Adaptive adjustment of (p,q)-analogues of Lupaş operators coefficients to cope with uncertainty in cable-driven parallel robots

This paper presents an observer-based adaptive control method for Cable-Driven Parallel Robots, employing the (p,q)-analogue of Lupaş operators as a universal approximator. The proposed controller effectively addresses system uncertainties, including unmodeled dynamics and external disturbances, within a robust adaptive framework. Stability-based adaptation laws are formulated to dynamically adjust the polynomial coefficients of the approximator. The control design also incorporates internal force regulation to ensure continuous tension in all cables. A key advantage of the method is its reliance solely on position feedback, thereby enhancing practical applicability and reducing implementation costs by eliminating the need for precise system modeling. System stability is rigorously established through a Lyapunov-based approach, ensuring uniform ultimate boundedness. Simulation results on a planar Cable-Driven Parallel Robot validate the effectiveness of the proposed strategy. Comparative analysis with both robust control and Chebyshev Neural Network approaches demonstrates superior tracking performance, particularly under external disturbances and modeling uncertainties, as confirmed by standard performance indices (ISE, IAE, ITAE).