Deformable mirrors are very efficient optical devices that are used in correcting wavefront aberrations and are core elements of adaptive optics systems. Its promising success allows it to operate in a large field of applications. Hence, one of the most important problems in the control of adaptive optics systems is to design a controller that can achieve perfect wavefront correction in completely unknown environmental conditions. To achieve this goal, this study proposes an adaptive internal model control design for deformable mirrors. Considering deformable mirrors as a flexible plate equation, an adaptive internal model-based controller is designed and the effectiveness of the proposed method despite abrupt changes in disturbance is proven by simulation results.