A model predictive control method for directional borehole trajectories in underground coal mines
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摘要:目的
针对煤矿井下复杂地层定向钻进过程中存在的实钻轨迹控制难度大、与设计轨迹偏差较大的问题，提出了基于模型预测控制(model predictive control，MPC)的定向钻孔轨迹跟踪控制方法。
方法以螺杆钻具定向钻进过程为研究对象，在分析煤矿井下复杂地层条件下定向钻进特性的基础上，研究定向钻具的运动规律，采用运动学理论建立滑动定向钻进的钻孔轨迹延伸模型，并用泰勒级数展开方式对模型进行线性化处理，以消除钻孔倾角与方位角等状态量之间的耦合关系，在此基础上构建钻孔轨迹预测模型和以最小轨迹偏差作为控制目标的目标函数，采用反馈校正方法解决预测模型的稳态误差问题，并设计具有预测模型、滚动优化、反馈校正功能的模型预测控制器，得到钻孔轨迹最优控制量的推荐−工具面向角，最终实现定向钻孔轨迹跟踪优化控制。最后，利用陕西韩城某煤矿钻孔实钻数据，对控制算法进行了验证。
结果和结论结果表明，线性化处理后的钻孔轨迹延伸模型有效保留了原有模型的特征，并简化了控制器的设计过程。改进后的定向钻孔轨迹反馈校正模型预测控制方法克服了模型适配和稳态误差的影响，相比于基于螺杆钻具造斜规律的人工经验控制决策方法，倾角平均绝对误差和方位角平均绝对误差分别降低79.5%和70.5%，为复杂地层定向钻孔轨迹控制提供了一种新的控制算法。
Abstract:ObjectiveIt is challenging to control the borehole trajectories during directional drilling in complex strata in underground coal mines, resulting in significant deviations from the designed trajectories. Given this, this study proposed a method for tracking and controlling directional borehole trajectories based on model predictive control (MPC).
MethodsFocusing on the directional drilling process conducted using a screw drill, this study investigated the movement patterns of the directional screw drill by analyzing the characteristics of directional drilling in complex strata in underground coal mines. Based on the kinematic theory, this study developed a borehole trajectory extension model for sliding directional drilling. Then, the model linearization was processed using Taylor series expansion, aiming to eliminate the coupling relationships between state variables such as dip angle and azimuth. Accordingly, this study constructed a borehole trajectory prediction model and an objective function with the minimum trajectory deviation as the control target. The steady-state errors of the prediction model were reduced using feedback correction. Furthermore, this study designed a model predictive controller with functions of predictive modeling, rolling optimization, and feedback correction. As a result, the optimal control variable for the borehole trajectory—toolface angle—was recommended. Accordingly, the optimized control for tracking directional borehole trajectories was achieved. Finally, the control algorithm was validated using the drilling data from a coal mine in Hancheng City, Shaanxi Province.
Results and ConclusionsThe results indicate that the linearized borehole trajectory extension model simplifies the design process of the controller while effectively preserving the characteristics of the original model. The improved MPC method with the feedback correction mechanism for predicting directional borehole trajectories removes the impacts of model adaptation and steady-state errors. Compared to the human experience-controlled decision-making method based on the deflection rules of a screw drill, the improved MPC method reduces the average absolute errors of the dip angle and azimuth by 79.5% and 70.5%, respectively, providing a novel control algorithm for directional borehole trajectories in complex strata.
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图 4 模型倾角和方位角线性化前后的对比
Fig. 4 Comparison of the tip angles and azimuths before and after model linearization
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图 5 人工经验轨迹倾角和轨迹方位角跟踪情况
Fig. 5 Tracked dip angles and azimuths of trajectories controlled based on human experience
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图 6 模型参数变化时倾角和方位角的跟踪情况
Fig. 6 Tracked dip angles and azimuths of trajectories under varying model parameters
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图 7 加入反馈校正机制的轨迹倾角和轨迹方位角跟踪情况
Fig. 7 Tracked dip angles and azimuths of trajectories under the introduction of the feedback correction mechanism
表 1 轨迹模型线性化参数
Table 1 Parameters for linearization of the trajectory model
参数 $ {\hat \theta _{\text{inc}}}/(^\circ ) $ $ {v}_{\text{rop}}/({\mathrm{m}}\cdot {{\mathrm{h}}}^{-1}) $ $ {K_{{\mathrm{dlc}}}}{{ /}}{{\mathrm{m}}^{ - 1}} $ $ {\theta _{\text{inc}}}{\text{ /}}(^ \circ ) $ $ {\theta _{\text{azi}}}{\text{ /}}(^ \circ ) $ 取值 8 6 0.08 2.2 2.2 
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表 2 轨迹控制仿真参数
Table 2 Parameters for trajectory control simulation
参数 $ a{{ /}}{{\mathrm{m}}^{ - 1}} $ $ b{{/}}{{\mathrm{m}}^{ - 1}} $ $ c/{{\mathrm{m}}^{ - 1}} $ $ {\theta _{\text{inc}}}{{/}}(^ \circ ) $ $ {\theta _{\text{azi}}}{{/}}( ^\circ ) $ 取值 16 16 −16 3 274
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