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This paper introduces a novel concept termed Smart Mesoflaps for Aeroelastic Recirculation Transpiration (SMART) to render mass and momentum transfer for controlling shock/boundary-layer interactions in supersonic jet inlets. The SMART concept consists of a matrix of small flaps designed to undergo local aeroelastic deflection to achieve proper mass bleed or injection when subjected to shock loads. To optimize the performance of this system, NiTi shape memory alloy is used as an actuator for the flaps to control the amount of recirculation. The focus of this paper will be the subsystem modeling and control of a single flap. After a relatively detailed model is developed, a simpler model is generated, and it is experimentally shown that this approximation is adequate for control purposes. Next, the control strategy for this subsystem, subject to hysteresis and actuator saturation, is presented. A basic proportional integral derivative (PID) controller is enhanced using a hysteresis compensator (HC) and an error governor (EG). A generalized error governing scheme for PID controllers to compensate for actuator saturations is also developed. This EG method is generalizable to any stable process controlled by a PID. Finally, the PID with HC and the error governing method is experimentally applied to a benchtop SMART subsystem.