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This paper discusses a reaction wheel control system. A reaction wheel pendulum is good example of a non linear and underactuated system, which attracts control system researchers to develop many control algorithm. The reaction wheel plant is usually used for studying advanced control system courses. In this paper, a mathematical model of the state space is discusses. A proposed LQR (Linear Quadratic Regulator) control algorithm is explained. Simulation and real time experiments have seen carried out to varify the performance of the proposed closed loop system. The LQR (Linear Quadratic Regulator) optimisation algorithm was able to find the optimum feed back gains. The simulation and real time experiments show that the reaction wheel pendulum could stabilize the pendulum at upright position.