Course detail

Control Theory I

FSI-VA1Acad. year: 2025/2026

The course provides preparation for mastering the fundamental principles of logical, continuous, and discrete feedback control. Control is understood as the interaction between two components—the controlled and the controlling object—whose connection forms a control system, designed to achieve optimal behavior. The course addresses not only simple control loops but also complex and multidimensional systems. It goes beyond traditional approaches, transitioning to modern solutions in state space and the use of state controllers.

Language of instruction

Czech

Number of ECTS credits

6

Mode of study

Not applicable.

Guarantor

doc. Ing. Pavel Škrabánek, Ph.D.

Department

Institute of Automation and Computer Science (ÚAI)

Entry knowledge

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

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 the 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 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.
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.

Study aids

Not applicable.

Prerequisites and corequisites

Not applicable.

Basic literature

ASTRÖM, K., HÄGGLUND, T. Advanced PID Control. ISA – Instrumentation, Systems, and Automation Society, Research Triangle Park, NC, 2006, ISBN 1-55617-942-1. (EN)
DORF, R. C., BISHOP, R. H. Modern Control Systems. Tenth Edition. Upper Saddle River – New Jersey: Pearson Prentice Hall, 2004, ISBN 0-13-145733-0.  (EN)
FRANKLIN, G. F., POWELL, J. D., Emami-Naeini, A. Feedback Control of Dynamic Systems. Fourth Edition. Prentice Hall, Upper Sadle River, 2002, ISBN 0-13-032393-4 . (EN)
GOODWIN G. C., GRAEBE, S. F., SALGADO, M. E. Control System Design. Pearson Education, Singapore, 2001, ISBN 81-297-0002-6 (EN)
OGATA,K.: Modern Control Engineering, Prentice Hall , fourth edition, New Jersey 2002, ISBN 0-13-043245-8 (EN)
ŠULC, B., VÍTEČKOVÁ, M. 2004. Teorie a praxe návrhu regulačních obvodů. Vydavatelství ČVUT, Praha, 2004, ISBN 80-01-03007-5 (CS)
VÍTEČKOVÁ, M., VÍTEČEK, A. Vybrané metody seřizování regulátorů. VŠB – TU Ostrava, Ostrava, 2011, ISBN 978-80-248-2503-8 (CS)

Recommended reading

Bernard Friedland: Control System Design: An Introduction to State-Space Methods. Dover Publications, 2005. (EN)
Morris, K.: Introduction to Feedback Control. Academic Press, London, 2002. (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 fakulty 2003. (CS)

Classification of course in study plans

  • Programme N-AIŘ-P Master's 1 year of study, winter semester, compulsory

Type of course unit

 

Lecture

39 hod., optionally

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Syllabus

  1. Introduction to the subject, definition of concepts and basics of feedback control of systems and processes, definition of knowledge for the subject.
  2. Control accuracy - steady state permanent control deviation. Control quality and adjustment of controllers in general.
  3. Linear and quadratic control surface and comparison with the practical Ziegler-Nichols controller tuning method. Optimal modulus method.
  4. Frequency methods for designing control circuits.
  5. Controllers with two degrees of freedom.
  6. Branching control circuits. Auxiliary controlled and auxiliary action variables. Circuits with disturbance measurement - circuit invariance. Transport delay compensation - Smith predictor.
  7. Multivariate (MIMO) control circuits. Their stability and autonomy.
  8. Discrete control, z-transforms and differential equations, mathematical description of discrete control systems. Discretization of continuous control systems.
  9. Discrete PSD controllers. Algorithm of digital controllers. Technical problems with the use of digital controllers.
  10. Stability of discrete systems. General stability condition, stability criteria, bilinear transformations.
  11. Control in state space. Introductory concepts. Conversion of differential equations into state equations.
  12. Conversion of state equations to transfer matrix. Solution of state equations.
  13. State controllers. State controllers with observer. Synthesis of circuits in state space.

Laboratory exercise

8 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Syllabus

1. Two-level temperature control.
2. Regulation of the water column height in the tank.
3. Control of DC motor.
4. Credit

Computer-assisted exercise

18 hod., compulsory

Teacher / Lecturer

doc. Ing. Pavel Škrabánek, Ph.D.

Syllabus

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, illustration of Lag, Lead and Lag–Lead compensation methods usage
6. Controller parameters tuning by Ziegler-Nichols method, controller parameters design by using frequency response
7. Controller parameters tuning by using optimization methods
8. Used structures of PID controllers
9. Illustrations of design and usage two-degrees-of-freedom controller