Google up "aeroelastic flutter".  The cause is the center of lift ahead or the center of gravity on a control surface.  The solution is to lighten the trailing edge ("back to the drawing board") or add weight at or ahead of the leading edge.  You'll see full-size planes with weights on the end of struts or with small surfaces out on the ailerons called "spades" that have a flutter-reducing effect. 

Many full size aircraft have an internal weight attached to a control surface that goes into the wing or fixed empennange to reduce flutter without being visible (or adding drag) outside of the plane.  That does limit the throw available