CFU: 6
Prerequisites
Basic knowledge about closed loop control systems.
Preliminary Courses
None.
Learning Goals
The course aims at providing students with
- a set of tools for the analysis and control of networks of dynamical systems, with a special emphasis on their optimization and safety, and on their possible use for the design and management in diverse engineering applications
- a set of tools to model discrete event systems in the context of industrial automation and to design supervisory control systems. The course will focus on the finite state automata and language theory, as well as on Petri nets.
Expected Learning Outcomes
Knowledge and understanding
The course provides students the tools to analyze the behavior of discrete event systems (DES) and to design supervisory control systems. The student needs to show that he/she understood the peculiarities of DES and he/she is able to analyze the behavior of this special class of nonlinear systems.
Applying knowledge and understanding
The student needs to show that he/she is able to model real systems, such as flexible manufacturing systems, logistic systems, IT systems, as DES by using either automata or Petri nets. The student needs also to show that he/she is able to formalize the control requirements for supervisory control and design the correspondent controller (supervisor).
Course Content - Syllabus
- Introduction to DES
- Systems and models
- Discrete event systems
- Logic and timed models
- Languages and automata
- Languages
- Operations on languages
- Definition of (logic and deterministic) automata
- Generated and marked languages of an automata
- Operations on automata
- Canonical recognizer of a regular language
- State space minimization
- Non-deterministic (logic) automata
- Observers
- Fault diagnosis and diagnosers
- Regular expressions
- The class of regular languages Reg(E) and recognizable languages. Kleene theorem
- Pumping lemmas for regular and context free languages
- Chomsky grammars
- Decidability and complexity
- Timed automata: the deterministic and the stochastic case
- Petri Nets
- Petri nets and Petri net systems
- Petri net languages
- Reachability set
- Labeled net systems: generated and marked language
- Reachability and coverability graphs
- Behavioural properties: reachability, boundedness, conservativity, repeatibility, reversibility, liveness
- Structural properties: P- and T-invariants, siphons and traps
- Estimation of the reachability set
- Classes of P/T nets and ordinary nets subclasses
- Observability of net systems with uncertain marking: the observer coverability graph
- K-diagnosability in bounded Petri nets via integer linear programming
- Timed Petri nets: the server semantic
- Supervisory control
- Control requirements
- The concept of supervisor and supervisory control under complete controllability and observability
- Supervisory control in presence of uncontrollable events
- Controllability theorem
- Controllable languages
- Controllability test for regular languages
- Supremal controllable sublanguage and infimal prefix-closed superlanguage
- Controllability and non-conflicting
- Basic Supervisory Control Problem e Dual Basic Supervisory Control Problem
- Controllability and non-blocking theorem
- Observable languages
- Controllability and observability theorem
- Supervisory control in Petri nets using Generalized Mutual Exclusion Constraints
Readings/Bibliography
C. G. Cassandras e S. Lafortune, Introduction to Discrete Event Systems. Springer, 2008.
A. Di Febbraro e A. Giua, Sistemi ad eventi discreti. McGraw-Hill, 2002.
Control of Discrete-Event Systems. Springer, 2013.
Material available at http://wpage.unina.it/detommas/dssc.html
Teaching Method
The teaching activities will be organized as follows: a) lectures for about 70% of the total hours, b) practical exercise in the classroom based on software tools (UMDES, TINA, ecc.) for about 30% of the total hours.
Examination/Evaluation criteria
Exam type
Only oral. The oral exam focused on the discussion of a homework assigned to student by the instructor. The oral examination will also aim at assessing the knowledge of all the concepts and contents given during the lectures.
Evaluation pattern
The final mark is weighted with respect to the CFU of each module as follows:
- Module Discrete event systems and supervisory control, 6 CFU, 50%
- Module Control of complex systems and networks, 6 CFU, 50%