Future space based deployable telescopes will be subject to non-atmospheric disturbances. Jitter and optical misalignment on a spacecraft can be caused by mechanical noise of the spacecraft, and settling after maneuvers. The introduction of optical misalignment and jitter can reduce the performance of an optical system resulting in pointing error and contributing to higher order aberrations. Adaptive optics can be used to control jitter and higher order aberrations in an optical system. In this paper, wavefront control methods for the Naval Postgraduate School adaptive optics testbed are developed. The focus is on removing structural noise from the flexible optical surface using discrete time proportional integral control with second order filters. Experiments using the adaptive optics testbed successfully demonstrate wavefront control methods, including a combined iterative feedback and gradient control technique. This control technique results in a three time improvement in RMS wavefront error over the individual controllers correcting from a biased mirror position. Second order discrete time notch filters are also used to remove induced low frequency actuator and sensor noise at 2Hz. Additionally a 2 Hz structural disturbance is simulated on a Micromachined Membrane Deformable Mirror and removed using discrete time notch filters combined with an iterative closed loop feedback controller, showing a 36 time improvement in RMS wavefront error over the iterative closed loop feedback alone.