The course aims to introduce students to the fundamental principles and methods of automatic control, including modeling, analysis, and synthesis of simple automatic control systems. Students will acquire basic theoretical and practical knowledge necessary for understanding the dynamic behavior of systems, stability analysis, and controller design. The course also aims to develop students’ ability to use MATLAB and master the basic tools for solving computational problems related to the presented material, as well as for the analysis and simulation of control systems.

Upon successful completion of the course, the student will be able to: • Understand and explain the fundamental concepts of automatic control systems, including open-loop and closed-loop configurations. • Derive and interpret input–output (IO) and state-space (ISO) models of linear time-invariant systems. • Apply Laplace transform techniques to obtain transfer functions and analyze system dynamics using block diagrams. • Analyze transient and steady-state responses of first-order and second-order systems using standard test signals. • Evaluate system performance using time-domain specifications and steady-state error analysis. • Assess system stability using classical methods, including the Hurwitz stability criterion. • Analyze frequency-domain characteristics using Bode and Nyquist diagrams and interpret stability margins. • Explain the structure and function of basic control strategies, including P, PI, and PID controllers. • Design and tune PID controllers for simple linear control systems.

Introduction to the basic concepts and terminology in the field of automatic control. Fundamental concepts of automatic control systems: open-loop and closed-loop control systems. Mathematical modeling of dynamical systems, including examples of mechanical, electrical, fluid, and thermal systems. Input–output (IO) models of linear time-invariant (LTI) dynamical systems. State-space modeling of dynamical systems, including input–state–output (ISO) representations of LTI systems. Modeling in the frequency domain: Laplace transform, transfer functions, and block diagrams. Transient and steady-state response analysis: system operating regimes, standard test signals, time-domain performance specifications, time responses of first-order and second-order systems, steady-state errors, error constants, and system gains. Stability of dynamical systems: concepts, definitions, Hurwitz stability criterion. Frequency-domain analysis: frequency response, Nyquist plots, Bode diagrams, stability and relative stability, and frequency-domain performance specifications. Basic types of control systems: proportional (P), proportional–integral (PI), and proportional–integral–derivative (PID) controllers and their effects on the dynamic and static properties of control systems. PID controller design and tuning methods.

PA: Practical work includes computational exercises aligned with the theoretical content of the course. Students solve problems related to modeling, analysis, and design of control systems, including transfer function derivation, time-domain response analysis, stability evaluation, and basic controller design. PL: Laboratory practice and experiments involve computer-based applications for the analysis, simulation, and evaluation of control systems. Emphasis is placed on the use of MATLAB/Simulink for modeling and simulation of linear time-invariant systems, state-space representations, and frequency-domain analysis. Practical implementation includes analysis and control of different physical systems using a modular educational real-time control platform, including coupled tank system (fluid level control), DC servo motor system (position/speed control), and heat flow system (thermal dynamics and control). Students perform system identification, model validation, controller design (P, PI, PID), and performance evaluation in both simulation and real-time experimental environments.

Defined by curriculum of the study programme.

• R. Jovanović, Fundamentals of automatic control, lecture notes in electronic format, Faculty of Mechanical Engineering, University of Belgrade, 2024. • Modular educational real time control system with various control plants (DC servo motor, inverted pendulum, heat flow experiment, coupled water tanks experiment), with acquisition hardware and software. • Intelligent Control Systems Laboratory.

Total assigned hours: 75

New material: 20
Elaboration and examples (recapitulation): 10

Auditory exercises: 9
Laboratory exercises: 5
Calculation tasks: 16
Seminar paper: 0
Project: 0
Consultations: 0
Discussion/workshop: 0
Research study work: 0

Review and grading of calculation tasks: 0
Review and grading of lab reports: 0
Review and grading of seminar papers: 0
Review and grading of the project: 0
Test: 10
Test: 0
Final exam: 5

Activity during lectures: 10
Test/test: 60
Laboratory practice: 0
Calculation tasks: 0
Seminar paper: 0
Project: 0
Final exam: 30
Requirement for taking the exam (required number of points): 20

R. Jovanović, Fundamentals of automatic control, lecture notes in electronic format, Faculty of Mechanical Engineering, University of Belgrade, 2024.; R. Jovanović, Mаtlab and Simulink in Automatic Control, Faculty of Mechanical Engineering, Belgrade, ISBN 978-86-7083-896-3, 2021 (in Serbian).; R. Dorf, R. Bishop, Modern Control Systems, 14th edition, Pearson Education Inc., 2022. ; N. S. Nise, Control Systems Engineering, 8th edition, John Wiley & Sons, Inc., 2019.