Enhanced constrained optimal sliding mode control for cable-driven parallel robots

Abstract

This paper introduces novel methodologies in Sliding Mode Control (SMC) for Cable-Driven Parallel Robots (CDPRs), featuring innovative nonlinear sliding surface formulations. The study commences with an examination of the CDPR model under dynamic uncertainties and external disturbances. In addition to the standard error equation surface, two carefully selected nonlinear surfaces—a novel odd-exponential surface and a hyperbolic tangent surface—are proposed and analyzed within the framework of conventional sliding mode control. Furthermore, recognizing the potential efficiency loss of conventional SMC approaches in CDPRs with both translational and rotational Degrees of Freedom (DoFs) due to uncertainties and disturbances, a robustness enhancement approach is developed. This approach ensures effective cable tension management in systems encompassing both translational and rotational DoFs. The asymptotic stability and robustness of all three sliding surfaces are rigorously analyzed using the Lyapunov theorem, both in conventional SMC and in the proposed robustness enhancement approach. Additionally, the reaching times of the three sliding surfaces are evaluated under various uncertainty scenarios for each control strategy. To validate the theoretical findings, simulations are conducted on a 6 DoFs spatial CDPR under different levels of uncertainty. The simulation results reveal the comparative performance of each of the three surfaces under different uncertainty conditions, evaluated based on specific performance criteria.