A Fractional-Order Dynamic Modelling and Robust Control of Nonlinear Robotic Manipulators: A Memory-Driven Framework with FOPID and FO-SMC}

Abstract

This paper develops a comprehensive fractional-order dynamic modelling and control framework for nonlinear robotic manipulators by integrating Caputo fractional derivatives to capture memory-dependent effects such as viscoelasticity, structural damping, and hysteresis—phenomena that classical integer-order models cannot represent accurately. Two fractional-order controllers, a fractional-order PID (FOPID) and a fractional-order sliding-mode controller (FO-SMC), are designed to exploit the long-term memory embedded in the system dynamics, thereby enhancing tracking accuracy, robustness, and transient behavior.