This paper deals with the design of a robust control scheme for a suspended Cable-Driven Parallel Robot (CDPR), composed of eight cables and a moving platform (MP), suitable for pick-and-place operations of heterogeneous objects with different shapes, sizes and masses, up to a total load of 700 kg. Dynamometers measure the force applied by each cable onto the moving-platform and are used to assess the payload mass at any time. In the proposed control solution, each motor of the CDPR is directly driven by a PD torque controller, which takes benefit of the real-time payload estimation in a feedforward term. In order to evaluate its performance, experiments on a typical pick and place trajectory are realized for different payloads. As a result, three control schemes: (i) a Proportional-Derivative (PD) torque controller; (ii) a PD controller with compensation of the MP mass only and (iii) a PD controller with real-time mass estimation and compensation are experimentally compared with respect to their positioning accuracy. It turns out that a good estimation of the payload is obtained in real-time thanks to the dynamometers. Moreover, the higher the payload mass, the more accurate the proposed controller with respect to its two counterparts.