Study Programmes 2016-2017
SYST0002-2  
Modelling and analysis of systems
Duration :
30h Th, 30h Pr, 15h Proj.
Number of credits :
Bachelor in engineering5
Master in aerospace engineering (120 ECTS)5
Master in mechanical engineering (120 ECTS)5
Master in mathematics (120 ECTS)6
Lecturer :
Guillaume Drion
Language(s) of instruction :
French language
Organisation and examination :
Teaching in the first semester, review in January
Units courses prerequisite and corequisite :
Prerequisite or corequisite units are presented within each program
Learning unit contents :
The course focuses on the mathematical representation and analysis of linear, time-invariant systems (LTI systems). It is decomposed into two main parts:
1. LTI systems analysis in time domain.
This part explores the notion of input-output representation of an LTI system on the one hand, and the notion of state-space representation on the other hand. It focuses on the concepts and mathematical tools that are required for the analysis of the dynamical behavior and the input-output response of an LTI system, taking advantage of the properties of linearity and invariance. This part will introduce the notions of convolution, impulse and step responses, variables and state-space models, etc.
  2. LTI systems analysis in frequency domain.
This part explores the notion of frequency response of an LTI system, introducing mathematical tools such as the Laplace and Z transforms, the Fourier transforms (continuous and discrete), the notion of transfer function, the construction of the Bode plots, etc. 
The different parts of the course will be motivated by diverse examples of application that are encountered in engineering. A more detailed description of the course is available on the course webpage:
http://sites.google.com/site/gdrion25/teaching/syst0002
Learning outcomes of the learning unit :
At the end of the course, the student will be able to
  • master the concepts of linearity and time invariance.
  • master the concepts of convolution, variables and state-space representation, Laplace and Z transforms, Fourier transforms (continuous and discrete).
  • construct a state-space model of a dynamical system.
  • linearize a nonlinear dynamical system around a working point.
  • compute the input-output reponse of an LTI system, including the impulse and step responses.
  • compute the transfer function of an LTI system, analyze its frequency response and sketch the Bode plots.
  • know the general form of the transfer function of first and second order systems. 
  • analyze the stability of LTI systems.
  • link the frequency response and time response of an LTI system.
Prerequisite knowledge and skills :
An introductory course on linear algebra and calculus. Basic knowledge in mechanics and electrical circuits is also useful. 
Planned learning activities and teaching methods :
The course is based on 9 lectures on theoretical concepts and applications and 9 tutorials.
For more informations, see the course webpage:
http://sites.google.com/site/gdrion25/teaching/syst0002
Mode of delivery (face-to-face ; distance-learning) :
Face-to-face.
Recommended or required readings :
Slides will be available on the course webpage along the year.
Textbooks on theory and tutorials are also available on the webpage, and printed versions can be bought at the CdC. 
Another useful reference: 'Signals and Systems (2nd Edition)', Alan V. Oppenheim and Alan S. Willsky.
Assessment methods and criteria :
A major project during the year and a written exam (theory + exercices) at the end of the semester.
Work placement(s) :
Organizational remarks :
Detailed informations about the organisation of the course are provided on the course webpage
http://sites.google.com/site/gdrion25/teaching/syst0002
Contacts :
G. Drion (gdrion@ulg.ac.be, Bat. B28, bureau I140).