A redundant Cable-Driven Platform (CDP) is composed of m cables that exceed the Degree of Freedom (DOF) of the end-effector. The choice of tension along the cables admits infinite solutions. This paper proposes the use of the Analytic Centre to solve the tension distribution problem. Adopting this technique allows finding tensions far from the tension limits namely, robust as well as tension profiles continuous and differentiable in time. The continuity, differentiability and uniqueness of the solution is also proved. Moreover, the possibility of including non-linear constraints acting on the tensions (e.g. friction) is a further contribution. The computational time of proposed approach is compared to the existing techniques to asses its real-time applicability. Finally, several simulations using several CDPRs' architectures are reported to demonstrate the method's capabilities.