Control Theory I (FSI-VA1)

The aim of the course is to familiarize students with the principles of automatic control in logical, continuous, and discrete control loops. Students will acquire the knowledge needed to optimize control loops by selecting appropriate controller parameter settings. The course also covers the analysis and solution of branched and multidimensional control loops, as well as understanding state-space control.

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

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 behaviour. 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. While "classical" control theory is based on the input-output (external) description of the controlled process, state theory is based on its state description (internal description), which is a natural product of analytical process modelling.

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.

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.

• Connection of a continuous PID controller in DC motor speed control and setting of optimal controller parameters.


• Change of individual P, I, PI, PD and PID controllers and monitoring of control quality during these changes.


• Excursion to Honeywell research and development facility. Familiarization with modern instruments in the company's laboratories.


• Credit.

• Design of controllers for control circuits in Simulink using Ziegler-Nichol’s method.


• Verification of the theoretical calculation of permanent control deviation on the simulation model in Simulink. Testing of controllers with and without integration component.


• Measurement of the frequency characteristics of the continuous/discrete control component on the simulation model.


• Modelling of simple control circuits and determination of their stability by calculation and subsequent verification on the model.


• Modeling circuits with a single degree of freedom controller and then with two degrees of freedom - to determine the advantages of 2 DOF controllers.


• Simulation of a branched control circuit with measurement of the disturbance variable - control flow without and with disturbance measurement.


• Modeling of multidimensional control circuits. Practical assurance of circuit autonomy.


• Modelling of different types of digital controllers and verification of their dynamic properties on transient, impulse and frequency characteristics.


• Design of a stateful controller circuit.

ASTRÖM, K., HÄGGLUND, T. Advanced PID Control. ISA – Instrumentation, Systems, and Automation Society, Research Triangle Park, NC, 2006, ISBN 1-55617-942-1.

GOODWIN G. C., GRAEBE, S. F., SALGADO, M. E. Control System Design. Pearson Education, Singapore, 2001, ISBN 81-297-0002-6

ŠULC, B., VÍTEČKOVÁ, M. 2004. Teorie a praxe návrhu regulačních obvodů. Vydavatelství ČVUT, Praha, 2004, ISBN 80-01-03007-5

VÍTEČKOVÁ, M., VÍTEČEK, A. Vybrané metody seřizování regulátorů. VŠB – TU Ostrava, Ostrava, 2011, ISBN 978-80-248-2503-8

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. 

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 .

OGATA,K.: Modern Control Engineering, Prentice Hall , fourth edition, New Jersey 2002, ISBN 0-13-043245-8