Fixed-Time Tracking Control of Two-Dimensional Trajectories for Directional Boreholes Based on Rotary Steerable System
-
摘要: 旋转导向技术凭借造斜可控、成孔质量高和复杂地层适应性强的优势，已在煤矿、工程地质和油气勘探等复杂环境中得到应用. 聚焦于上述领域中的工作面超前探查与地质异常体识别等任务，针对倾角调控响应滞后导致的靶点偏移与轨迹偏差累积问题，提出一种面向旋转导向系统的定向钻孔二维轨迹固定时间跟踪控制方法. 首先，在描述钻孔延伸的时滞微分方程基础上，建立定向钻孔轨迹模型的状态空间表达式. 然后，设计含幂次反馈项的非线性控制器，实现轨迹误差的快速收敛. 并进一步构造李雅普诺夫函数，推导收敛时间上界，证明闭环系统具备固定时间收敛特性. 最后，通过仿真实验证明了所提方法具有收敛速度快、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: Rotary steering technology, with the advantages of controllable inclination building, high borehole quality, and strong adaptability to complex formations, has been applied in complex environments such as coal mines, engineering geology, and oil-gas exploration. This paper focuses on tasks like advanced working face exploration and geological anomaly identification in the aforementioned fields. To address the issues of target point deviation and trajectory deviation accumulation caused by the lag in inclination adjustment response, a fixed-time tracking control method for the two-dimensional trajectory of directional drilling holes oriented to rotary steering systems is proposed. Firstly, based on the time-delay differential equation describing borehole extension, a state-space representation of the directional drilling trajectory model is established. Then, a nonlinear controller with a power feedback term is designed to achieve rapid convergence of trajectory errors. Furthermore, a Lyapunov function is constructed to derive the upper bound of the convergence time, proving that the closed-loop system has fixed-time convergence characteristics. Finally, simulation experiments demonstrate that the proposed method features fast convergence speed, high trajectory control accuracy, and strong robustness, and has good application value in enhancing exploration efficiency and reducing operational risks.
-
图 1 二维钻孔轨迹跟踪控制系统结构
Fig. 1. Structure of two-dimensional drilling trajectory tracking control system
图 2 二维定向钻孔轨迹控制流程图
Fig. 2. Flow chart of two-dimensional directional borehole trajectory control
图 3 不同初始状态下的二维轨迹跟踪效果
Fig. 3. Tracking effects of two-dimensional trajectories under different initial states
图 4 基于4组模型参数组合的轨迹跟踪仿真结果对比
Fig. 4. Comparison of trajectory tracking simulation results based on four sets of model parameter combinations
图 5 基于4组模型参数组合的轨迹跟踪结果局部放大对比（150~154）
Fig. 5. Local enlarged comparison of trajectory tracking results based on four sets of model parameter combinations (150~154)
图 7 快速倾角变化时的轨迹跟踪效果
Fig. 7. Trajectory tracking effect during rapid inclination variation
图 8 快速倾角变化时的倾角跟踪误差
Fig. 8. Inclination tracking error during rapid inclination variation
表 1 定向钻进系统各参数及取值
Table 1. Parameters and their values of the directional drilling system
参数 取值 参数 取值 $ {\ell}_{1} $ 3.66 m $ {\nu }_{1} $ 1 $ {\ell}_{2} $ 6.10 m $ {\nu }_{2} $ 2/1.2 $ \mathrm{\Delta } $ 0.167 $ \mathrm{\Delta }{\ell}_{1} $ 0.61 m $ {i}_{r} $ 0.053 m $ {o}_{r} $ 0.086 m $ \chi $ 0.1 $ \upsilon $ 0.002 4 
下载: 导出CSV
表 2 基于4组模型参数组合的轨迹跟踪仿真动态性能参数对比
Table 2. Comparison of dynamic performance parameters of trajectory tracking simulation based on four sets of model parameter combinations
模型参数 峰值时间 收敛时间 超调量(%） $ \eta =0.05, \Pi=3 $ 0.12 3.11 0.08 $ \eta =0.1, \Pi=5 $ 0.21 4.00 0.12 $ \eta =0.2, \Pi=10 $ 0.09 1.21 0.06 $ \eta =0.3, \Pi=30 $ 0.03 0.72 0.01
