Ternopil Ivan Puluj National Technical University

Каф. електричної інженерії

Automatic Control Theory


1. Educational programs for which discipline is mandatory:

# Educational stage Broad field Major Educational program Course(s) Semester(s)
1 bachelor's 14. Електрична інженерія 141. Електроенергетика, електротехніка та електромеханіка (бакалавр) 3 6

2. The course is offered as elective for all levels of higher education and all educational programs.

3. Information about the author of the course

Full name Myroslav Nakonechnyi
Academic degree PhD
Academic title none
Link to the teacher`s page on the official website of the University
Е-mail (in the domain

4. Information about the course

Study hours structure Lectures: 36
Practical classes: 0
Laboratory classes: 36

Amount of hours for individual work: 78
ECTS credits: 5.0
Teaching language english
Form of final examination exam
Link to an electronic course on the e-learning platform of the university

5. Program of discipline

Description of academic discipline, its goals, subject of study and learning outcomes

The purpose of studying the discipline "Theory of automatic control" is to gain knowledge about the principles of constructing automatic systems, methods of studying the established and transitional processes occurring in control systems, methods for analyzing the stability and quality of the functioning of automatic systems, assessing the impact of changing the parameters of control devices.

The place of academic discipline in the structural and logical scheme of study according to the educational program

Prerequisites. List of disciplines, or knowledge and skills, possession of which students needed (training requirements) for successful discipline assimilation


Contents of the academic discipline

Lectures (titles/topics)

Theme 1. Basic concepts and definitions. Brief information on the development of the theory of management. The setting of the task of management, the purpose and the criteria of the quality of management. Problems of research of systems of automatic control, tasks of the analysis and synthesis. Functional schemes of automatic control systems, main elements - object and control device.
Theme 2. Formation of equations of dynamics of elements. Linearization. Analytical and experimental construction of the model of elements and systems. Models of external actions. Forms of presentation of mathematical models, differential equations, state in the form of a Cauchy.
Theme 3. Main characteristics of automatic control.
Using the Laplace and Fourier transforms to analyze the dynamic properties of the automatic control system. Concept of transfer function. Time and frequency characteristics
Theme 4. Typical dynamic links. Equations, transfer functions, time and frequency functions and characteristics of the proportional aperiodic link of the first order, aperiodic link of the second order. Examples of typical links. Equation, transfer functions, time and frequency functions and characteristics of the oscillation link, conservative link. Examples of typical links. Equations, transfer functions, time and frequency functions, and the characteristics of the ideal integration unit, the integrating link, the integrating link with delay, the ideal differentiating link, the differentiating link with delay, links with delay. Examples of typical links.
Theme 5. Transmission functions and structural schemes and characteristics of automatic control systems.
Transfer functions of the system with different connection of the links: consecutive, parallel with the feedback. Transmission functions of closed systems for control, perturbation and error. Rules for the transformation of structural schemes, the transfer of branch points and summation. Construction of frequency characteristics on the frequency characteristics of the links.
Theme 6. Stationary modes of automatic control systems.
ACS steady at the determined actions. Stationary modes of static systems. Ways to eliminate static deviation. Dynamic stationary modes of ACS. Stationary dynamic mode of ACS under action that changes with constant derivative. Ways to eliminate static deviation: using static ACS; compensation of perturbations that change with a constant derivative.

Theme 7. Stability of automatic control systems. Algebraic stability criteria. Works of Lyapunov on the stability of motion. Relationship of the stability conditions with the roots of the characteristic equation. Algebraic criteria for the stability of Raus and Hurwitz. Determination of boundary values of system parameters.
Theme 8. Frequency stability criteria. Frequency stability criteria of Mikhailov, Nyquist and criteria using logarithmic characteristics. Stability reserve.
Theme 8. Area of stability of linear systems. Isolation in the space of system parameters. D-split by one and two parameters. Stability of systems with delay.
Theme 10. Research of quality of continuous automatic control systems. The quality of transient processes in the SAC. Basic Quality Scores. Accuracy of systems in steady state under deterministic actions. Root methods for assessing the quality (duration, volatility) of transients for the allocation of zeros and poles of the transfer function, along the root hodograph.
Theme 11. Correction of dynamic properties of linear volt-ampere characteristics.
Appointment, types of corrections. The main types of correction of the dynamic properties of the system. Technical implementation of adjusting devices. Sequential correction of links. Proportionally-differentiating link (ideal and real). Proportionally-integrating link. Proportional–integral–derivative link.
Theme 12. General information about discrete automatic control systems
Classification and basic concepts of discrete ACS. Definition of discrete systems. Discrete signal. Types of quantization. Classification of impulse systems by types of modulation. Disadvantages and advantages of discrete systems. Pulse element and its characteristics. Transmitting function of real pulse element. Operator method in the study of pulsed ACS.
Theme 13. Stability and quality of discrete systems.
Stability of discrete ACS. Conditions of ACS stability. Algebraic stability criteria. Frequency stability criteria. An analogue of Mikhailov's criterion. Analogue of the Nyquist criterion. The quality of transient processes of discrete systems. Basic Quality Scores.
Theme 14. General information about nonlinear automatic control systems.
General information about nonlinear elements. Typical is not linearity. Stationary modes of nonlinear systems with deterministic actions. Mathematical models of nonlinear systems.
Stability of nonlinear systems and methods of its determination.
Features of the dynamics of nonlinear systems. Phase portraits of nonlinear systems, phase portraits of linear systems. Investigation of nonlinear systems by the phase plane method.

Laboratory classes (topics)

Study of time and frequency characteristics of the aperiodic link of the first order.
Investigation of time and frequency characteristics of the aperiodic link of the second order.
Investigation of time and frequency characteristics of oscillatory link.
Investigation of time and frequency characteristics of the real integration links.
Investigation of properties and characteristics of sequentially connected links.
Investigation of properties and characteristics of automatic control systems.
Investigation of properties and characteristics of the automatic control system covered by negative feedback.
Investigation of the stability of linear continuous systems.
Increasing the stock of stability and performance of continuous linear systems.

Learning materials and resources

Golnaraghi F., Kuo B. Automatic Control Systems. Tenth Edition. — McGraw-Hill Education, 2017.
Bubnicki Z. Modern Control Theory. Springer, Berlin, 2005.
Kuo Benjamin. Automatic Control Systems. Third Edition. — London: Prentice-Hall International. Inc., 1975
Hussein A.M. Automatic Control Systems. Lecture notes. — Al-Kharj,‎ Saudi Arabia: Prince Salman bin Abdulaziz University
Wang L. PID Control System Design and Automatic Tuning using MATLAB/Simulink: Design and Implementation using MATLAB/Simulink. Wiley-IEEE Press, 2020
Kuntsevich V., Gubarev V., Kondratenko Y. (eds.) Control Systems: Theory and Applications. Delft: River Publishers, 2018.
Lyshevski S.E. Control Systems Theory with Engineering Applications. Springer Science+Business Media New York, 2001.
The MathWorks, Inc. MATLAB Control Sytem Toolbox User's Guide. Natick: The MathWorks, Inc., 2020.

6. Policies and assessment process of the academic discipline

Assessment methods and rating system of learning results assessment

Current control consists of assessment of theoretical knowledge - two modules (25 points maximum each) and performance and defense of laboratory work (25 points maximum).
Examination control is determined by the answers to theoretical questions and is estimated at 25 points maximum.

Table of assessment scores:

Assessment scale
(100 points)
(4 points)
90-100 Excellent А
82-89 Good B
75-81 C
67-74 Fair D
60-66 E
35-59 Poor FX
1-34 F
Approved by the department
(protocol №
on «