In this paper, we apply a fast model predictive control (MPC) for unmanned bicycle system (bike robot) with a configurable balancer. The balancer can be configured to a flywheel mode or a balancer mode by shifting the center of gravity of the balancer according to the situation of the bicycle system. We use MPC because of its advantage, i.e., it is applicable to multi-input multi-output systems, able to handle constraints on actuators, etc. In general, when MPC is applied to a mechanical system, the calculation time is usually larger than one sampling period. To deal with this problem, we propose to use a feedback compensation in the algorithm which make MPC faster than the conventional one.