Nonlinear stabilization of a spherical particle trapped in an optical tweezer

We describe the nonlinear equations of motion of a spherical particle trapped in an optical tweezer and outline the use of nonlinear feedback control to achieve global asymptotic stability of the origin. Control algorithms are derived for both an inertial system model and for a reduced order non-inertial model. The latter is well-suited for practical implementation and computer simulations show that the non-inertial control algorithm achieves not only global asymptotic stability, but also a faster settling time than the open loop system. We also show that the controller is very effective in reducing random position fluctuations due to thermal noise.