Frequential Analysis of Nonlinear Systems

As its name suggests, a non-linear system is a system that is not linear, i.e. a system for which the principle of superposition does not apply. This characteristic often gives rise to phenomena that cannot be explained by linear automatics. In this context, the aim of this course is to analyze the cause of observed phenomena, predict their characteristics and propose solutions to reduce their inconvenience. The course is illustrated by examples that enable students to apply the tools studied.
The course outline is as follows:
* Definition and illustration of non-linear systems. * Stability of a looped nonlinear system (Popov criterion, circle criterion, off-axis circle criterion). * Presentation and application of the First Harmonic Method for the analysis of a nonlinearity. * Pumping of nonlinear systems: Rewriting the backhand criterion Extension to nonlinear systems Modification of a pumping phenomenon Nonlinear servoing of a linear system Defects in the First Harmonic method.

Linear systems and linear control of systems.
Basic integral calculus.
Mastery of calculations and graphical representations relating to complex numbers.

Automatic

50-page handout