A sliding mode control (SMC) strategy is proposed for a second-order non-linear system using fractional calculus and adaptive fuzzy compensator, named fuzzy fractional-order SMC (FFOSMC). The major contribution of this research includes the formulation of a robust fractional-order controller based on a novel non-integer sliding manifold. The proposed controller utilizes reduced discontinuous switching gain using a fuzzy logic system. A fractional-order adaptation law is derived to update the fuzzy logic system, which has more degrees of freedom to achieve the desired performance. The stability of the closed-loop system is guaranteed using fractional-order Lyapunov theory. The parameters of the proposed control method are optimized using Simulink response optimization. Finally, the performance of the FFOSMC is fully investigated and compared with a conventional SMC controller and an integral SMC controller. From simulation results, it is concluded that the proposed algorithm is effective and more robust.
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