Course detail
Control Theory I
FSI-VA1 Acad. year: 2025/2026 Winter semester
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.
Language of instruction
Czech
Number of ECTS credits
6
Supervisor
Department
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.
The study programmes with the given course
Programme N-AIŘ-P: Applied Computer Science and Control, Master's, compulsory
Type of course unit
Lecture
39 hours, optionally
Syllabus
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
Laboratory exercise
8 hours, compulsory
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 hours, compulsory
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