### Popis predmeta

#### Course Description

The course begins with definitions of signals and systems, and mathematical models of continuous-time linear control systems. Block diagrams and block algebra are presented. Representation of systems in state-space is described. Computation of continuous-time system responses to input signals (e.g. step, impulse) in described. The Laplace transform is introduced, system transfer function defined, and zero-pole analysis performed. All previous concepts are also described for discrete-time domain, in particular modelling of discrete control systems, and state-space representation of such systems. Finally, a PID controller is introduced for discrete systems, with explanation how to tune PID controller with the Ziegler-Nichols methods, and presentation of some practical aspects of computer controlled systems.

#### Learning Outcomes

1. Classify systems using their basic properties
2. Compute and analyse a transfer function of a LTI system
3. Compute and analyse a frequency response of a LTI system
4. Use a computer to simulate a LTI system
5. Conclude if a control system is stable
6. Compute state-space representation of a system
7. Compute a discrete transfer function
8. Compute recursive differential equations of a control system
9. Apply a PID controller

#### Forms of Teaching

Lectures

Lectures will be performed every week in the classroom for a duration of 3 school hours.

Exercises

Auditorium exercises will be performed within the Lecture hours.

Laboratory

Laboratorium exercises will be performed periodically after relevant material given in the Lectures.

#### Week by Week Schedule

1. Modeling of signals and systems, Linear differential and difference systems
2. Motivation for using control systems, Block diagrams and algebra
3. State space representation of continuous control systems , Transient and impulse system response, Forced and natural system response
4. Examples and properties of Laplace transform, Inverse transform; Convolution
5. Pole and zero influence on LTI system time response, Control system quality criteria in time domain
6. Z-transform, Modeling of digital control system elements
7. Euler forward and backward discretization, Difference equations
8. Midterm exam
9. Transfer function of discrete control systems
10. Block diagrams of discrete control systems
11. State-space representation of discrete control systems
12. PID controller structures, Tuning of PID controller parameters; Ziegler-Nichols methods
13. Tuning of PID controller parameters; Ziegler-Nichols methods, Practical aspects of PID controller design; Filtering; Anti-windup
14. Digital PID controller synthesis
15. Final exam

#### Study Programmes

Audio Technologies and Electroacoustics (profile)
Free Elective Courses (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Core-elective courses 1 (1. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Elective Course of the profile (3. semester) Elective Course of the Profile (1. semester)

#### Literature

(.), N. Perić, Z. Vukić, M. Baotić, M. Vašak, N. Mišković (2010.), Automatsko upravljanje - predavanja, Sveučilište u Zagrebu Fakultet elektrotehnike i računarstva,
(.), Z. Vukić, Lj. Kuljača (2005.), Automatsko upravljanje - analiza linearnih sustava upravljanja, Kigen,
(.), Gene F. Franklin, J. David Powell, Michael L. Workman (1997.), Digital Control of Dynamic Systems - Third Edition, Prentice Hall,
(.), Karl J. Astrom, Bjorn Wittenmark (1996.), Computer-Controlled Systems, Theory and Design, Prentice Hall,

#### General

ID 222760
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
15 Exercises
12 Laboratory exercises

Excellent
Very Good
Good
Acceptable

#### Learning Outcomes

1. Classify systems using their basic properties
2. Compute and analyse a transfer function of a LTI system
3. Compute and analyse a frequency response of a LTI system
4. Use a computer to simulate a LTI system
5. Conclude if a control system is stable
6. Compute state-space representation of a system
7. Compute a discrete transfer function
8. Compute recursive differential equations of a control system
9. Apply a PID controller

#### Forms of Teaching

Lectures

Lectures will be performed every week in the classroom for a duration of 3 school hours.

Exercises

Auditorium exercises will be performed within the Lecture hours.

Laboratory

Laboratorium exercises will be performed periodically after relevant material given in the Lectures.

#### Week by Week Schedule

1. Modeling of signals and systems, Linear differential and difference systems
2. Motivation for using control systems, Block diagrams and algebra
3. State space representation of continuous control systems , Transient and impulse system response, Forced and natural system response
4. Examples and properties of Laplace transform, Inverse transform; Convolution
5. Pole and zero influence on LTI system time response, Control system quality criteria in time domain
6. Z-transform, Modeling of digital control system elements
7. Euler forward and backward discretization, Difference equations
8. Midterm exam
9. Transfer function of discrete control systems
10. Block diagrams of discrete control systems
11. State-space representation of discrete control systems
12. PID controller structures, Tuning of PID controller parameters; Ziegler-Nichols methods
13. Tuning of PID controller parameters; Ziegler-Nichols methods, Practical aspects of PID controller design; Filtering; Anti-windup
14. Digital PID controller synthesis
15. Final exam

#### Study Programmes

Audio Technologies and Electroacoustics (profile)
Free Elective Courses (1. semester) (3. semester)
Communication and Space Technologies (profile)
Free Elective Courses (1. semester) (3. semester)
Computational Modelling in Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Computer Science (profile)
Free Elective Courses (1. semester) (3. semester)
Control Systems and Robotics (profile)
Core-elective courses 1 (1. semester)
Data Science (profile)
Free Elective Courses (1. semester) (3. semester)
Electrical Power Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electric Machines, Drives and Automation (profile)
Free Elective Courses (1. semester) (3. semester)
Electronic and Computer Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Electronics (profile)
Free Elective Courses (1. semester) (3. semester)
Information and Communication Engineering (profile)
Free Elective Courses (1. semester) (3. semester)
Network Science (profile)
Free Elective Courses (1. semester) (3. semester)
Software Engineering and Information Systems (profile)
Elective Course of the profile (3. semester) Elective Course of the Profile (1. semester)

#### Literature

(.), N. Perić, Z. Vukić, M. Baotić, M. Vašak, N. Mišković (2010.), Automatsko upravljanje - predavanja, Sveučilište u Zagrebu Fakultet elektrotehnike i računarstva,
(.), Z. Vukić, Lj. Kuljača (2005.), Automatsko upravljanje - analiza linearnih sustava upravljanja, Kigen,
(.), Gene F. Franklin, J. David Powell, Michael L. Workman (1997.), Digital Control of Dynamic Systems - Third Edition, Prentice Hall,
(.), Karl J. Astrom, Bjorn Wittenmark (1996.), Computer-Controlled Systems, Theory and Design, Prentice Hall,

#### General

ID 222760
Winter semester
5 ECTS
L3 English Level
L1 e-Learning
45 Lectures
15 Exercises
12 Laboratory exercises