This work describes the modeling and identification of the parameters of an actual under actuated pendulum that uses an inertial wheel to produce the torque that moves the pendulum arm. The results are validated using a prototype constructed in the System and Control Laboratory at Hope College. This mechanical system is a useful tool for teaching and research. This paper describes the parameter identification methodology of the proposed model. A comparison between simulation and experimental data are included to analyze the accuracy of the model. Different models for non-lineal behavior like certain kinds of frictions and dead-zone effect are presented. This work concludes with a simple strategy to control the swing up and catching the pendulum in its inverted position.