In this paper we present preliminary, experimental results of an Adaptive Super-Twisting Sliding-Mode Controller with time-varying gains for redundant Cable-Driven Parallel Robots. The sliding-mode controller is paired with a feed-forward action based on dynamics inversion. An exact sliding-mode differentiator is implemented to retrieve the velocity of the end-effector using only encoder measurements with the properties of finite-time convergence, robustness against perturbations and noise filtering. The platform used to validate the controller is a robot with eight cables and six degrees of freedom powered by 940 W compact servo drives. The proposed experiment demonstrates the performance of the controller, finite-time convergence and robustness in tracking a trajectory while subject to external disturbances up to approximately 400% the mass of the end-effector.