Cable driven systems have been applied in several manipulators and due to their high backdrivability and apparent low inertia have been successfully used in telemanipulation systems. However, in order to achieve high performances, a control to keep the cables taut is needed. In this paper, a position control in the null and range space is used to avoid cables from slacking and to achieve the desired performances. Indeed, a cable driven manipulator is a redundant system and its null space represents the internal forces, that is the tensions of the cables. To guarantee robustness against model parametric uncertainties and external disturbances, a position based disturbance observer has been designed. Proof of stability of the proposed control and bounds of the estimation error have been given. Simulation and experimental results show that the proposed control achieve the desired performances keeping the cables taut.