In this paper, a new robust model-based supertwisting algorithm is proposed as a control solution for parallel kinematic manipulators (PKMs). The conventional supertwisting algorithm for robot manipulators has the structure of a computed-torque control which can be sensitive to measurement noise. This issue may deteriorate the dynamic performance of the manipulator and reduce its robustness towards changes in the operating conditions. The proposed approach, relying on the desired trajectory, is more computationally efficient and more robust. It includes a feedforward dynamic compensator, the super-twisting feedback control, and a feedback stabilizing term. As a validation, real-time experiments have been conducted on a 5-DOF redundantly actuated PKM. Several scenarios have been tested including nominal case and the robustness towards speed variations. The relevance of the proposed control solution is proved through the improvement of the tracking performance at different dynamic operating conditions.