### Computer Controlled Systems

Data is displayed for academic year: 2023./2024.

#### 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.

#### Study Programmes

[FER3-EN] Control Systems and Robotics - profile
(1. semester)

#### 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.

Continuous Assessment Exam
Laboratory Exercises 10 % 20 % 0 % 20 %
Mid Term Exam: Written 0 % 40 % 0 %
Final Exam: Written 0 % 40 %
Exam: Written 0 % 40 %
Exam: Oral 40 %
##### Comment:

Student must complete all laboratory exercises and achieve at least 10 out of a total of 20 points, i.e. at least 2.5 points out of a possible 5 on each of the 4 exercises. At least 50 out of total 100 points is required to pass the course.

#### Week by Week Schedule

1. Historical overview of control systems, Motivation for using control systems, Classification of signals and systems, Basic control system structures
2. Block diagrams and algebra, Modeling of signals and systems, Linear differential and difference systems, Linearization
3. Transient and impulse system response, Forced and natural system response, State space representation of continuous control systems
4. Laplace transform for continuous linear systems, Transfer function of continuous control systems, Inverse transform
5. Pole and zero influence on linear time-invariant system time response, Control system quality criteria in time domain
6. Stability of LTI systems, Stability from transfer function, Algebraic stability criteria (Hurwitz)
7. Frequency characteristic, Nyquist diagram, Bode diagram, Graphic stability criteria (Nyquist and Bode)
8. Midterm exam
9. Z-transform, Modeling of digital control system elements, Euler forward and backward discretization, Difference equations
10. Transfer function of discrete control systems, 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

#### 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 (1998.), Digital Control of Dynamic Systems, Prentice Hall
Karl J Åström, Björn Wittenmark (2013.), Computer-Controlled Systems, Courier Corporation
GENE F.. POWELL FRANKLIN (J. DAVID. EMAMI NAEINI, ABBAS.), J. David Powell, Abbas Emami-Naeini (2019.), Feedback Control of Dynamic Systems, Global Edition,
Katsuhiko Ogata (2014.), Modern Control Engineering,

#### General

ID 223132
Winter semester
5 ECTS
L1 English Level
L1 e-Learning
60 Lectures
0 Seminar
0 Exercises
12 Laboratory exercises
0 Project laboratory
0 Physical education excercises

87.5 Excellent
75 Very Good
62.5 Good
50 Sufficient