PRESENTAZIONE

Systems' Theory is one of the first discipline where mathematical and real aspects of engineering meet. Different skills are integrated to build and analyze mathematical models representing actual systems, in order to understand, foresee and control their behaviour.

OBIETTIVI E CONTENUTI

OBIETTIVI FORMATIVI

The teaching unit aims to provide students with the theoretical and methodological tools for modelling, analysing, and controlling linear dynamic systems.
The topics covered are presented to students in a way that helps them become familiar with essential tools from mathematics and geometry needed for systems modelling and control.

OBIETTIVI FORMATIVI (DETTAGLIO) E RISULTATI DI APPRENDIMENTO

The course aims to provide the students with the necessary methods to analyze mathematical models for dynamic systems. The learning outcomes of the course refer to the capacity of

-        understanding the main features of the system dynamics;

-        knowing the formal representations of continuous-time and discrete-time linear time-invariant dynamic systems

-        knowing the structural properties of continuous-time linear time-invariant dynamic systems, with main focus on stability properties

-        analyzing several stability properties of a given system;

-        verifying structural properties (reachability, observability) of a given system;

-        designing stabilizing actions possibly also aimed at improving the dynamics of continuous-time linear time-invariant systems, by means of algebraic feedback;

-        designing a state observer in case the system state is not accessible.

PREREQUISITI

The student must have adequate knowledge of Mathematics, Physics, and Geometry.

MODALITA' DIDATTICHE

The course offers classroom lessons that cover detailed methods for analyzing and controlling dynamic systems, including numerical examples also using the Matlab software environment.

Depending on particular weather alerts, lessons may be taught in blended modality and/or with the availability of video lessons.

Students with valid certifications for Specific Learning Disorders (SLD), disabilities, or other educational needs are invited to contact the teacher and the disability referent of the Polytechnic School, Prof. Federico Scarpa (federico.scarpa@unige.it), at the beginning of the course to discuss potential teaching methods that, while respecting the course objectives, take individual learning styles into account.

Student workers can contact the teacher at the beginning of the course to receive information about the teaching materials.

PROGRAMMA/CONTENUTO

Dynamic systems: types and representations.

Generalized functions for continuous-time and discrete-time systems. Laplace transform: properties, rules, transformation and antitransformation, time limits theorems. Zeta transform: properties, rules, transformation and antitransformation, time limits theorems.

Calculation of transition function for linear stationary systems represented in SISO external form. Transfer function, impulse response, frequency response.

Internal representation and state variables: computation of the transition function.

Structural stability and BIBO stability.

Definitions of reachability and observability: criteria and conditions.

Design of algebraic state-feedback and output-feedback schemes.

Design of the Luenberger state observer.

Effects on the structural properties of the blocks connections and of possible simplifications.

TESTI/BIBLIOGRAFIA

All teaching materials will be available on Aulaweb. Generally, notes taken during lessons and the slides provided on Aulaweb are sufficient to meet the learning objectives.

Potential books for comprehensive analysis are the following:

• Rinaldi Piccardi: I sistemi lineari: teoria ed applicazioni. CLUP
• Bolzern, Scattolini, Schiavoni: Fondamenti di Controlli Automatici, McGraw Hill
• Antsaklis Michell: Linear Systems

DOCENTI E COMMISSIONI

LEZIONI

INIZIO LEZIONI

https://easyacademy.unige.it/portalestudenti/index.php?view=easycourse&_lang=it&include=corso

Orari delle lezioni

L'orario di questo insegnamento è consultabile all'indirizzo: Portale EasyAcademy

ESAMI

MODALITA' D'ESAME

The student must undergo a compulsory written examination. An additional oral exam can be done, but it is not mandatory. During the exam the student has to solve numerical exercises and to explain the theoretical notions necessary for their solution

MODALITA' DI ACCERTAMENTO

The exam aims to assess the following aspects of the student’s preparation:

• the ability to analyze the structural and behavioural characteristics of linear time-invariant dynamic systems;
• the ability to design actions to improve the dynamic behaviour of the system under consideration;
• the ability to design state observation techniques for a linear dynamic system.

The exam assessment will take into account not only knowledge of the course contents, but also calculation skills and logical reasoning abilities in solving numerical examples.

ALTRE INFORMAZIONI

Students with certified SLD, disabilities, or other special educational needs are advised to contact the teacher at the beginning of the course to agree on assessment methods, considering individual learning needs while respecting the teaching objectives.

Student workers are advised to contact the teacher to agree on assessment methods.