A fuzzy fractional-order control of robotic manipulators with PID error manifolds.

The present paper proposes a model-free implementation and output feedback control for robust tracking of robotic manipulators. By considering the salient advantages of fuzzy logic techniques for the control of uncertain dynamic systems, as well as the intrinsic properties of fractional-order (FO) operators for modelling and control of complex engineering processes, this paper proposes a control scheme that relies on fuzzy logic and FO tools. Firstly, a proportional–integral–derivative (PID) error manifold is synthesised to enhance the tracking capabilities of the closed-loop system. Then, in order to guarantee that the PID extended error evolves close to the origin, the dynamic controller is build upon a Takagi–Sugeno inference system, which is based on the PID extended error and on its FO integral. Finally, the reliability of the proposed method is demonstrated by means of a numerical simulation, and comparisons are carried out in experiments versus trustworthy discontinuous and continuous sliding mode based controllers.