OVERVIEW

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.

AIMS AND CONTENT

LEARNING OUTCOMES

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.

AIMS AND LEARNING OUTCOMES

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.

PREREQUISITES

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

TEACHING METHODS

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.

SYLLABUS/CONTENT

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.

RECOMMENDED READING/BIBLIOGRAPHY

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

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

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

Class schedule

The timetable for this course is available here: Portale EasyAcademy

EXAMS

EXAM DESCRIPTION

Oral examination. Students with learning disorders ("disturbi specifici di apprendimento", DSA) will be allowed to use specific modalities and supports that will be determined on a case-by-case basis in agreement with the delegate of the Engineering courses in the Committee for the Inclusion of Students with Disabilities.

ASSESSMENT METHODS

Analysis of the properties of a dynamic system. Starting from an exercise students are required to show theircomprehension about the behavior of dynamical systems and the characterizing  properties.