NFIRAOS is the facility AO system for TMT. NFIRAOS does not have a separate tip-tilt mirror. Instead one of its two deformable mirrors will be mounted on a tip-tilt platform, which, due to the weight of the deformable mirror, will only have a ~ 20 Hz bandwidth. This is too slow to correct the tip-tilt disturbance well enough, especially the windshake, which, in the case of TMT, is much more challenging to correct than the atmospheric tip-tilt. Tip-tilt can also be corrected directly on the deformable mirrors, but only a fraction of the incoming tip-tilt can be corrected that way, because of the limited stroke of the actuators. In this paper, we propose a woofer-tweeter approach, by which the high amplitude low temporal frequencies of tip-tilt are corrected by the tip-tilt platform, whereas the low amplitude high temporal frequencies are corrected by the deformable mirrors. This approach is based on a double integration control scheme and provides a much better attenuation of the windshake: 0.4 mas rms instead of 3.6, corresponding to an equivalent high order error of 20 nm rms instead of 180 nm rms. We find that only ~ 10% of the initial 25 mas rms windshake needs to be corrected by the DMs. With a 5-σ margin, this corresponds to only an extra ~1 micron of stroke for the actuators at the edge of the pupil, which are the most affected.