In a drilling process, stick-slip vibrations are one of the main resources resulting in unstable motions or drillstring failures. In this paper, combined with a LuGre bit-rock interaction, the drillstring system is modeled as lumped parameters to capture the main features of stick-slip vibrations. Then, a novel control configuration involving five modules is developed in order to track a desired speed while suppressing the vibration, where the equivalent-input-disturbance method is skilfully employed to suppress such vibrations. In such five modules, the state observer is combined with the friction estimator to obtain the equivalent friction torques, which are corresponding to downhole frictions, on the surface control platform. In addition, the internal model and the state feedback are utilized to get the speed tracking torques so as to guarantee the desired tracking precision. Based on the dual conversion and two quadratic performances, the closed-loop stability is guaranteed by appropriate design of the controller and observer's gain matrices. Simulation is conducted to compare our method with an LQR method, showing our method's superiority and effectiveness.
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