Stick-slip-induced time delays in reconfigurable systems: data-driven estimation and sliding mode control

Abstract Stick-slip friction in reconfigurable mechanisms, such as cable-driven and tensegrity systems, introduces operating-condition-dependent time delays that degrade trajectory tracking and control stability. To address this challenge, this paper proposes a hybrid control architecture that integrates data-driven delay prediction with a robust Super-Twisting Sliding Mode Controller. An experimental testbed is used to characterize stick-slip latency across stiffness, pretension, load, and velocity, leading to the development of a shallow Artificial Neural Network (ANN) that predicts the stick-slip delay from measurable physical parameters, attaining a held-out test Root Mean Square Error (RMSE) of 0.36 s at an inference cost suitable for real-time deployment. This neural predictor feeds a historical state buffer, injecting the delayed state directly into the equivalent control law for active latency compensation without requiring complex analytical friction models. Furthermore, asymptotic stability of the sliding dynamics, established for a constant (quasi-static) delay, is formally guaranteed using a delay-dependent Lyapunov–Krasovskii functional and Linear Matrix Inequalities (LMI) to systematically synthesize stabilizing sliding-surface gains. Validation in simulation on a cable-driven rehabilitator and a rotational tensegrity system shows that the LMI-synthesized gains reduce the RMSE of the Super-Twisting controller by up to 96.4% relative to the same controller under conventional heuristic tuning, and that the Super-Twisting structure lowers the total variation of the control input by 95.6% on the tensegrity platform.