Automatic Control

Course Description

Introducing course, terminology, historical overview. Classification of control systems. Principle of feedback. Formal representation of control systems. Mathematical modelling. Static and dynamic working regime. Linearization. Responses of linear time invariant (LTI) systems. Use of Laplace transform. Basic dynamic components of control systems. Transfer function and frequency characteristics. Stability analysis: Lyapunov, algebraic and frequency methods. Internal model principle. Sensitivity. Digital control systems. Choice of the sampling period. Mathematical description of A/D and D/A converters, quantization. Discretization methods. Mathematical models of discrete-time systems. Controllability and observability. Performance indices of control systems. Introduction to design. PID regulator and parametrization of PID regulators. Feedforward and cascade control. Digital PID regulator. Windup and antiwindup. Design of digital control system by emulating continuous system.

General Competencies

Understanding the role of control related to flow of matter, energy and information. Understanding the basic control systems analysis and design techniques. Ability to design and tune classical controllers.

Learning Outcomes

  1. explain the pricinple of feedback in control systems
  2. apply laws of conservation of energy and matter in mathematical modelling of dynamical systems; linearize nonlinear model
  3. employ block agebra and Laplace transform in transfer function calculation
  4. compute frequency characteristics of linear systems
  5. apply methods of analysis of stability of linear continuous-time control systems in frequency domain
  6. apply discretization on a linear continuous-time system
  7. apply methods of analysis of stability of dicrete time systems
  8. apply tuning rules for PID regulator based on experiments (Ziegler-Nichols).

Forms of Teaching


Two times per week two hours of lectures.


One midterm and one final exam in written form, or an exam in a written and oral form.

Laboratory Work

Laboratory exercises consist of 6 exercises. Each exercise is worth 3 points: 1 point for homework which is evaluated during the exercise, 0.5 for the laboratory work and 1.5 for a quiz written at the end of the exercise.


After each lecture.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Comment: Percent of Grade
Laboratory Exercises 0 % 3 % 0 % 1.5 %
Homeworks 0 % 6 % 0 % 3 %
Quizzes 0 % 9 % 0 % 4.5 %
Mid Term Exam: Written 0 % 35 % 0 %
Final Exam: Written 0 % 47 %
Exam: Written 0 % 41 %
Exam: Oral 50 %

On midterm exam and final exam at least 40 out of total 82 points is required. At least 50 out of total 100 points is required to pass the course.

Week by Week Schedule

  1. Overview of thematic subjects, references, organization of the course and exams. Historical background of automatic control development. Examples and research trends.
  2. Systems and control systems. Examples of various systems. System classification. Formal representation of control systems. Block algebra.
  3. Modeling of dynamical systems.
  4. Linearization of nonlinear systems. Systems representations: impulse system response, step system response, state-space representation.
  5. Use of Laplace transform. Transfer function.
  6. System frequency characteristics. Various representations (Nyquist, Bode, Nichols). Examples.
  7. Poles, zeros and time responses of linear dynamical systems. Control systems structures.
  8. Midterm exam.
  9. Stability of linear continuous-time control systems. Stability analysis by frequency method (Nyquist, Bode).
  10. Time performance indices for control system steady-state response. Introduction to digital control systems.
  11. Mapping of poles and zeros from s-domain to z-domain.
  12. Discretization of continuous-time systems. Models of digital control systems.
  13. Stability of discrete-time control systems. PID controller.
  14. Parametrization of PID controllers. PID - additional functions.
  15. Final exam.

Study Programmes

Control Engineering and Automation -> Electrical Engineering and Information Technology (Module)

Electrical Power Engineering -> Electrical Engineering and Information Technology (Module)

Electronic and Computer Engineering -> Electrical Engineering and Information Technology (Module)

Electronics -> Electrical Engineering and Information Technology (Module)

Wireless Technologies -> Electrical Engineering and Information Technology (Module)


Prerequisites for


Zoran Vukić, Ljubomir Kuljača (2005.), Automatsko upravljanje,
N. Mišković, S. Jurić-Kavelj, M. Đakulović, V. Petrović i ostali (2012.), Automatsko upravljanje - zbirka zadataka, FER
J. Matuško, M. Vašak, M. Seder. (2006.), Automatsko upravljanje - zbirka zadataka., FER
N. Perić (1998.), Automatsko upravljanje - auditorne vježbe, FER
N. Perić (2005.), Automatsko upravljanje-predavanja, FER
(.), Feedback Control of Dynamical Systems. G.F. Franklin, J.D. Powell, A. Emami.Naeini. 4th edition, Prentice Hall, 2002.,
(.), Digital Control of Dynamic Systems. G. F. Franklin, J.D. Powell, M.L. Workman. 3rd edition, Prentice Hall, 1997.,
(.), Linear Control System Analysis and Design - Conventional and Modern. J.J. D´Azzo, C.H. Houpis. 4th edition, McGraw-Hill, 1995.,
(.), Control System Design. G.C. Goodwin, S.F. Graebe, M.E. Salgado. Prentice Hall, 2001.,

Grading System

L0 English Level
L1 e-Learning
60 Lecturers
0 Exercises
15 Laboratory exercises


87,5 Excellent
75 Very Good
62,5 Good
50 Acceptable