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The control of multibody drill-string systems is not easy and designing such systems is considered challenging because of the difficulty in the dynamic analysis of its nonlinear characteristics and parametric uncertainties. An optimal hybrid interval Type-2 fuzzy PID&#x002B;I logic controller (OH-IT2FPID&#x002B;I) using a practical swarm optimization algorithm for a multi-degree-of-freedom oil well drill-string system is proposed in this paper. The suggested control concept is aimed to overcome several bit sticking troubles and stick&#x2013;slip vibration by regulating the rotary velocities of drill-string components, especially rotary table velocity and drill bit velocity, to a predefined value. The drill-string system considered here has four degrees of freedom in the down-hole parts and the model takes the nonlinear interactions of the drill bit and the rocks into account, including friction torque and the mud drilling effect. Extensive simulations in Matlab/Simulink and experimental validations through a real-time hardware in the loop (HIL) system were performed to demonstrate the effectiveness of the suggested controller in comparison with sliding mode, Type 1 fuzzy logic and PID controllers. The quantitative comparison performed using simulation results proves that the proposed OH-IT2FPID&#x002B;I provides higher control performance in terms of settling time and peak overshoot under variation of the weight on bit, the desired drill bit rotary speed, and handling parametric uncertainties. On the other hand, HIL results confirm the control performance provided by the proposed control under all different testing scenarios.

Hybrid Interval Type-2 Fuzzy PID+I Controller for a Multi-DOF Oilwell Drill-String System