Interval type-2 fuzzy sliding mode control for a cable-driven parallel robot with elastic cables using metaheuristic optimization methods

In this paper, a supervisory interval type-2 fuzzy adaptive sliding mode control scheme is addressed for cable robots. In the proposed control scheme, intelligent methods are combined with conventional sliding mode control to achieve optimal adjustment of control parameters. This approach ensures accurate tracking performance, despite the structural constraints of cable robots. These constraints include the production of purely tensile forces and the effects due to inherent elasticity, which will make the design of the controller challenging. For this purpose, the internal force concept is utilized to ensure the tension style of cables. Additionally, considering a compensator part in the proposed controller and applying the singular perturbation theorem, the vibration effects of elastic cables are handled, and stability is proved through the second Lyapunov method. Therefore, the desired performance of the control system will be guaranteed for the movements that stimulate the vibration modes of cables. An interval type-2 fuzzy logic controller is proposed to adjust the control gain, effectively reducing the chattering level. Moreover, a supervisory interval type-2 fuzzy logic control system is introduced to regulate the gains within the sliding surface. The Grasshopper Optimization Algorithm is employed to select the optimal parameters for the membership functions of the fuzzy system. The results of the conducted simulations show that the desired tracking performance is provided, despite different uncertain parameters and the structural constraints of the considered cable robot.