While it is attractive to integrate a deformable mirror (DM) for adaptive optics (AO) into the telescope itself rather than using relay optics within an instrument, the resulting large DM can be expensive, particularly for extremely large telescopes. A low-cost approach for building a large DM is to use voice-coil actuators, and rely on feedback from mechanical sensors to improve the dynamic response of the mirror sufficiently so that it can be used in a standard AO control system. The use of inexpensive voice-coil actuators results in many lightly- damped structural resonances within the desired control bandwidth. We present a robust control approach for this problem, and demonstrate performance in a closed-loop AO simulation, incorporating realistic models of low-cost actuators and sensors. The first contribution is to demonstrate that high-bandwidth active damping can be robustly implemented even with non-collocated sensors, by relying on the "acoustic limit" of the structure where the modal bandwidth exceeds the modal spacing. Next we introduce a novel local control approach, which significantly improves the high spatial frequency performance relative to collocated position control, but without the robustness challenges associated with a global control approach. The combination of these "inner" control loops results in DM command response that is demonstrated to be sufficient for integration within an AO system.