Takagi–Sugeno fractional-order interval type-2 fuzzy proportional–integral–derivative controller with real-time application to a magnetic levitation system

This paper introduces a novel Takagi–Sugeno fractional-order interval type-2 fuzzy proportional–integral–derivative (TSFOIT2FPID) controller, addressing a critical gap in the literature. In sheer contrast to the existing Takagi–Sugeno integer-order interval type-2 fuzzy proportional–integral–derivative (TSIOIT2FPID) controllers, by incorporating the rich concept of fractional-order (FO) calculus, the proposed controller offers a more sophisticated control framework with additional tunable parameters. Due to the plant-model-free nature, intrinsically nonlinear dynamics, and the incorporation of footprints of uncertainty (FoUs) at the time of controller design, the proposed controller is well-suited for the control of complex, uncertain, and nonlinear systems, thereby overcoming the limitations associated with conventional and type-1 (T1) fuzzy proportional–integral–derivative (PID) controllers. Further, by excluding AND or OR operators from the mathematical modeling, the present approach allows independent tuning of the controller gains, thus enhancing the flexibility of the proposed control scheme. Apart from addressing the properties and computational aspects of the proposed controller, the superiority of the newly introduced controller over the existing conventional and fuzzy PID controllers is validated through rigorous hardware experiments on the magnetic levitation (MagLev) system, demonstrating its potential and usefulness for real-world control applications. Additionally, simulation results comparing the performance of the proposed controller and an FO integral-proportional-derivative (FOIPD) controller are also presented to offer a more thorough understanding of the effectiveness of the proposed control scheme.