Detection and Characterization of extrasolar terrestrial planets using coronagraphic techniques requires wavefront control algorithms to relax tolerances in a space-based observatory. To minimize the time spent correcting aberrations, the algorithms must function in broadband light. Two deformable mirrors in series can correct for both amplitude and phase aberrations. By taking a linear approximation of the propagation between the deformable mirrors we show an approach for broadband correction given a monochromatic estimate. We present progress in monochromatic light, initial experiments for broadband wavefront correction. We also address the additional challenges for a broadband controller such as limitations due to aberrations from spatial frequency folding that exhibit a wavelength squared dependence, which requires a third deformable mirror to correct in broadband. From these results we also discuss controllability of spatial frequencies and show its consequences for both monochromatic and broadband correction when using two deformable mirrors in series.