### Discrete Event Control Systems

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

#### Course Description

The notion of events and discrete event systems, and their relation to time-driven systems. Discrete event system states. Basics of graph theory. Modeling and simulation of discrete event systems. Static, dynamic and colored Petri nets. Basics of max-plus algebra. String algebra and matrix description of discrete event systems. Discrete-event system analysis (observability, stability, conflict, and deadlock). Synthesis of discrete-event systems and feedback. Controllability, control methods and design of supervisors. The concept of hybrid automata and modeling of hybrid systems. Examples of systems with discrete events (transport systems, warehouses, automated production lines, communication systems, networks).

#### Study Programmes

[FER3-EN] Control Systems and Robotics - profile
Elective course (3. semester)

#### Learning Outcomes

1. Recognize discrete event systems
2. Explain functioning of discrete event systems
3. Apply formal modelling methods of discrete event systems
4. Analyze structural properties of discrete event systems based on Petri nets
5. Develop control algorithms for discrete event systems

#### Forms of Teaching

Lectures

lectures

Exercises

exercise in problem solving

Laboratory

simulations

#### Week by Week Schedule

1. Graph representation of max-plus model
2. Basic max-plus algebraic properties
3. State-space equations, Cyclic behavior and eigenvalues
4. Petri net graph representation, System modeling by Petri nets
5. State-transition equation, Structural properties of Petri nets
6. Structural properties of Petri nets
7. System control by Petri nets
8. Midterm exam
9. System matrices
10. Matrix based system analysis
11. Matrix based system synthesis
12. Implementation aspects of matrix controller
13. Hybrid automaton, Modeling and simulation of hybrid systems
14. Stability of hybrid systems
15. Final exam

#### Literature

(.), S. Bogdan, F.L. Lewis, Z. Kovacic, J. Mireles (2005.), Manufacturing Systems Control Design, Springer-Verlag,
(.), C.G. Cassandras, S. Lafortune (1999.), Introduction to Discrete Event Systems, Kluwer,
(.), F. Baccelli, G. Cohen, G.J. Olsder, J.P. Quadrat (1995.), Synchroniyation and Linearity: An Algebra for Discrete Event Systems, MIT Press,

#### General

ID 223751
Winter semester
5 ECTS
L1 English Level
L1 e-Learning
30 Lectures
0 Seminar
15 Exercises
8 Laboratory exercises
0 Project laboratory