| Citation: | SHEN Zhi-peng, DAI Chang-sheng, ZHANG Ning. Trajectory tracking control of underactuated ship based on adaptive iterative sliding mode[J]. Journal of Traffic and Transportation Engineering, 2017, 17(6): 125-134.
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At present, most single propeller and single rudder ships sailing at sea are typical underactuated system ships, in which the rudder device controls the ship's bow turning motion, the main engine propeller controls the ship's speed, and the ship lacks a driving device in the transverse direction[1]When ships are carrying out specific tasks such as laying pipelines, laying mines, and maneuvering, they need to accurately track the path according to the set route, and the trajectory tracking of the ship also requires the target ship to track the preset path at regular intervals according to time parameters[2]It is difficult to track the trajectory of underactuated ships using conventional control methods, and exploring new adaptive nonlinear control strategies has attracted widespread attention from scholars at home and abroad.
In recent years, there have been many research achievements on ship trajectory tracking control problems[3-4]Wondergen et al. designed an output feedback controller based on a 1:70 actual model to achieve real-time tracking of ship trajectories[5]Ashrafiuon et al. used sliding mode method to track the trajectory of underactuated ships, solving the problem of parameter uncertainty[6-7]Jia Heming et al. designed an adaptive inversion control strategy to effectively track the trajectory of underactuated underwater robots[8]Liao Yulei et al. proposed a sliding mode control method for underactuated unmanned boat trajectory tracking, ensuring asymptotic stability of the tracking error signal[9]Xing Dodge et al. designed an exponentially convergent sliding mode controller that uses coordinate transformation to transform the nonlinear ship model into a chain form[10]Xu Jian et al. designed an inverse dynamic sliding mode controller for 3D trajectory tracking of underactuated UUVs[11]Liao Yulei et al. combined inversion adaptive and sliding mode methods to achieve exponential asymptotic stability of underactuated ship path tracking error[12].
Currently, Fossen ship motion model is used to study ship trajectory tracking control[5, 8, 10-11]The calculation output usually consists of three control variables: longitudinal and transverse thrust and turning torque of the ship. For conventional single propeller and single rudder underactuated ships, these three control variables need to be converted into the set speed of the diesel engine and the commanded rudder angle of the servo. Therefore, compared with practical applications of ship control, the control variables designed using the Fossen model cannot be directly used. To be consistent with practical engineering applications, this paper will design a controller based on the MMG separation model, directly obtaining control variables such as diesel engine speed and rudder angle. The MMG model for underactuated ship horizontal motion can be represented as
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In the formula:uFor the longitudinal velocity of the vessel;vFor the lateral velocity of the vessel;rShake the angular velocity of the bow;x、yThe vertical and horizontal positions of the ship's center of gravity in a fixed coordinate system;ψFor heading angle;X1、Y1、N1The longitudinal and transverse forces, as well as the rotational moment, generated by the fluid dynamics of the bare hull;X2、Y2、N2They are the longitudinal and transverse forces and rotational torque of the propeller, respectively;X3、Y3、N3They are the longitudinal and transverse forces and rotational torque of the rudder;X4、Y4、N4The longitudinal and transverse forces, as well as the rotational moment, generated by the wind;X5、Y5、N5The longitudinal and transverse forces and rotational moments generated by waves respectively;mFor the quality of ships;mx、myThey are the vertical and horizontal components of the additional mass of water in the attached coordinate system;I、JShip hull pairs in inertial coordinate system and attached coordinate system respectivelyzThe moment of inertia of the vertical axis.
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System controller design objective: To design an adaptive trajectory tracking controller for the ship trajectory tracking mathematical model defined by equation (1) and the ship trajectory tracking error defined by equation (2), ensuring that all signals in the system converge asymptotically while allowing underactuated ships to track the preset trajectory within a limited time.
in compliance withFigure 2As shown, this paper proposes an adaptive iterative sliding mode trajectory tracking control method for underactuated ship neural networks with reinforcement learning. The output of the control system isx、yandψEnter as the set trajectory. The system first calculates the trajectory error and obtainsxeandyeThen, longitudinal error iterative sliding surface 1 and lateral error iterative sliding surface 2 are designed, and the diesel engine command speed is calculated separately through sliding surface feedback controlnAnd command rudder angleδThus driving the executing mechanism toxeandyeTowards zero, ultimately achieving the goal of ship trajectory tracking.
To effectively suppress the chattering output of the control rudder angle and the main engine speed, and enhance the adaptability of the controller,Figure 2Two parameter optimizers for diesel engine speed and rudder angle control were also designed in the middle. The parameter optimizer calculates the error separatelyxeandyeConstruct RBF neural network as input and output as control parametersk15andk25At the same time, to optimize the output parametersk15andk25According to the speed of the diesel enginenAnd rudder angleδConstruct a reinforcement signal based on the vibration measurement values and adjust the RBF neural network structure online. Under different operating conditions, through adaptive optimization of parameters, the controller can effectively reduce the oscillation of control rudder angle and main engine speed, and improve the overall control performance of the system.
To reduce longitudinal errorsxeConvergence, design diesel engine speed iterative sliding mode controller as
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In the formula:σ11、σ12They are the first and second order sliding mode surfaces for diesel engine speed control;k11、k12respectivelyσ11Convergence speed and input domain control parameters;k13、k14respectivelyσ12Convergence speed and input domain control parameters;k15、k16They are the convergence law of sliding mode surface feedback control and the zero domain convergence parameter.
