  We consider feedback cooling in a cavityless levitated optomechanics setup,
and we investigate the possibility to improve the feedback implementation. We
apply optimal control theory to derive the optimal feedback signal both for
quadratic (parametric) and linear (electric) feedback. We numerically compare
optimal feedback against the typical feedback implementation used for
experiments. In order to do so, we implement a tracking scheme that takes into
account the modulation of the laser intensity. We show that such a tracking
implementation allows us to increase the feedback strength, leading to faster
cooling rates and lower center-of-mass temperatures.
