Abstract Torsional vibrations due to stick-slip phenomena may yield large variations in the drilling angular velocity which in turn may cause failures in the drilling process such as damage in drill pipes, due to large torsional deformation, and in drill bits, due to large angular velocities. It has been shown that standard linear proportional-integral (PI) control laws, in which the control torque is proportional to the differences between actual and reference drive table angular velocity and displacement, may lead to an oscillating angular velocity at the drill-bit due to stick-slip phenomenon. Aiming at reducing this effect through properly designed control gains, stability regions were defined for these parameters, and for a given drilling condition, using as a criteria the average deviation from expected/target angular velocity. This is done using a finite element model for the drilling system together with a dry friction model for a simplified representation of the interaction between drill-bit and rock formation. In order to provide robustness for the analysis, given the complexity of actual bit-rock interaction, it is proposed to consider uncertain parameters for the dry friction model. This is done using a stochastic model for the bit-rock interaction torque followed by a Monte Carlo simulation, which then leads to stochastic results for the angular velocity response, when subject to a linear PI control, and, thus, for the angular velocity deviation stability regions. Confidence intervals for the control gains, performance and stability regions are presented. Results suggest the use of a more robust criteria for the design of control parameters leading to a substantial increase in the performance robustness while not affecting much the nominal performance.

中文翻译：

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具有不确定钻岩非线性相互作用的油井钻井系统稳定区域的稳健评估

摘要 粘滑现象引起的扭转振动可能导致钻井角速度的较大变化，进而可能导致钻井过程中的故障，例如由于大扭转变形导致钻杆损坏，以及由于大角速度导致钻头损坏。速度。已经表明，标准线性比例积分 (PI) 控制法则，其中控制扭矩与实际和参考驱动台角速度和位移之间的差异成正比，可能会导致钻头处的摆动角速度由于粘滑现象。为了通过适当设计的控制增益减少这种影响，为这些参数和给定的钻井条件定义了稳定区域，使用与预期/目标角速度的平均偏差作为标准。这是使用钻井系统的有限元模型和干摩擦模型来完成的，用于简化表示钻头和岩层之间的相互作用。为了为分析提供稳健性，考虑到实际钻头-岩石相互作用的复杂性，建议考虑干摩擦模型的不确定参数。这是使用钻头-岩石相互作用扭矩的随机模型完成的，然后是蒙特卡罗模拟，当受到线性 PI 控制时，这会导致角速度响应的随机结果，因此，角速度偏差稳定区域。提供了控制增益、性能和稳定性区域的置信区间。