Preview-based optimal inversion for output tracking: application to scanning tunneling microscopy

Abstract

Optimal inversion of system dynamics can be used to design inputs that achieve precision output tracking. However, a challenge in implementing the optimal-inversion approach is that the resulting inverse input tends to be noncausal. The noncausality of the optimal inverse input implies that the desired output trajectory must be prespecified, and cannot be changed online. Therefore, the optimal inverse can only be used in trajectory planning applications (where the entire desired output is known in advance). The article shows that the noncausal optimal inverse input can be computed using a preview-based approach. Properties of the optimal inverse are analyzed and the amount of preview time needed is quantified in terms of the required accuracy in output tracking, the poles and zeros of the system, and the cost function used to design the optimal inverse. The proposed approach is applied to precision (nanoscale) positioning of a scanning tunneling microscope (STM). Experimental results are presented to show that finite preview of the desired output-trajectory is sufficient to achieve a substantial increase in the STM's operating speed.