use for the plant identification, the Popov and circle stability criterion, stability checking by the first and second Lyapunov method. Furthermore the fuzzy control and the method of aggregation of the state variables. are considered. Attention is devoted to extremal control systems too.

Teaching methods



The subject “Nonlinear Control” belongs among theoretical subjects which form the graduate profile of the student in master study program in the field of automatic control. Its objective is acquainting students with the advanced control methods of nonlinear control.

Compulsory literature:

VÍTEČKOVÁ, Miluše a Antonín VÍTEČEK, 2019. Nelineární systémy [online]. Ostrava: VŠB-TU Ostrava [cit. 2020-04-20]. ISBN 978-80-248-4302-5. Dostupné z: http://books.fs.vsb.cz/NelSys/NelSys.pdf. VÍTEČKOVÁ, Miluše a Antonín VÍTEČEK, 2020. Nelineární systémy. Fuzzy řízení [online]. Ostrava: VŠB-TU Ostrava. ISBN 978-80-248-4414-5. Dostupné z: http://books.fs.vsb.cz/NelSysFuzzy/Viteckova-Vitecek-Nelinearni-systemy-Fuzzy-rizeni.pdf. JURA, Pavel, 2003. Základy fuzzy logiky pro řízení a modelování. Brno: Vysoké učení technické v Brně, Nakladatelství VUTIUM. ISBN 80-214-2261-0. ZÍTEK, Pavel a Antonín VÍTEČEK, 1999. Návrh řízení podsystémů se zpožděními a nelinearitami. Praha: Vydavatelství ČVUT. ISBN 80-010-1939-X. KHALIL, Hassan K. Nonlinear systems. 3rd ed. Upper Saddle River: Prentice Hall, c2002. ISBN 0-13-067389-7. SASTRY, Shankar. Nonlinear systems: analysis, stability, and control. New York: Springer, c1999. Interdisciplinary applied mathematics. Systems and control, v. 10. ISBN 0-387-98513-1. ARIMOTO, Suguru. Control theory of non-linear mechanical systems: a passivity-based and circuit-theoretic approach. Oxford: Clarendon Press, 1996. Oxford engineering science series, 49. ISBN 0-19-856291-8. VEČEŘA, Leo a Renata WAGNEROVÁ, 2005. Návrh robustních algoritmů řízení technologických procesů. Elektronické učební texty [online]. Ostrava: VŠB-TU Ostrava [cit. 2020-04-20]. Dostupné z: http://books.fs.vsb.cz/Agregace/index.html

Recommended literature:

FRANKLIN, Gene F., J. David POWELL a Abbas EMAMI-NAEINI. Feedback control of dynamic systems. 6th ed., international ed. Upper Saddle River: Pearson, c2010. ISBN 978-0-13-500150-9. VÍTEČKOVÁ, Miluše a Antonín VÍTEČEK, 2011. Vybrané metody seřizování regulátorů [online]. Ostrava: Vysoká škola báňská - Technická univerzita [cit. 2018-01-04]. ISBN 978-80-248-2503-8. Dostupné z: http://books.fs.vsb.cz/ZRMS/vybrane-metody-serizovani-regulatoru.pdf

Way of continuous check of knowledge in the course of semester

Credit 35 points (minimum 20 points) Students have to elaborate 3 programs and pass 2 tests, each activity maximum 7 points. Exam 65 points written exam (max. 45 points) oral exam (max. 20 points)



Other requirements

The elaboration of the individual tasks from the area of nonlinear control. Evaluation - according to the level of elaboration of the individual tasks.


Subject codeAbbreviationTitleRequirement
352-0516 TAŘ Automatic Control Theory Compulsory


Subject has no co-requisities.

Subject syllabus:

1. Mathematical models of nonlinear dynamical systems. Basic interconnections of nonlinear static systems. 2. State and phase space method. Stability in Lyapunov sense. Basic types of singular points and limit cycles. 3. Popov and circle stability criterion. 4. Linearization, the first Lyapunov method. 5. The second Lyapunov method. 6. Describing function method. 7. Relay method – use for identification. 8. Two- and thre-position control. 9. SISO extremal control systems. 10. Essential of theory of fuzzy sets and logic. 11. Linguistic and fuzzy control algorithms. 12. Fuzzification, inference mechanism and defuzzification. 13. Method of aggregation of state variables. 14. Robust control methods.

Conditions for subject completion

Conditions for completion are defined only for particular subject version and form of study

Occurrence in study plans

Academic yearProgrammeField of studySpec.ZaměřeníFormStudy language Tut. centreYearWSType of duty
2022/2023 (N0714A270011) Control of Machines and Processes TAŘ K Czech Ostrava 1 Compulsory study plan
2022/2023 (N0714A270011) Control of Machines and Processes TAŘ P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0714A270011) Control of Machines and Processes TAŘ P Czech Ostrava 1 Compulsory study plan
2021/2022 (N0714A270011) Control of Machines and Processes TAŘ K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0714A270011) Control of Machines and Processes TAŘ K Czech Ostrava 1 Compulsory study plan
2020/2021 (N0714A270011) Control of Machines and Processes TAŘ P Czech Ostrava 1 Compulsory study plan

Occurrence in special blocks

Block nameAcademic yearForm of studyStudy language YearWSType of blockBlock owner

Assessment of instruction

2021/2022 Summer