The use of numerical methods for solving problems whose analytical solution is unknown is of fundamental importance not only in the field of engineering. A goal of particular interest in the field of naval engineering is the numerical simulation of dynamic systems. The course aims to provide the student knowledge about numerical methods for naval engineering problems, particularly with regard to the solution of systems of nonlinear equations, dynamic systems, data fitting and optimization.
Providing students with the theoretical foundations of numerical methods and application examples in the naval sector.
Active participation in lectures and individual study will allow the student to:
- choose the most appropriate numerical method to solve some problems that require numerical resolution;
- understand why numerical instabilities or lack of convergence may appear and how to avoid such difficulties;
- know the basics of numerical methods for solving systems of nonlinear equations, data fitting and least squares, systems of differential equations and constrained and unconstrained optimization, finite differences for partial derivative equations;
- implement these methods using Matlab, the most widely used scientific computing software in the world;
- be able to use Matlab functions other than those seen in the course and debug the code;
- analyze the stability of a dynamic system in closed loop;
- design and simulate a regulator for dynamic systems in closed loop.
Each lecture consists of a frontal lecture in which the numerical methods are described, and an exercise carried out in Matlab in which the methods seen are applied to a problem of interest to Naval Engineering.
Since the theoretical lectures are complemented by implementation in Matlab, the theoretical part is not particularly extensive. The focus is mainly on the practical aspects of the numerical methods considered.
The main topics covered are listed below:
- introduction to Matlab: matrices and vectors, 1d and 2D graphics, control structures, functions, creation of an app;
- numerical methods for solving equations and nonlinear systems;
- polynomial interpolation, data fitting, least squares method;
- numerical resolution of systems of ordinary differential equations;
- numerical methods for constrained and unconstrained optimization;
- state observer for dynamic systems;
- output feedback through state observers.
The notes taken during the lessons and the material provided ( notes of the theoretical part and tutorial of Matlab) are sufficient for the preparation of the exam. The books listed below are suggested as possible support texts and in-depth study.
- Quarteroni, F. Saleri, Introduzione al Calcolo Scientifico, Sprinter-Verlag 2006.
- Quarteroni, Modellistica Numerica per Problemi Differenziali, Springer-Verlag 2008.
- S. Chapra, R. Canale, Numerical methods for Engineers, McGraw-Hill, 2018.
- D. Xue, Y. Chen, D.P. Atherton, Linear Feedback Control: Analysis and Design with MATLAB (Advances in Design and Control), SIAM, 2007.
- T. Kailath, Linear Systems, Paperback, Prentice Hall, 2016.
- T.I. Fossen, Guidance and Control of Ocean Vehicles, Wiley, Chichester, NY.
Ricevimento: By appointment, to be scheduled by contacting on Teams or by mail to patrizia.bagnerini@unige.it.
Ricevimento: For questions, contact the lecturer to agree on the time of meeting.
PATRIZIA BAGNERINI (President)
ANGELO ALESSANDRI (President Substitute)
ENRICO MASSA (President Substitute)
https://corsi.unige.it/8738/p/studenti-orario
The exam consists in passing an oral test. Examination dates are arranged with the teacher by appointment.
In the oral test is required to perform a short application in Matlab (with the possibility of using the help) and answer some questions on the theoretical part.
