Improving Single-Molecule Experiments With Feedback Control of Optical Traps

D. G. Cole
This article explores various types of feedback control—position feedback, which was shown to be equivalent to force feedback, rate feedback, andintegral feedback—for the purpose of improving instrument performance for single-molecule experiments. The ability of each of each types of feedbackto lower the measurement signal-to-noise ratio (SNR) is evaluated andcompared to the open-loop case. While position feedback does not result in any improvement in the SNR, the cases of rate feedback and integral feedback both resulted in improvements in the measurement's SNR. Rate feedback is shown to effectively “cool” the beads held in the optical trap, thereby limiting the effect that Brownian disturbances have on the beads' motion. Integral feedback is shown to improve the SNR of the measuredsignal of interest and is robust and easy to implement. It is also shown that integral feedback acts as an exogenous force estimator. Ultimately, feedback does not provide better resolution as measured by SNR than an open-loop filtering approach can but does provide other advantages, including the ability to control other variables and to make a more robust instrument that can be easily adapted to changes in experimental conditions or the environment.
DOI

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

D. G. Cole and J. G. Pickel

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 tolower the measurement SNR is evaluated and compared to the variational open-loop case. A simulation demonstrating the performance of thenonlinear PI control is presented.

DOI