Nonlinear Proportional Plus Integral Control of Optical Traps for Exogenous Force Estimation

This article explores nonlinear proportional plus integral (PI) feedback for controlling the position of an object held in an optical trap. In general, nonlinearities in the spatial dependence of the optical force complicate feedback control for optical traps. Nonlinear PI control has been shown to provide all of the benefits of integral control: disturbance rejection, servo tracking, and force estimation. The controller also linearizes the closed-loop system. More importantly, the nonlinear controller is shown to be equivalent to an estimator of the exogenous force. The ability of nonlinear PI control to lower the measurement SNR is evaluated and compared to the variational open-loop case. A simulation demonstrating the performance of the nonlinear PI control is presented.