OVERVIEW

This subject provides analytical and numerical (in MATLAB environment) tools for the analysis, modelling, simulation, and synthesis/design of nonlinear dynamical systems.

Several case studies and working examples are proposed, with emphasis on models of circuit oscillators, PLLs, and Sigma-Delta modulators.

AIMS AND CONTENT

LEARNING OUTCOMES

This subject aims to provide analytical and numerical skills for the analysis, modelling (both physics-based and data-driven), parameter setting, and simulation of nonlinear circuits and systems. The theory is substantiated through SW implementation in MATLAB code and HW demonstrations.

AIMS AND LEARNING OUTCOMES

It is expected that at the end of this subject the student will be able to analyze (analytically and/or numerically) a nonlinear dynamical system, even if dependent on parameters. Moreover, he/she should be able to synthesize some classes of nonlinear dynamical systems. To this end, during the lectures the student will have to learn and apply analytical and numerical (MATLAB) tools for simulation, analysis and synthesis of nonlinear dynamical systems.

PREREQUISITES

Basic concepts of mathematics, physics, signal processing, automatic controls, electronics.

TEACHING METHODS

Combination of:

-) traditional lectures (about 30 hours), including demos with hardware-implemented real systems

-) MATLAB sessions (about 20 hours), about simulation and analysis of dynamical systems

Students with valid certifications for Specific Learning Disorders (SLDs), disabilities or other educational needs are invited to contact the teacher and the School's contact person for disability at the beginning of teaching to agree on possible teaching arrangements that, while respecting the teaching objectives, take into account individual learning patterns. Contacts of the School's disability contact person can be found at the following link Comitato di Ateneo per l’inclusione delle studentesse e degli studenti con disabilità o con DSA | UniGe | Università di Genova

SYLLABUS/CONTENT

-) Modeling of nonlinear systems

-) Numerical methods for integrating ordinary differential equations and finding roots of nonlinear functions

-) Continuous-time and discrete-time "smooth" dynamical systems

-) Analysis with fixed parameters

-) Stationary (equilibrium points), periodic (limit cycles), quasi-periodic (tori), aperiodic (chaos) steady state

-) Coupled oscillators and networks of dynamical systems

-) Analysis with varying parameters (bifurcations)

-) Electronic oscillators (Van der Pol, Colpitts), phase-locked loops (PLLs), and Sigma-Delta modulators

Some lectures are concerned with MATLAB computer simulation exercises, aimed to apply and reinforce the main teaching topics.

RECOMMENDED READING/BIBLIOGRAPHY

-) Notes provided by the lecturer (partially in Italian)

-) M. Parodi, M. Storace, Linear and Nonlinear Circuits: Basic & Advanced Concepts, Vol. 2, Lecture Notes in Electrical Engineering, Springer, 2020, ISBN: 978-3-030-35044-4 (ebook) or 978-3-030-35043-7 (hardcover), DOI: 10.1007/978-3-030-35044-4

-) S.H. Strogatz, Nonlinear dynamics and chaos, Addison-Wesley, 1994

All the above material contains written parts, illustrative figures and diagrams, so it should be suitable also for students with disabilities or specific learning disorders (DSA). Alternative solutions will be evaluated on a case-by-case basis.

TEACHERS AND EXAM BOARD

LESSONS

LESSONS START

See

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.

Upon student demand, the oral examination can be focused on the analysis of a specific nonlinear dynamical system (assigned by the teacher), using the analytical and numerical tools introduced during the lectures.

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

The assessment will be based on:

-) communication skills

-) knowledge and comprehension of the subject topics

-) ability of drawing connections among ideas

-) ability of analyzing nonlinear dynamical systems

-) ability of deciding what subset of tools can be (or must be) used to analyze a given system (i.e., of using information in partially new situations) and of justifying each decision

FURTHER INFORMATION

Students who have valid certification of physical or learning disabilities on file with the University and who wish to discuss possible accommodations or other circumstances regarding lectures, coursework and exams, should speak both with the instructor and with Professor Federico Scarpa (federico.scarpa@unige.it ), the School's disability liaison.