Although the control of cable tensions plays a paramount role in the control of Cable-Driven Parallel Robots (CDPRs), studies addressing the subject are very few. The present paper proposes and experimentally validates a simple cable tension feedback control scheme. In order to avoid issues related to friction and saturation of the feedback correction, a velocity-controlled winch is considered. The closed-loop scheme consists of an ordinary PI applied with respect to the measured cable tensions. Thanks to its simplicity, the main advantage of the proposed scheme is its ease of implementation. The experimental validation is performed using two scenarios. First, a simplified case consisting of a single degree-of-freedom CDPR is considered. Finally, the performance is validated with a a six degrees-of-freedom CDPR fully-constrained by eight cables.