Piezoelectric nanopositioning actuators are widely employed in many applications, including the hard disk drives [1–3], gyroscopes [4] and the scanning probe microscopes [5]. Besides the precise position control, high-bandwidth tracking control is crucial for the applications of piezoelectric actuators, since, for example, it will allow hard disk drives to meet the demand for higher data storage capacities with lower access times [6]. However, the existence of vibration dynamics, the coupled hysteresis and other uncertainty (e.g. creep) greatly limit the positioning and tracking performance of the piezoelectric actuators over a broad bandwidth. As a solution to tackle this problem and achieve precise control over a broad frequency range, stiffer piezoelectric actuators that have higher resonant frequencies can be employed. In this way, the scan frequency at which the vibration is significant becomes higher, while, as a major disadvantage, the range of motion is reduced [7]. This highly motivates the development of control techniques that enable high-bandwidth nanopositioning of piezoelectric-actuated systems.

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