The shaking motion of a Wheeled Inverted Pendulum (WIP) is attenuated. There is a dead zone inside the actuators in a WIP, which leads to a limit cycle like manifested as a shaking motion. In this study, an estimator based on the behavior of the energy applied to the pendulum is proposed to identify the magnitude of the dead zone, which is used for dead zone compensation. The amount of the energy is increasing when using an underestimated compensator and is decreasing when using an overestimated compensator. The estimator is updated to increase or decrease the magnitude of the dead zone according to the energy slope. Two parameters are used for the dead zone compensator: unit increment Δ and update period T. It is not rigorous to select the parameters of the compensator.