下载: 导出CSV
表 3 两种控制策略的跟踪动态性能指标对比
Table 3. Comparison of tracking dynamic performance indexes for two control strategies
控制策略 峰值时间 收敛时间 超调量(%) 固定时间控制器 0.07 7.02 0.01 Hassan et al. (2024)控制器 0.75 9.12 0.29
下载: 导出CSV
-
Cheng, Q. M., 2011. Singularity Modeling of Geo-Anomalies and Recognition of Anomalies Caused by Buried Sources. Earth Science, 36(2): 307-316 (in Chinese with English abstract). Fang, P. H., 2024. Application of Underground Directional Drilling Technology in Mine Geological Exploration. West-China Exploration Engineering, 36(11): 191-192, 195 (in Chinese). Gao, D. L., Huang, W. J., 2024. Basic Research Progress and Prospect in Deep and Ultra-Deep Directional Drilling. Natural Gas Industry, 44(1): 1-12, 201 (in Chinese with English abstract). Geng, H., Xie, Y. J., Liu, Q. B., et al., 2025. Review of Technological Breakthroughs and Industrial Chain Synergy Innovations in China's Domestic High-Temperature High-Pressure Rotary Steerable Drilling System: a Global Context. Processes, 13(9): 2968. https://doi.org/10.3390/pr13092968 Gu, J. H., Wang, X. Q., Yan, H. F., et al., 2024. Observer-Based Adaptive Sliding Mode Compensation Position-Tracking Control for Drilling Tool Attitude Adjustment. Sensors, 24(8): 2404. https://doi.org/10.3390/s24082404 Guo, X. S., 2022. Discussion and Research Direction of Future Onshore Oil and Gas Exploration in China. Earth Science, 47(10): 3511-3523 (in Chinese with English abstract). Hao, J. S., You, Q. T., Peng, Z. N., et al., 2024. A Model-Free Toolface Control Strategy for Cross-Well Intelligent Directional Drilling. Engineering Applications of Artificial Intelligence, 133: 108272. https://doi.org/10.1016/j.engappai.2024.108272 Hassan, I. A., Abed, I. A., Al-Hussaibi, W. A., 2024. Path Planning and Trajectory Tracking Control for Two-Wheel Mobile Robot. Journal of Robotics and Control (JRC), 5(1): 1-15. https://doi.org/10.18196/jrc.v5i1.20489 Inyang, I. J., Whidborne, J. F., 2019. Bilinear Modelling, Control and Stability of Directional Drilling. Control Engineering Practice, 82: 161-172. https://doi.org/10.1016/j.conengprac.2018.10.008 Kang, M. X., Hua, D. Z., Guo, X. Q., 2023. Review on the Influence of Complex Stratum on the Drilling Trajectory of the Drilling Robot. Applied Sciences, 13(4): 2532. https://doi.org/10.3390/app13042532 Kremers, N. A. H., Detournay, E., van de Wouw, N., 2016. Model-Based Robust Control of Directional Drilling Systems. IEEE Transactions on Control Systems Technology, 24(1): 226-239. https://doi.org/10.1109/TCST. 2015. 2427255 doi: 10.1109/TCST.2015.2427255 Li, W. N., Yang, X., Lu, C. D., et al., 2025. Modeling and Optimization of Trajectory Deviation for Compound Directional Drilling in Coal Mines. Neurocomputing, 618: 129029. https://doi.org/10.1016/j.neucom.2024.129029 Liang, W. L., 2023. Application Study of High-Level Directional Borehole Gas Drainage Technology in Roof Strata. Petrochemical Industry Technology, 30(9): 241-242, 244 (in Chinese). Liu, Y., Li, H. Y., Lu, R. Q., et al., 2022. An Overview of Finite/Fixed-Time Control and Its Application in Engineering Systems. IEEE/CAA Journal of Automatica Sinica, 9(12): 2106-2120. https://doi.org/10.1109/JAS.2022.105413 