Digital Control Systems

Course Description

Introduction to linear control system design. Performance indices in frequency and time domain. Input/output (external) and (internal) state variable mathematical models. Series compensator design by frequency methods. Lead and lag compensators. Design by linear algebraic methods. Diophant equation. System sensitivity and robustness. System analysis and controller design with root locus methods. Structural characteristics: eigenvalues, stability, controllability, observability, canonic forms and minimal realization. State space controller design. Reference tracking and disturbance compensation. State space observers. Total regulator. Linear quadratic regulator. Cascade control systems. Controller design by symmetric and technical optimum.

Learning Outcomes

  1. apply discretization approches of continuous dynamic systems
  2. analyze discrete systems dynamic behaviors
  3. design of digital controllers
  4. assess stabilty of digital control systems

Forms of Teaching


Two times per week two hours of lectures.

Independent assignments

5 homework assignments as preparation for laboratory exercises.


Laboratory exercises comprise 5 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.

Grading Method

Continuous Assessment Exam
Type Threshold Percent of Grade Threshold Percent of Grade
Laboratory Exercises 0 % 2.5 % 0 % 2.5 %
Homeworks 0 % 5 % 0 % 5 %
Quizzes 0 % 7.5 % 0 % 7.5 %
Class participation 0 % 5 % 0 % 5 %
Mid Term Exam: Written 0 % 35 % 0 %
Final Exam: Written 0 % 45 %
Exam: Written 0 % 60 %
Exam: Oral 20 %

To pass the course student must achieve at least 50 points, of which at least 40 points must be from the midterm exam and final exam (Continuous Assessment) or 30 points from the written exam (Exam).

Week by Week Schedule

  1. Process of control system design
  2. Control system objectives, models and structures, Loop shaping; Lead and lag compensator
  3. Loop shaping; Lead and lag compensator
  4. Linear algebraic methods (model matching, pole placement, Diophantine equation)
  5. Linear algebraic methods (model matching, pole placement, Diophantine equation)
  6. Ploting of root loci: amplitude and phase condition
  7. Controller design using the Root-Locus method
  8. Midterm exam
  9. Controlability and observability of LTI systems
  10. Pole placement; Ackerman formula; Dead-beat controller
  11. Separation principle (state feedback and state observers)
  12. Linear quadratic regulator
  13. Cascade control systems, Magnitude optimum
  14. Magnitude optimum, Symmetric optimum
  15. Final exam

Study Programmes

University undergraduate
Computing (study)
Elective Courses (6. semester)
Electrical Engineering and Information Technology (study)
Elective Courses (6. semester)
University graduate
Audio Technologies and Electroacoustics (profile)
Elective Courses (1. semester)
Communication and Space Technologies (profile)
Elective Courses (2. semester)
Computational Modelling in Engineering (profile)
Elective Courses (2. semester)
Computer Engineering (profile)
Elective Courses (2. semester)
Computer Science (profile)
Elective Courses (2. semester)
Control Systems and Robotics (profile)
Elective Courses (2. semester) Elective Courses of the Profile (2. semester)
Data Science (profile)
Elective Courses (2. semester)
Electrical Power Engineering (profile)
Elective Courses (2. semester)
Electric Machines, Drives and Automation (profile)
Elective Courses (2. semester)
Electronic and Computer Engineering (profile)
Elective Courses (2. semester)
Electronics (profile)
Elective Courses (2. semester)
Information and Communication Engineering (profile)
Elective Courses (2. semester)
Network Science (profile)
Elective Courses (2. semester)
Software Engineering and Information Systems (profile)
Elective Courses (2. semester)


Mato Baotić (2016.), Sinteza linearnih sustava upravljanja, Sveučilišni priručnik, Sveučilište u Zagrebu Fakultet elektrotehnike i računarstva
Chi-Tsong Chen (1999.), Linear System Theory and Design; 3rd edition, Oxford University Press
Katsuhiko Ogata (1997.), Modern controle engineering; 3rd edition, Prentice-Hall
Zoran Vukić, Ljubomir Kuljača (2005.), Automatsko upravljanje - analiza linearnih sustava, Kigen d.o.o. Zagreb

For students


ID 229634
  Summer semester
L3 English Level
L1 e-Learning
60 Lectures
8 Exercises
12 Laboratory exercises

Grading System

Very Good