Control Systems Synthesis

Learning Outcomes

  1. design controller with frequency design methods
  2. design lead and lag compensators
  3. apply root-locus method for analysis and synthesis
  4. analyze controllability and observability of linear systems
  5. design state-space controller and appropriate (deterministic) observer
  6. design linear quadratic regulator
  7. design cascade control system

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

By decision of the Faculty Council, in the academic year 2019/2020. the midterm exams are cancelled and the points assigned to that component are transferred to the final exam, unless the teachers have reassigned the points and the grading components differently. See the news for each course for information on knowledge rating.
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 %
Attendance 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)


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 control engineering; 3rd edition, Prentice-Hall
Zoran Vukić, Ljubomir Kuljača (2005.), Automatsko upravljanje - analiza linearnih sustava, Kigen d.o.o. Zagreb


ID 183452
  Summer semester
L3 English Level
L1 e-Learning
60 Lectures
0 Exercises
12 Laboratory exercises
0 Project laboratory

Grading System

87.5 Excellent
75 Very Good
62.5 Good
50 Acceptable