This paper introduces a novel concept termed Smart Mesoflaps for Aeroelastic Recirculation Transpiration SMART for controlling shock boundary layer interactions SBLI in supersonic jet inlets. The control strategy for a subsystem of the SMART project, subject to hysteresis and actuator saturation, is presented. A Hysteresis Compensation scheme, as well as results from experimental application of HC to the SMART subsystem are presented next. A generalized Error Governor EG for PID controllers to compensate for actuator saturations is developed. Finally, the PID with HC and modified EG applied to a benchtop system is shown to be successful at preventing excessive control efforts.