Self-balancing mobile platforms with single spherical wheel, generally called ballbots, are suitable example of underactuated systems. Balancing control of a ballbot platform, which aims to maintain the upright orientation by rejecting external disturbances, is important during station keeping or trajectory tracking. In this paper, acceleration based balancing and position control of a single spherical wheeled mobile platform that has three single-row omniwheel drive mechanism is examined. Robustness of the balancing controller is achieved by employing cascaded position, velocity and current control loops enhanced with acceleration feedback (AFB) to provide higher stiffness to the platform. The effectiveness of the proposed balancing controller is compared with commonly used optimal state feedback method. Additionally, the position controller is designed by utilizing the dynamic conversion of desired torques on the ball that are calculated from virtual control inputs generated in the inertial coordinates. Dynamical model of a ballbot platform is investigated by considering highly nonlinear couplings. Performance of the controllers are presented via simulation results where the external torques were applied on the body in order to test disturbance rejection capabilities.