Optical membranes are being pursued for their ability to replace the conventional mirrors that are used to correct wave front aberration and space based telescopes. Among some of the many benefits of using optical membranes, is their ability to considerably reduce the weight of the structure. As a secondary effect, the cost of transportation, which is of great interest in space applications, is reduced as well. Another interesting advantage is the ability to have a continuous surface for the attenuation of wave front aberrations, instead of a discrete grid of rigid mirrors that have to be individually controlled. The effects of adding a pressurized cavity behind an optical membrane are examined in this paper by coupling an acoustic cylindrical cavity to a cylindrical membrane at the top boundary. This paper also looks at using a positive position feedback controller for vibration suppression of the membrane. This is done by using a centralized acoustic source in the cavity as the method of actuation. The acoustic actuation is of great interest since it does not mass load the membrane in the conventional way, as most methods of actuation would.