Modelling and analysis of dynamical systems [ LINMA2370 ]

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

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

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.

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.

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

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

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

Notes available on iCampus.