Acrobot, a planar two-link robot with an actuator only at its elbow, is a typical example for underactuated systems. We stabilize the Acrobot by using a linear quadratic controller with a fixed set of coefficients. The difficulty of the problem arises from the real uncertainties in its parameters. In the presence of real uncertainties, stabilizing two joint angles using a single actuator, resembles a variety of electromechanical motion control problems in many senses. We model the problem as a real structured singular value model so that the designer knows in advance that which size of uncertainty does not harm the achievement of the stabilization objective. It is well known that compared to unstructured models, the structured models provide less conservative results, which is the main motivation in selecting this kind of modeling. As a natural consequence of using the structured singular value modeling, the size of the uncertainty is expressed as a scalar quantity called mu. We present the uncertain system model in SIMULINK environment, and validate our results through a set of simulations.