Purpose of this paper is realization of high-speed measurement atomic force microscope (AFM) from view point of the control technology without modification of the hardware. Almost commercial AFM, 3D-image is obtained from control input. High-speed imaging is possible if we can design feedback controller which achieves the high-bandwidth servo design. However, we know that it is restricted by bode integral theorem as resonance peak of the plant. For high-speed imaging, our research group proposed surface topography observer which based on the disturbance observer theory. we can locate the pole of the observer without considering of the resonance of the plant. Thus, we succeeded in high-speed imaging by our proposed observer. On the other hand, as the scanning speed of the X scanner becomes faster, the tracking error increases, because the feedback characteristic is same as conventional system. Not only the high-speed imaging but the suppression of the tracking error is important, because the tracking error express the contact force to the sample. Our research group proposed the tracking error suppression methods which are feedforward compensation. This paper describes the dual-directional type surface topography learning observer. This paper shows our proposed methods which are effective for the high-speed AFM by simulation and experimental results.