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Modelling and analysis of dynamical systems [ LINMA2370 ]


5.0 crédits ECTS  30.0 h + 22.5 h   1q 

Teacher(s) Dochain Denis (coordinator) ; Delvenne Jean-Charles ;
Language French
Place
of the course
Louvain-la-Neuve
Online resources

> https://icampus.uclouvain.be/claroline/course/index.php?cid=LINMA2370

Prerequisites

Basic calculus and linear algebra, such as taught in LFSAB1101 (Mathématiques I) et LFSAB1102 (Mathématiques II)

Main themes

First part : presentation of the modelling principles and methods in various areas of engineering sciences : electricity, mechanics, chemical and biochemical processes, environment. Second part : presentation of the major methods for the analysis of the structural properties of state space models : state transformations, equilibria, stability and attractors, controllability, singular perturbations.

Aims

Learning outcomes:

  • AA1 : 1,2,3
  • AA4 : 1,2,3,4  
  • AA5 : 2,3,5,6       

More specifically, at the end of the course the student:

  • will be aware of the unifying character of the state space model concept in engineering sciences.
  • will be able to model a wide span of situations encountered in diverse engineering sciences
  • will be able to analyze the properties of those dynamical systems defined on a state space

Transversal learning outcomes:

  • Using Matlab and Simulink for the modelling and simulation of dynamical systems.
Evaluation methods

Project during the semester, with oral and written report. Written exam.

Teaching methods

Ex cathedra, with reading of notes by the students previously to the course.

Content

MODELING - mechanical, electrical, electromechanical systems - compartmental systems - reactional systems - systematic applications in various areas ANALYSIS - state transformations - equilibria - qualitative analysis of trajectories in the plane, periodical solutions, limited cycles, bifurcations - stability analysis : Lyapunov methods - controllability and stabilisation of linear and nonlinear systems

Bibliography

Notes available on iCampus.

Cycle et année
d'étude
> Master [120] in Statistics: General
> Master [120] in Biomedical Engineering
> Master [120] in Mathematical Engineering
> Master [120] in Electro-mechanical Engineering
> Master [120] in Chemical and Materials Engineering
Faculty or entity
in charge
> MAP


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