Theory of automatic control



Industrial Cooperation and Creative Engineering Education based on Remote Engineering and Virtual Instrumentation



Internal Deliverable 3.4.1

Learning Module: Theory of automatic control


Editor:       Vira Shamardina


Executive Summary

The course provides knowledge of fundamental principles of electromechanical systems control; main types of automatic control; forms of mathematical description of systems; time and frequency characteristics of systems and their components; methods of systems control quality analysis and systems synthesis of the desired characteristics.

Course objectives

Course objectives – to build students’ theoretical and practical skills on fundamental principles of ACS control and algorithms of their operation, basic rules for mathematical description of separate elements and systems as a whole, the ability to determine their properties on the basis of time and frequency characteristics, to assess the quality of systems control and also to conduct the synthesis of systems with the desired quality control in steady-state and transient operation.

The total scope of the course for postgraduate engineering education constitutes 20 hours: lectures – 10 hours, lab works – 5 hours, individual tasks – 5 hours. The course consists of 5 lectures, 2 laboratory works using the National Instrument educational platform with the «DC Motor» board and individual tasks.

Course Content

Theoretical Unit

Theme 1. The concept of sampled-data systems of automatic control

1.1 Classification and structure of sampled-data systems of automatic control
1.2 Mathematical description of sampled-data systems
1.3 Sampling theorem

Theme 2. Methods of sampled-data АСS examination

2.1 Z – transformation
2.2  Calculation of  Z – transformation
2.3 Properties of Z -transformation
2.4 Transfer function of the pulse ACS in Z- transform
2.5 Representation of pulse element
2.6 Transfer function of the forming element
2.7 Definition of the transfer function W RCP (s)
2.8 Block diagrams and transfer functions of closed-loop sampled-data АCS

Theme 3. Frequency responses (FR) of pulse systems

3.1 Analytic definition of FR
3.2 FR properties of pulse ACS
3.3 FR frequency
3.4 W- transformation
3.5 Plotting of frequency-response characteristic of pulse АСS

Theme 4. Stability of pulse АСS

4.1 General information (background)
4.2 Stability criteria

Theme 5. Quality of pulse АСS

5.1 Accuracy of pulse АСS
5.2 Astatism of АСS
5.3 Error signal at a continuous input signal
5.4 Error signal at a discrete input signal
5.5 Dynamic modes analysis of pulse АСS
5.6 Pulse systems correction
5.7 Digital АСS synthesis according to the pulse function of the analogue equivalent
5.8 Synthesis of a digital АСS according to the transient function of the analogue equivalent
5.9 Synthesis of digital АСS in the frequency-domain
5.10 Technical implementation of CD of the digital АСS

Laboratory workshop

Laboratory work 1. Determination of discrete transfer function of the DC motor

Laboratory work 2. Speed control of DC motor using a proportional-integral controller

Practical work (individual tasks): Mathematical description and analysis of discrete closed systems


 tshamardina Shamardina ViraPh.D, Assoc. Prof. of Automated electromechanical systems Department of National Technical University “Kharkiv Polytechnic Institute”, Dean of the German Technical Faculty


Expertise: Automatic control system, The actuators of general industrial mechanisms