Lu, C. D., Gan, C., Chen, L. F., et al., 2023. Development and Prospect of Intelligent Control of Geological Drilling Process. Coal Geology & Exploration, 51(9): 31-43 (in Chinese with English abstract). Lu, C. D., Tian, S. N., Wu, M., et al., 2025. Generalized Incremental Dissipative Control of Drill-String System Based on Equivalent Input-Disturbance Approach with Stubborn State Observer. Automatica, 181: 112501. https://doi.org/10.1016/j.automatica.2025.112501 Marck, J., Detournay, E., Kuesters, A., et al., 2014. Analysis of Spiraled-Borehole Data by Use of a Novel Directional-Drilling Model. SPE Drilling & Completion, 29(3): 267-278. https://doi.org/10.2118/167992-pa Mechali, O., Xu, L. M., Huang, Y., et al., 2021. Observer-Based Fixed-Time Continuous Nonsingular Terminal Sliding Mode Control of Quadrotor Aircraft under Uncertainties and Disturbances for Robust Trajectory Tracking: Theory and Experiment. Control Engineering Practice, 111: 104806. https://doi.org/10.1016/j.conengprac.2021.104806 Polyakov, A., 2012. Nonlinear Feedback Design for Fixed-Time Stabilization of Linear Control Systems. IEEE Transactions on Automatic Control, 57(8): 2106-2110. https://doi.org/10.1109/TAC.2011.2179869 Ren, H. R., Ma, H., Li, H. Y., et al., 2023. Adaptive Fixed-Time Control of Nonlinear MASs with Actuator Faults. IEEE/CAA Journal of Automatica Sinica, 10(5): 1252-1262. https://doi.org/10.1109/JAS.2023.123558 Song, Z. K., Sun, K. B., 2014. Adaptive Backstepping Sliding Mode Control with Fuzzy Monitoring Strategy for a Kind of Mechanical System. ISA Transactions, 53(1): 125-133. https://doi.org/10.1016/j.isatra.2013.07.017 Su, Y. X., Zheng, C. H., Mercorelli, P., 2020. Robust Approximate Fixed-Time Tracking Control for Uncertain Robot Manipulators. Mechanical Systems and Signal Processing, 135: 106379. https://doi.org/10.1016/j.ymssp.2019.106379 Wang, T. R., Ji, X. B., Wang, J. B., et al., 2025. Implicit 3D Geological Modeling Based on Machine Learning: A Case Study of Lazigou Gold Deposit in Muping-Rushan Metallogenic Belt. Earth Science, 50(8): 3167-3181 (in Chinese with English abstract). Wang, Y., Chen, X. F., Di, Q. Y., et al., 2025. Deep Mineral Exploration: Opportunities and Challenges in Reflection Seismics. Earth Science, 50(11): 4284-4299 (in Chinese with English abstract). Zhang, C., Zou, W., Cheng, N. B., et al., 2022. Adaptive Fault-Tolerant Control for Trajectory Tracking and Rectification of Directional Drilling. International Journal of Control, Automation and Systems, 20(1): 334-348. https://doi.org/10.1007/s12555-020-0923-6 成秋明, 2011. 地质异常的奇异性度量与隐伏源致矿异常识别. 地球科学, 36(2): 307-316. doi: 10.3799/dqkx.2011.032 房培洪, 2024. 井下定向钻进技术在矿井地质勘探中的应用. 西部探矿工程, 36(11): 191-192, 195. 高德利, 黄文君, 2024. 深层、超深层定向钻井中若干基础研究进展与展望. 天然气工业, 44(1): 1-12. 郭旭升, 2022. 我国陆上未来油气勘探领域探讨与攻关方向. 地球科学, 47(10): 3511-3523. doi: 10.3799/dqkx.2022.873 梁万林, 2023. 顶板高位定向钻孔抽采瓦斯治理技术应用研究. 石化技术, 30(9): 241-242, 244. 陆承达, 甘超, 陈略峰, 等, 2023. 地质钻进过程智能控制研究进展与发展前景. 煤田地质与勘探, 51(9): 31-43. 王统荣, 纪旭波, 王江波, 等, 2025. 基于机器学习的隐式三维地质建模: 以牟乳成矿带腊子沟金矿为例. 地球科学, 50(8): 3167-3181. doi: 10.3799/dqkx.2025.048 王赟, 陈晓非, 底青云, 等, 2025. 深部找矿: 金属矿地震技术的机遇与挑战. 地球科学, 50(11): 4284-4299. doi: 10.3799/dqkx.2025.109 -
点击查看大图
计量
- 文章访问数: 313
- HTML全文浏览量: 44
- PDF下载量: 56
- 被引次数: 0
