Modeling and control of dynamic systems

Objectives

Presentation of the state formalism with respect to the transfer function, implementation for modeling the dynamic behavior of an aeronautical system and implementation in Matlab-Simulink.

Skills acquired

Knowledge of the notions of state representation of dynamic systems for flight control.
Mobilize a broad field of fundamental and technical sciences related to avionics and space systems, and have the associated analytical and synthesis skills
Have a global systems approach
Communicate and work as part of a team

Laplace transform matrix algebra transfer functions : AP5SIMAI

Contents

The first chapter recalls the notion of dynamic system and equilibrium point. The dynamic system presented in this chapter corresponds to the longitudinal behavior of an aircraft. This non-linear behavior is modeled as a state and then linearized around an equilibrium point, which corresponds to cruising flight
The second chapter deals with the notion of state associated with a linear dynamic system and the link with the notion of transfer function studied in the 1st year course
The third chapter deals with the different canonical forms of state representation (comp, diagonal/Jordan) and the associated block diagrams
The final chapter is devoted to determining the solution to the equation of state either directly by calculating the matrix exponential in the diagonal/Jordan basis, or using Laplace's operational calculus. Once the solution has been established, the notion of internal stability is recalled and the internal stability criterion is given

Teaching method
This course will be taught in the form of integrated lectures using Matlab-Simulink, preceded by preparatory work online. The concepts studied will be put to practical use on a real process.

Digital maintenance