Application de la commande B à un quadricoptère

Abstract

Constant improvement of electronics speed computing makes possible the implementation of more efficient control algorithms. The patented B-control from Professor Bensoussan's takes advantage of this faster computation speed to combine simultaneously a faster temporal response and better stability and robustness objectives compared to other controls. Its effectiveness was proved by simulations relating to the control of a hard disk reading arm and then, experimentally, on an unstable system: a magnetic levitation experimentation. These two applications have resulted in excellent results. To confirm the potential of this algorithm, the next step is to develop it for a multi-variable system. The quadcopter appears as an ideal candidate to test the feasibility of the B control. A quadcopter is a multirotor helicopter with four arms, each with a motor and a propeller at the end. This type of drone evolves in a 3-dimensional space from the control of its four motors. This multiplicity of input-outputs makes the system difficult to control because they influence each other. In addition, in flight the quadcopter is subject to many external disturbances such as wind, obstacles, wind back from the ground when approaching or radiation near a wall. To absorb these many interferences, it is necessary to have a robust control. The experiments carried out previously with the B control have proved its ability to combine a very fast time response while maintaining an excellent robustness, whereas the other control algorithms need to make a compromise between these two performances (frequency and time). This thesis was an opportunity to write the theoretical foundations of a new control method: The B control. The design method of this command, in the mono-variable then multivariable case, was detailed. Then, capability of the B control to effectively decouple inputs and outputs on a 2×2 system has been proven by simulation. The numerous simulations result made possible to appreciate the good temporals, frequency and energetics performances of the B control relatively to other linear commands of reference such as: H2; H∞; μ-synthesis; PID; backstepping et hiérarchique. The practical part has detailed the dimensioning of a real drone. Then, steady flights tests shown in the case of B control a better minimization of the displacements along the horizontal axes as well as a minimization of the amplitude of the signals of commands relatively to a classic control like the PID. Limitations of the drone model used for the practical tests and suggestions for improvements were exposed.

Date	14 Aug 2019
Original language	French
Awarding Institution	École de technologie supérieure
Supervisor	David Bensoussan (Supervisor) & René Jr. Landry (Co-supervisor)