Unmanned Aerial Vehicles (UAVs) have been used extensively in many applications, such as surveillance, medical transportation and delivery tasks. These applications usually involve an attachment system to connect a payload. However, when connected to such a coupled system, the UAV exhibits lower flight performance mainly due to gust loads. Mathematical modeling is used in this paper to illustrate the comparison between an UAV with a coupled system and a conventional UAV. Proportional Derivative (PD) and Sliding Mode Control (SMC) approaches are used to evaluate the vibrations of the payload, and the UAV trajectory subjected to Dryden gust. This work therefore uses these methods to investigate the dynamic response of a quadrotor-type UAV equipped with a payload and a flexible attachment system.