针对具有外部复杂扰动和未知系统动态的水下潜航器轨迹跟踪控制问题，本文研究一种基于固定时间并带有预设性能函数的积分滑模精确控制方案，该控制器保证了闭环系统的稳态响应始终在预定义范围内。构造新的固定时间干扰观测器，用于实时估计和补偿未知扰动量。将预设性能控制、固定时间方法和非奇异快速终端滑模相结合设计控制算法，使轨迹跟踪误差收敛到预定范围内。同时，为改善滑模控制带来的抖振问题，引入双曲正切函数代替符号函数。最后，理论分析证明该闭环系统的稳定性，仿真及仿真对比结果验证了所设计控制律的有效性和优越性。
In this paper, for the underwater submarine trajectory tracking control problem with external complex perturbations and unknown system dynamics, an integral sliding mode exact control scheme based on fixed time with a preset performance function is investigated, and the controller ensures that the steady-state response of the closed-loop system is always within a predefined range. A new fixed-time integral sliding mode disturbance observer（FISMDO） is constructed for real-time estimation and compensation of unknown disturbances. The control algorithm is designed by combining the preset performance control, the fixed-time method, and the non-singular fast terminal sliding mode so that the trajectory tracking error converges to a predefined range. Meanwhile, in order to improve the jitter problem caused by the sliding mode control, the hyperbolic tangent function is introduced instead of the sign function. Finally, the theoretical analysis proves the stability of the closed-loop system, and the simulation and simulation comparison results verify the effectiveness and superiority of the designed control law.
2025,47(5): 118-125 收稿日期：2024-9-6
DOI：10.3404/j.issn.1672-7649.2025.05.018
分类号：TP242
基金项目：国家自然科学基金资助项目（62303157）
作者简介：刘萌萌（2000 – ），女，硕士研究生，研究方向为水下潜航器运动控制及轨迹跟踪
参考文献：
[1] 于浩淼, 任思函. 基于tan型障碍函数的欠驱动UUV轨迹跟踪控制[J]. 应用科技, 2024, 51(6): 8–17+25.
[2] XU F, ZHANG L, ZHONG J. Three-dimensional path tracking of over-actuated AUVs based on MPC and variable universe S-Plane algorithms[J]. Journal of Marine Science and Engineering, 2024, 12(3): 418-421.
[3] JIE Z, CHENGTAO C, RENJIE Q. 未知扰动下的无人水面艇有限时间动态预设性能控制[J]. 2023, 18(4): 849-587.
[4] 郑宇鑫. 欠驱动高速无人艇航迹跟踪控制研究[D]. 哈尔滨: 哈尔滨工程大学, 2021.
[5] HONG M, GU X, LIU L, et al. Finite time extended state observer based nonsingular fast terminal sliding mode control of flexible-joint manipulators with unknown disturbance[J/OL]. Journal of the Franklin institute, 2020, 218(12): 1–10.
[6] 刘丽萍, 王红燕. 基于海流观测的欠驱动AUV自适应反演滑模轨迹跟踪[J]. 天津大学学报（自然科学与工程技术版）, 2020, 53(7): 745–753.
[7] 陈浩华, 赵红, 王宁, 等. 复杂扰动下水下机器人的轨迹精确跟踪控制[J]. 中国舰船研究, 2022, 17(2): 98-108.
[8] 于浩淼, 刘承蔚, 郭晨, 等. 基于PSO-NTSMC的UUV有限时间路径跟踪控制[J]. 兵工学报, 2022, 43(8): 1939-1946.
[9] 潘伟, 曾庆军, 姚金艺, 等. 全驱动自主水下机器人回收路径跟踪模糊滑模控制[J]. 船舶与海洋工程, 2022, 38(5): 45-50.
[10] GONZALEZ-GARCIA J, GOMEZ-ESPINOSA A, GARCIA-VALDOVINOS L G, et al. Experimental validation of a model-free high-order sliding mode controller with finite-time convergence for trajectory tracking of autonomous underwater vehicles[J]. SENSORS, 2022, 22(2): 4-8.
[11] HU Y, SONG Z, ZHANG H. Adaptive sliding mode control with pre-specified performance settings for AUV’s trajectory tracking[J]. Ocean Engineering, 2023, 287: 115882.
[12] LI J, DU J, SUN Y, et al. Robust adaptive trajectory tracking control of underactuated autonomous underwater vehicles with prescribed performance[J]. International Journal of Robust and Nonlinear Control, 2019, 29(14): 4629-4643.
[13] NA J, WANG S, LIU Y J, et al. Finite-Time convergence adaptive neural network control for nonlinear servo systems[J]. IEEE Transactions on Cybernetics, 2020, 50(6): 2568-2579.
[14] FOSSEN T I, SAGATUN S I, SRENSEN A J. Identification of dynamically positioned ships[J]. IFAC Proceedings Volumes, 1995, 28(2): 362-369.
[15] JIANG X, WANG Y. Prescribed performance control of marine surface vessel trajectory tracking in finite-time with full-state constraints and input saturation[J]. Journal of Marine Science and Engineering, 2021, 9(8): 866-903.
[16] BO S, HONG-BIN W, YUELING W. Dynamic event-triggered formation control for AUVs with fixed-time integral sliding mode disturbance observer[J]. Ocean Engineering, 2021, 240: 57-59.
[17] ZUO Z. Nonsingular fixed-time consensus tracking for second-order multi-agent networks[J]. Automatica, 2015, 54: 305-309.
[18] HONGDE Q, JINSHUAI S, NING W, et al. Fast fixed-time nonsingular terminal sliding-mode formation control for autonomous underwater vehicles based on a disturbance observer[J/OL]. Ocean Engineering, 2023, 270(2): 1-11.
[19] ZHANG M, GUAN Y, ZHAO W. Adaptive super-twisting sliding mode control for stabilization platform of laser seeker based on extended state observer[J]. Optik, 2019, 199: 163337.
