The objective of this article is to make a contribution relating to the modeling, control, simulation and stabilization of a complex system, with six degrees of freedom of a particular drone which presents many advantages and challenges. On the technological, military, political and other levels with an enormous and beneficial social contribution, it is a quadrotor which is a nonlinear, strongly coupled and unstable system. Such a structure is difficult to master, because the control is multivariable in the sense that six degrees of freedom are to be controlled simultaneously and operating in an environment subject to disturbances. Two commands, in particular Backstepping and PID, will be applied to obtain the stabilization of the quadcopter at the desired values, in attitude and in altitude. This article presents the comparative results of the performance of the quadcopter under the two controls. The effect of the parameters of each command on the response time of the system is elucidated under the Matlab/Simulink environment. For a simulation time of up to 10 seconds minimum with a less good response time of almost 2 seconds for the PID control, these results prove the robustness of the Backstepping command.