Course detail

Control Theory II

FSI-VA2Acad. year: 2026/2027

The introduction to the modern control theory is presented in the course. We focus on linear time-invariant systems (LTI) without delay with more degree of freedom in the state space and on the synthesis of state controllers. The interpretation is demonstrated through the illustrations from different application areas. Synthesis of control systems can be easily carried out with the use of Matlab Control System Toolbox.
The course completes theory of nonlinear systems and design of their control.

Language of instruction

Czech

Number of ECTS credits

5

Mode of study

Not applicable.

Guarantor

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

To be well informed about the foundations of classical control theory. To be able to choose and use adequate methods of PID controller synthesis for the solution of the given tasks.

Rules for evaluation and completion of the course

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.
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.

Aims

The aim of the course is to formulate and establish a basic knowledge of modern control theory. To strengthen the knowledge by the understanding the context of the different methods of state controller synthesis. To learn the methods of the synthesis.
To be well informed about the foundations of modern control theory. To be able to choose and use adequate methods of state controller synthesis for the solution of the given tasks.

Study aids

Presentations of lectures (available in e-learning) and examples solved in exercises, including modelling in MATLAB/Simulink environment.

Prerequisites and corequisites

Not applicable.

Basic literature

Dorf, R.C. and Bishop, R.H.: Modern Control Systems. Addison-Wesley, New York, 2010. (EN)
Ogata, K.: Modern Control Engineering. Prentice-Hall, New Jersey, 2009. (EN)
Schwarzenbach,J.-Gill,F.K.:System Modelling and Control, Butterworth-Heinemann, Oxford 2002, ISBN 0 340 54379 5 (EN)

Recommended reading

Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. ISBN-10: 0486442780. (EN)
Donald E. Kirk: Optimal Control Theory: An Introduction. Dover Publications, 2004. ISBN-10: 0486434842. (EN)
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 N-AIŘ-P Master's 2 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hours, optionally

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Syllabus

1. State-space representation
2. State model conversions
3. Controllability, observability and pole placement
4. Design of control systems
5. State observer
6. Quadratic optimal control systems
7. Robust control systems
8. Robust control system synthesis
9. Synthesis of control system with observer
10. Nonlinear system description, typical nonlinearities
11. State-plane method,
12. Methods of linearization, verification of linearized model
13. Control system synthesis

Laboratory exercise

8 hours, compulsory

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Syllabus

1. Measurement of selected non-linearities of mechanical and electrical devices.
2. State control of DC motor without integration.
3. State control of DC motor with integration.
4. Credit

Computer-assisted exercise

18 hours, compulsory

Teacher / Lecturer

prof. RNDr. Ing. Miloš Šeda, Ph.D.

Syllabus

1. Illustrations of LTI technical systems, simple mechanical and electrical systems representation in the state space. Transformations between inner and outer description of system
2. State-space representation of more complex mechanical and electrical systems using MATLAB/Simulink
3. Controllability, observability of technical systems in status space, pole placement method with use of MATLAB, illustrations of technical systems
4. Synthesis in state space, design of state controller
5. Design of state space controller with state observer. Design of state space controller with state observer and fault compensation
6. Quadratic optimal controller design
7. Robust controller design
8. Modelling of nonlinear system using the state plane method
9. Models linearization, behavior of linearized model assessment. Control system design with linearized model.