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In next generation optical disk system, the disk rotation speed becomes nearly equal to 10000[rpm]. Since the optical disk systems have a radial run-out, its phenomenon becomes the periodic disturbance whose bandwidth depends on the disk rotational speed. Hence, the tracking control system of next generation optical disk recording system should have the robust precision control against the high speed periodic disturbance whose rotational speed is nearly equal to 10000[rpm]. Moreover, this tracking servo system should have and the wide bandwidth. For this purpose, the feedforward controllers such as Zero Error Phase Tracking (ZPET) control and Perfect Tracking Control (PTC), have been proposed the tracking control for the mass strage system. However, for the next generation optical disk system, it is sometimes diffcult to realize the feedforward controller for suppression of high speed periodic disturbance. This paper proposes the structure of feedforward controller based on the prediction of tracking error. Moreover, the total control structure realizes the proposed feedforward controller with a new robust feedback control system. The experiment results point out that the proposed system well regulates the high precision tracking control on condition of the disk rotation speed 8000[rpm], which is equal to the rotation speed of 40 X speed on CD system.