An online adaptive fuzzy fractional-order controller for self-excited torsional vibrations in drilling systems

This paper presents the design of a novel Adaptive Fuzzy Fractional-Order Controller (AFFOC) to mitigate torsional vibrations in drill-string systems while maintaining the drill-string velocity at its desired reference. The proposed AFFOC combines fractional-order tools with fuzzy logic adaptation techniques, enabling real-time tuning of the controller parameters to effectively suppress torsional vibrations under different operating conditions. The control parameters are automatically tuned to compensate for noise disturbances and model uncertainties. The advantages of fractional calculus in the proposed strategy are thoroughly analysed. A lumped-parameter torsional model with four degrees of freedom is adopted to capture uncertainties in the torsional oscillations of the drill-string system. The effectiveness of the proposed controller is investigated and compared with classical methodologies, including Proportional Integral Derivative (PID), Sliding Mode Control (SMC), and Fractional-Order PID (FOPID). Numerical results based on detailed simulations demonstrate that the proposed algorithm exhibits superior robustness to external and internal disturbances while ensuring improved closed-loop performance for the drilling system. It is also shown that the proposed AFFOC achieves shorter settling times with minimal overshoot and undershoot, while providing superior robustness compared to classical control schemes, confirming its effectiveness in mitigating torsional vibrations.