The evolution and control of a two-dimensional wave packet developing on a flat plate with a leading edge is investigated by means of direct numerical simulation. The aim is to identify and suppress the wave packets generated by freestream perturbations. A sensor is placed close to the wall to detect the upcoming wave packet, while an actuator is placed further downstream to control it. A plasma actuator is modeled as an external forcing on the flow using a model based and validated on experimental investigations. A linear quadratic Gaussian controller is designed, and an output projection is used to build the objective function. Moreover, by appropriate selection of the proper orthogonal decomposition modes, we identify the disturbances to be damped. A reduced-order model of the input–output system is constructed by using system identification via the eigensystem realization algorithm. A limitation of the plasma actuators is the unidirectional forcing of the generated wall jet, which is predetermined by the electrodes’ location. In this paper, we address this limitation by proposing and comparing two different solutions: 1) introducing an offset in the control signal such that the resulting total forcing is oriented along one direction, and 2) using two plasma actuators acting in opposite directions. The results are compared with the ideal case where constraints are not accounted for the control design. We show that the resulting controllers based on plasma actuators can successfully attenuate the amplitude of the wave packet developing inside the boundary layer.