This article studies ultrahigh-precision positioning with piezoactuators in scanning probe microscopy (SPM) applications. Loss of positioning precision in piezoactuators occurs: 1) due to hysteresis during long range applications; 2) due to creep effects when positioning is needed over extended periods of time; and 3) due to induced vibrations during high-speed positioning. This loss in precision restricts the use of piezoactuators in high-speed positioning applications like SPM-based nanofabrication, and ultra-high-precision optical systems. An integrated inversion-based approach is presented to compensate for all three adverse affects-creep, hysteresis and vibrations. The method is applied to an atomic force microscope, and experimental results are presented that demonstrate substantial improvements in positioning precision and operating speed.