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In the recent years, the control of Unmanned Aerial Vehicles (UAV) has become one of the most interesting field of research, especially for Vertical Take-Off and Landing vehicles (V TOL) , due to the needs to such system, the simplicity of their construction and due to the important technological advances in control boards, sensors, communication tools, energy storage. In this paper, a mathematical model has been developed with Lagrange formalism and a control approach based on Propor tional Derivative PD controller has been built and provided with numerical simulation in MATLAB/Simulink. Index Terms-Quadrotor,Unmanned Aerial Vehicles(UAV), Modelling, PD control, Trajectory. I. IN TRODUCTIONThe UAVs are used in large variety of fields such as surveil lance, commercial delivery, military, rescue. Due to their great manoeuvrability, ability to take off and land vertically, hover performance and higher payload, the quadrotor aircraft is the optimal solution for dangerous mission and access into several areas which cannot be accessed by traditional air planes nor helicopters. The quadrotor is a Ve rtical Ta ke-Off and Landing (VTOL) aircraft. It consists of 4 propellers arranged on X or + configuration, every arm holds a rotor (motor + propeller) on its end as shown in figure 1. The motion of the quadrotor can be controlled through varying the speed of the propellers which can produce one of the following motions : Roll: This motion is accomplished by increasing (decreasing) the speed of the motor 1 and decreasing (increasing) the speed of the motor 3, Pitch: It is the rotation around the Y axis, it can be done by increasing (decreasing) the speed of the motor 2 and decreasing (increasing) the speed of the motor 4, Yaw: To rotate the quadrotor around the Z axis, it's provided 978-1-4799-5907-5/14/$31.00 ©2014 IEEE

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Model estimation is an important step in quadrotor control design because model uncertainties can cause unstable behavior especially with non-robust control methods. In this paper, a modeling approach of a quadrotor prototype has been proposed. First an initial dynamic model of quadrotor UAV based on Euler-Lagrange formalism was developed. Then the roll system has been estimated using closed loop identification method and frequency domain analysis. An experimental tests has been performed for the roll system to validate the estimated dynamic model.

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