Course detail

Control Theory II

FSI-VA2Acad. year: 2017/2018

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.

Learning outcomes of the course unit

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.


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.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Donald E. Kirk: Optimal Control Theory: An Introduction. Dover Publications, 2004. ISBN-10: 0486434842. (EN)
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)
Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. ISBN-10: 0486442780. (EN)
Schwarzenbach,J.-Gill,F.K.:System Modelling and Control, Butterworth-Heinemann, Oxford 2002, ISBN 0 340 54379 5 (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)

Planned learning activities and teaching methods

The course is taught through lectures explaining the basic principles and theory of the discipline. Exercises are focused on practical topics presented in lectures.

Assesment methods and criteria linked to learning outcomes

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.

Language of instruction


Work placements

Not applicable.


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.

Specification of controlled education, way of implementation and compensation for absences

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.

Classification of course in study plans

  • Programme M2I-P Master's

    branch M-AIŘ , 1. year of study, summer semester, 6 credits, compulsory
    branch M-AIŘ , 1. year of study, summer semester, 6 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


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

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


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