Dr. Xing and Professor Refvem are working to research and develop a quadruped robot that is capable of basic movements including walking, running, and jumping. As senior project group F-11, we are joining a team of engineers to assist in the development of the quadruped. Our team was tasked with creating a mathematical model, designing a control method, and implementing that control method for the quadruped's legs in Simulink. This will allow both current and future students to understand the response of the system and provide a building point for future researchers to create working quadrupedal robots. This report documents our research and cumulative work to reach our goals. The report highlights our final design for the controller loop, our implementation process for each controller component, and our design verification tests to justify our work.