Course detail

Theory of Automatic Control

FSI-VZR Acad. year: 2025/2026 Winter semester

The primary aim of the course is to provide the students with the complete knowledge of the automation and control systems.
The first part of the course makes the students familiar with the logic circuits. It presents logic functions, logic elements, combinational and sequential logic circuits. Minimization of logic functions (Karnaugh map) is discussed.
The second part includes the foundations of linear continuous systems analysis using the transfer function and impulse response of feedback control systems. Mathematical preliminary is the Laplace transform. This part covers the basic feedback theory and stability, accuracy and quality of regulation.
The third part of the course includes the foundations of digital control. It presents mathematical preliminary (Z – transform), digital transfer function and difference equations. It deals with stability condition, stability analysis through bilinear transformation and PID – control algorithm through Z – transform.

Language of instruction

Czech

Number of ECTS credits

5

Supervisor

doc. Ing. Pavel Škrabánek, Ph.D.

Department

Institute of Automation and Computer Science

Entry knowledge

Fundamental concepts in mathematics including the solution of the system of differential equations. Fundamental concepts in physics (particularly dynamics) and electrical engineering.

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 basic conceptions of automatic control, computational models, theories and algorithms of control systems.

Analysis and design of linear continuous-time and discrete feedback control systems. Students will obtain the basic knowledge of automation, description and classification of control systems, determination of their characteristics. Students will be able to solve problems stability of control systems.

The study programmes with the given course

Programme B-MET-P: Mechatronics, Bachelor's, compulsory

Programme B-STR-P: Engineering, Bachelor's
specialization AIŘ: Applied Computer Science and Control, compulsory

Type of course unit

 

Lecture

39 hours, optionally

Syllabus


  1. Introduction to automation. Logic control, logic functions, Boolean algebra, expression of Boolean functions, minimization by Boolean algebra rules and Karnaugh.

  2. NAND and NOR logic functions, combinational and sequential logic circuits, programmable automata.

  3. Continuouscontrolcircuit, Laplacetransform, mathematicaldescriptionofcontrolsystems, differentialequations, transfer.

  4. Impulse and transition functions and characteristics, division of control terms. Frequency transfer, frequency characteristics in the complex plane and in logarithmic coordinates, poles and zeros, block algebra.

  5. Transport delay systems, controllers and their dynamic properties.

  6. Stability of the control circuit in general, stability criteria. Steady state control accuracy.

  7. Cascadecontrol.

  8. Qualityofcontrol and adjustmentofcontrollers, Ziegler-Nicholsmethod, adjustmentofcontrollersaccording to minimum oflinear and quadraticcontrol area.

  9. Discretecontrolcircuit, sampler, shapers, Z-transform, differentialequations.

  10. Z-transfer, discrete impulse and transient function and characteristic, frequency transfer and frequency characteristic of discrete systems.

  11. Block algebra ofdiscretesystems, digitalcontrollers (position and incrementalalgorithm), stability ofdiscretecontrolcircuit in general.

  12. Stability criteria of discrete control circuits.

  13. Controllerswithtwodegreesoffreedom.


Laboratory exercise

8 hours, compulsory

Syllabus


  1. Logic control (Siemens LOGO!Soft, control of the combination circuit using a programmable logic controller).

  2. Logic control (control of the sequential circuit using a programmable logic controller).

  3. Continuous linear control (feedback loop with a DC motor).

  4. Continuous linear control (Ziegler-Nichols method applied to a DC motor circuit).




Computer-assisted exercise

18 hours, compulsory

Syllabus


  1. Logical Control (Boolean Algebra, Algebraic Minimization of Logical Functions, Block Diagrams, Introduction to Siemens LOGO!Soft).

  2. Logical Control (Word Problems, Truth Tables, Minimization Using Karnaugh Maps, Combinational Logic Circuits – Simulation).

  3. Introduction to Simulink.

  4. Continuous Linear Control (Differential Equations, Transfer Functions, Impulse and Step Responses, Impulse and Step Characteristics, Simulation in MATLAB).

  5. Continuous Linear Control (Frequency Transfer, Frequency Characteristics in the Complex Plane, Frequency Characteristics in Logarithmic Coordinates, Simulation).

  6. Continuous Linear Control (Block Algebra, Controllers, Control Loops, Stability Simulation).

  7. Discrete Control (Discrete Control Loop, Z-Transform, Difference Equations).

  8. Discrete Control (Impulse and Step Functions, Stability).

  9. Final Test.