Course detail

Control Theory I

FSI-VA1Acad. year: 2017/2018

The introduction to the classical control theory is presented in the course. We focus on linear time-invariant systems (LTI) without delay with one degree of freedom in the transfer form and on the synthesis of PID 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 classical control theory. To be able to choose and use adequate methods of PID controller synthesis for the solution of the given tasks.


The knowledge of essential principles and terms of automation, the knowledge of mathematics gained within the bachelor's study programme, using of Matlab.


Not applicable.

Recommended optional programme components

Not applicable.

Recommended or required reading

Švarc, I., Matoušek, R., Šeda, M., Vítečková, M.: Automatizace-Automatické řízení, skriptum VUT FSI v Brně, CERM 2011. (CS)
Ogata,K.: Modern Control Engineering, Prentice Hall , fourth edition, New Jersey 2002, ISBN 0-13-043245-8 (EN)
Schwarzenbach,J.-Gill,F.K.: System Modelling and Control, Butterwoth Heinemann, third edition, Oxford 2002, ISBN 0-340-54379-5 (EN)
Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. (EN)
Švarc, I.: Teorie automatického řízení, podpory FSI, www stránky fakulty 2003. (CS)
Franklin, G.F., Powell, J.D. and Emami-Naeini, A.: Feedback Control of Dynamic Systems. Prentice-Hall, New Jersey, 2009. (EN)
Morris, K.: Introduction to Feedback Control. Academic Press, London, 2002. (EN)
Stefani, R.T., Shanian, B., Savant, C.L. and Hostetter, G.H.: Design of Feedback Control Systems. Oxford University Press, 2002. (EN)

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 classical control theory. To strengthen the knowledge by the understanding the context of the different methods of PID 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 the 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, winter semester, 5 credits, compulsory
    branch M-AIŘ , 1. year of study, winter semester, 5 credits, compulsory

Type of course unit



39 hours, optionally

Teacher / Lecturer


1. Continuous vs. discrete systems/models, stability
2. Illustrations of models from different application domains
3. Analytical assembly of the transfer model
4. Introduction to the identification of transfer model
5. Quality of regulation. Synthesis of control systems using Root-Locus method
6. Lag, lead and lag–lead compensation
7. Ziegler–Nichols rules for tuning PID controllers
8. PID synthesis from frequency response
9. PID synthesis by computational optimization
10. Modifications of PID structures
11. Two-degrees-of-freedom control
12. Response improving by zeros placement
13. More detailed discussion of discrete models

Computer-assisted exercise

26 hours, compulsory

Teacher / Lecturer


1. Continuous and discrete variables, models
2. Illustrations of continuous and discrete models
3. Transfer models of technical systems and their parameters
4. Methods of technical systems identification
5. PID controller design by using Root-Locus method
6. Illustration of Lag, Lead and Lag–Lead compensation methods usage
7. Controller parameters tuning by Ziegler-Nichols method
8. Controller parameters design by using frequency response
9. Controller parameters tuning by using optimization methods
10. Used structures of PID controllers
11. Illustrations of design and usage two-degrees-of-freedom controller
12. Illustrations of control quality improvements
13. Credit