A ball-on-plate system is a mechanical control system for measuring the position of a ball placed on a touch panel and controlling the ball to move to a desired position. This system has been applied to a shelf cart. A hole was made in the center of the top shelf of the cart with a ball-on-plate system installed, allowing objects to be placed on the plate. The cart equipped with this system is named a "level-maintaining shelf cart". When external disturbances act on the cart, the ball- on-plate system ensures that the plate remains level, preventing objects on the plate from sliding or toppling. However, when the cart passes over uneven surfaces or experiences disturbances with acceleration beyond the system's allowable limits, the ball on the touch panel may detach, resulting in an "air ball" state, in which the system cannot measure the position of the ball, leading to instability. To address the air ball state, a compensator consisting of a closed-loop observer and full-state feedback for the ball-on-plate system is designed. A model for the closed-loop observer was created by modeling the ball-on-plate system. Experiments confirmed that the system could maintain stable control even in an air ball state.