Stability Analysis and Robust PID Control of Parallel Cable Robots with Positive Tensions

In this paper dynamic analysis and robust PID control of fully-constrained parallel cable driven manipulators are studied in detail. Since in this class of manipulators, cables should remain in tension for all maneuvers in their workspace, feedback control of such robots becomes more challenging than that of conventional parallel robots and research on this topic especially on robust stability analysis is limited. In this paper, structured and unstructured uncertainties are considered in the dynamic model and Jacobian of therobot, and a robust PID controller is proposed for the cable driven parallel robot. To ensure that all the cables are in tension, a corrective term is used in the proposed PID control based on the internal force concept. Then, robust stability of the closed-loop system is analysed through Lyapunov’s second method and it is shown that by suitable selection of the controller gains, the closed-loop system would be robustly stable. Finally, the effectiveness of the proposed PID algorithm is examined through experiments on a planar cable driven robot and it is shown that the proposed control structure is able to provide suitable performance in practice.