The purpose of this honors thesis was to create a quadcopter equation of motion software model in order to develop a control system to make the quadcopter autonomous. This control system was developed using Matlab and Simulink, and the aspects of the quadcopter's flight that were chosen to be controlled were the roll angle, pitch angle, and height of the quadcopter. Upon the completion of this control system model, the actual quadcopter was to be constructed, flown, and used to collect experimental data for comparison to the model. However, the hardware was never made available due to back order problems, and so unfortunately no experimental data from actual test flights was able to be gathered and compared to the Simulink control system model. None the less, the final Simulink model is still accurate because the actual geometry of the chosen quadcopter was used during simulation (including the moments of inertia and moment arm lengths). To begin, background research into quadcopter design is presented to give insight into the progress that has been made in the design of this type of aircraft. The equations of motion for the quadcopter considered in the control system are then derived through the use of twelve state variables. The Simulink model for the open loop system was then constructed in a fashion that converts the change in rotor thrust to the associated orientation angles of the quadcopter. Linear approximations were then used to distinguish the open loop transfer functions for each controlled variable (roll angle, pitch angle, and height), and compensators were designed for the control system in order to produce a natural frequency and damping that allowed for a 5% settling time of approximately two seconds.