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Another thing you can do is to add feedforward control to your system -- that is, to sense the input signal and add (or subtract) a scaled (and filtered) version of this from your control signal.
Note that feedforward does not change the poles (natural frequencies) of your system but it will change the zeros of your system. In this respect, I suspect feedforward control is similar to adding zeros to your compensator as mentioned by VVV in the previous post.