This paper presents the use of a quadratic band controller in an autonomous vehicle (AV) to regulate emergent traffic waves resulting from traffic congestion. The controller dampens the emergent traffic waves through modulating its velocity according to the relative distance and velocity of the immediately preceding vehicle in the flow. At the same time, it prevents any collision within the range specified by the design parameters. The approach is based on a configurable quadratic band that allows smooth transitions between (i) no modification to the desired velocity; (ii) braking to match the speed of the preceding vehicle; and (iii) braking to avoid collision with the lead vehicle. By assuming that the lead vehicle's velocity will be oscillatory, the controller's smooth transition between modes permits any vehicle following the AV to have a smoother reference velocity. The configurable quadratic band allows design parameters, such as actuator and computation delays as well as the dynamics of vehicle deceleration, to be taken into account when constructing the controller. Experimental data, software-in-the-loop distributed simulation, and results from physical platform performance in an experiment with 21 human-driven vehicles are presented. Analysis shows that the design parameters used in constructing the quadratic band controller are met, and assumptions regarding the oscillatory nature of emergent traffic waves are valid.