Extended-State-Observer-Based Trajectory-Tracking Model Predictive Control for Sliding Directional Drilling
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摘要: 滑动定向钻进作为定向钻进中常用的钻进技术，已广泛应用于工作面超前探查、地质灾害异常体识别与瓦斯抽采等任务，以提升地质识别精度与钻进作业效率. 针对滑动定向钻进过程中复杂地层扰动导致轨迹跟踪精度下降的问题，提出一种基于扩张状态观测器的轨迹跟踪模型预测控制方法. 首先，分析钻具运动学特性，建立滑动定向钻进轨迹延伸模型，在此基础上构建钻进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，并设计模型预测控制器. 然后，为补偿地层扰动带来的稳态误差，设计具备扰动观测能力的扩张状态观测器，实现最优控制输入的求解，从而实现轨迹跟踪控制. 最后，通过仿真实验证明了所提方法具有扰动反馈补偿、轨迹控制精度高及鲁棒性强等特点，在提升勘探效率以及降低作业风险等方面具有良好的应用价值.Abstract: Sliding directional drilling is widely used in directional boreholes for tasks such as advance probing, detection of abnormal bodies related to geological hazards, and gas drainage, helping improve geological interpretation and drilling efficiency. This paper addresses the problem of reduced trajectory tracking accuracy caused by complex formation disturbances during sliding directional drilling, and proposes an extended-state-observer-based model predictive control method for trajectory tracking. First, the kinematic behavior of the drilling tool is analyzed and a trajectory extension model for sliding drilling is built. Based on this model, a trajectory prediction model is constructed, and an objective function that minimizes trajectory error is designed to develop the MPC controller. Then, to reduce steady tracking errors caused by formation disturbances, an extended state observer with disturbance estimation is designed to compensate the control input. Simulation results show that the proposed provides disturbance compensation, high tracking accuracy, and strong robustness, with practical value for improving exploration efficiency and reducing designed to operational risk.
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图 1 定向钻进三维轨迹延伸示意图
Fig. 1. Schematic chart of the extension of the directional drilling trajectory
图 5 有无扰动观测补偿的轨迹跟踪曲线
Fig. 5. Trajectory tracking curves with and without disturbance observer compensation
表 1 定向钻进预设轨迹数据
Table 1. Preset trajectory data for directional boreholes
孔深(m) 倾角(°) 方位角(°) 上下位移(m) 左右位移(m) 0 9.00 28.00 -2.00 0.00 2 9.00 28.00 -2.19 0.74 4 9.00 27.50 -1.87 1.47 $ ⋮ $ $ ⋮ $ $ ⋮ $ $ ⋮ $ $ ⋮ $ 298 -2.00 6.00 30.63 20.85 300 -2.00 6.00 30.56 20.85 
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表 2 实验仿真参数
Table 2. Parameters of the experimental simulation
参数 取值 含义 $ L $ 2 孔深离散步长 $ {K}_{\mathrm{d}\mathrm{l}\mathrm{s}} $ $ 0.25°/\mathrm{m} $ 造斜能力参数 $ {N}_{p} $ 5 预测步长 $ Q $ $ {\left(1\;\mathrm{698, 7}\;\mathrm{000, 0.070}\;\mathrm{4, 5.467}\right)}^{\mathrm{T}} $ 状态加权矩阵 $ R $ $ {\left[0.130\;\mathrm{4, 4}\;000\right]}^{\mathrm{T}} $ 控制加权矩阵 $ {u}_{\mathrm{m}\mathrm{i}\mathrm{n}} $ $ {\left[-1.5, -1.5\right]}^{\mathrm{T}} $ 控制输入下限 $ {u}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ $ {\left[\mathrm{1.5, 1.5}\right]}^{\mathrm{T}} $ 控制输入上限 $ {L}_{x} $ $ {\left(\mathrm{0.55, 0.55, 0.25, 0.25}\right)}^{\mathrm{T}} $ 状态观测增益 $ {L}_{d} $ $ {\left[\mathrm{0.12, 0.06}\right]}^{\mathrm{T}} $ 扰动观测增益 $ {\gamma }_{d} $ 0.003 遗忘系数 $ {\widehat{d}}_{\mathrm{m}\mathrm{a}\mathrm{x}} $ 0.5 扰动估计限幅 $ {u}_{f, \mathrm{m}\mathrm{a}\mathrm{x}} $ $ {\left[\mathrm{1.5, 1.5}\right]}^{\mathrm{T}} $ 补偿输入限幅
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表 3 轨迹跟踪控制效果评价
Table 3. Evaluation of trajectory tracking control performance
方法 目标 RMSE(m) MaxE(m) MPC 上下位移 1.500 3.220 左右位移 9.269 14.392 Li et al. (2025) 上下位移 1.476 2.375 左右位移 2.420 4.465 ESO-MPC 上下位移 0.607 1.237 左右位移 0.912 1.561
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