ON NONLINEAR CONTROL OF OPTICAL TRAPS USING PULLING TRAJECTORY TRACKING FOR SINGLE-MOLECULE EXPERIMENTS

摘要

This article explores nonlinear position plus integral (PI) feedback for controlling an optical trap used in single-molecule experiments. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Furthermore, the extension of a molecule creates an additional feedback path that puts constraints on the PI control gains. The nonlinear PI control presented here is shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The ability of nonlinear PI control to lower the measurement SNR is evaluated. Finally, constraints on the pulling rate are given to ensure the system trajectory remains in a quasi-static condition, stable, and the bead remains held in the trap.