This paper presents a theoretical study of an inertial actuator connected to an accelerometer by a local feedback loop for active vibration control on a floating raft. On the criterion of the minimum power transmission from the vibratory machines to the flexible foundation in the floating raft, the best mounting positions for the inertial actuator on the intermediate mass of the floating raft are investigated. Simulation results indicate that the best mounting positions for the inertial actuator vary with frequency. To control time-varying excitations of vibratory machines on a floating raft effectively, an automatic control system based on real-time measurement of a cost function and automatically searching the best mounting position of the inertial actuator is proposed. To the best of our knowledge, it is the first time that an automatic control system is proposed to move an actuator automatically for controlling a time-varying excitation.