Point $P$ is inside equilateral $△ABC$ with side length $AB=6\sqrt{3}$. Points $Q$, $R$, and $S$ are the feet of the perpendiculars from $P$ to $\overline{AB}$, $\overline{BC}$, and $\overline{CA}$, respectively. Given that $PQ=2$ and $PR=3$, what is the length of $PS$?