Fractional-order ultra-local model-based direct adaptive fuzzy sliding mode control for mechatronic systems with mismatched disturbances and input nonlinearities

Abstract

Aiming at the trajectory tracking problem of the mechatronic systems in the presence of uncertainties, matched and mismatched disturbances, and input nonlinearities, a fractional-order ultra-local model-based direct adaptive fuzzy controller (FO-DAFC) is proposed in this paper. To reduce the difficulty of controller design, the fractional-order ultra-local model is constructed to reformulate the complex mechatronic system. Then, a global sliding surface is proposed to eliminates the reaching phase and ensures the global robustness. Furthermore, an ideal global sliding mode controller is designed to converge the tracking error. However, the unknown and unmeasured parameters are existed in the ideal controller. The fuzzy logic system is thus established to approximate the ideal control law. And the fuzzy weight adaptive law is designed by using gradient descent method. Correspondingly, the direct adaptive fuzzy controller is proposed. After that, the stability of the closed-loop system with the proposed FO-DAFC is analyzed through using Lyapunov theorem. Ultimately, the numerical simulation of 2-DOF robotic manipulator with different input nonlinearities and co-simulation of 4-DOF robotic manipulator compared with other controllers are completed. The obtained results demonstrate the effectiveness and superiority of the proposed controller.