From equation (3), it can be concluded that whenσ12At 0:00, there isσ11→ 0, and then obtainxe→ 0, therefore, the control objective becomes how to adjust the speednachieveσ12Converge and remain calm.
answerσ12Expand to obtain
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In the formula:tFor time.
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When the ship is sailing normally, the lateral thrust generated by the propeller is small and its influence can be ignored, so the above equation can be approximated as
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During normal navigation, ships generally do not track their trajectory laterally or backwards, meaning that the error between the actual heading and the expected direction is usually less than 90 °. Additionally, the relationship between propeller thrust and diesel engine speed is a monotonically increasing function
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According to equation (4), if the designed ship trajectory is smooth enough and the diesel engine speed system is controllable, there are parameters presentk11、k12、k13、k14∈R+And expected rotational speedn*∈[-nmax, nmax], makingσ12→0, nmaxFor the forward speed threshold. According to the literature[24]The asymptotic stability theorem of nonlinear scalar systems can be obtained, and the diesel engine speed control law designed by equation (3) can makeσ12Asymptotically converge to zero, and then combineσ11The definition of longitudinal trajectory tracking error is knownxeIt will also converge asymptotically.
Utilize lateral erroryeAnd heading errorψe=ψ-ψrThe iterative sliding surface for designing a ship rudder angle controller is
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In the formula:σ21、σ22、σ23、σ24They are the first to fourth order sliding surfaces for rudder angle control;k21、k22、k23、k24∈R+The convergence speed parameters for the four sliding surfaces are respectively, andk23< k24.
Designing a fourth-order sliding surface is to make the highest order sliding surfaceσ24There is a heading error in the middleψeThe second derivative term of, thus obtainingσ24With rudder angleδThe functional relationship.
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| [1] |
GUO Chen, WANG Yang, SUN Fu-chun, et al. Survey for motion control of underactuated surface vessels[J]. Control and Decision, 2009, 24 (3): 321-329. (in Chinese). doi: 10.3321/j.issn:1001-0920.2009.03.001
|
| [2] |
YANG Yang, DU Jia-lu, LIU Hong-bo, et al. A trajectory tracking robust controller of surface vessels with disturbance uncertainties[J]. IEEE Transactions on Control Systems Technology, 2014, 22 (4): 1511-1518. doi: 10.1109/TCST.2013.2281936
|
| [3] |
DUAN Hai-qing, ZHU Qi-dan. Trajectory tracking control of ships based on an adaptive backstepping neural network[J]. CAAI Transactions on Intelligent Systems, 2012, 7 (3): 259-264. (in Chinese). doi: 10.3969/j.issn.1673-4785.201205056
|
| [4] |
ZHANG Wei, TENG Yan-bin, WEI Shi-lin, et al. Underactuated UUV tracking control of adaptive RBF neural network and backstepping method[J]. Journal of Harbin Engineering University, 2018, 39 (1): 93-99. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201801015.htm
|
| [5] |
WONDERGEN M, LEFEBER E, PETTERSEN K, et al. Output feedback tracking of ships[J]. IEEE Transactions on Control Systems Technology, 2011, 19 (2): 442-448. doi: 10.1109/TCST.2010.2045654
|
| [6] |
ASHRAFIUON H, MUSKE K R, MCNINCH L C, et al. Sliding-mode tracking control of surface vessels[J]. IEEE Transactions on Industrial Electronics, 2008, 55 (11): 4004-4012. doi: 10.1109/TIE.2008.2005933
|
| [7] |
YU Rui-ting, ZHU Qi-dan, XIA Gui-lin, et al. Sliding mode tracking control of an underactuated surface vessel[J]. IET Control Theory and Applications, 2012, 6 (3): 461-466. doi: 10.1049/iet-cta.2011.0176
|
| [8] |
JIA He-ming, CHENG Xiang-qin, ZHANG Li-jun, et al. Three-dimensional path tracking control for underactuated AUV based on adaptive backstepping[J]. Control and Decision, 2012, 27 (5): 652-657, 664. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201205005.htm
|
| [9] |
LAO Yu-lei, ZHUANG Jia-yuan, LI Ye, et al. Sliding-mode trajectory tacking control for underactuated autonomous surface vehicle[J]. Journal of Applied Sciences, 2011, 29 (4): 428-434. (in Chinese). doi: 10.3969/j.issn.0255-8297.2011.04.016
|
| [10] |
XING Dao-qi, ZHANG Liang-xin. Sliding-model control for trajectory tracking of surface vessels[J]. Ship and Boat, 2011, 22 (5): 10-14. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-CBZZ201105005.htm
|
| [11] |
XU Jian, WANG Man, QIAO Lei, et al. Backstepping dynamical sliding mode controller for three-dimensional trajectory tracking of underactuated UUV[J]. Journal of Huazhong University of Science and Technology: Natural Science Edition, 2015, 43 (8): 107-113. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HZLG201508023.htm
|
| [12] |
LIAO Yu-lei, WAN Lei, ZHUANG Jia-yuan. Backstepping adaptive dynamical sliding mode control method for path following of underactuated surface vessel[J]. Journal of Central South University: Science and Technology, 2012, 43 (7): 2655-2661. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-ZNGD201207029.htm
|
| [13] |
ELMOKADEM T, ZRIBI M, YOUCEF-TOUMI K. Trajectory tracking sliding mode control of underactuated AUVs[J]. Nonlinear Dynamics, 2016, 84 (2): 1079-1091.
|
| [14] |
HWANG C L, CHIANG C C, YEH Y W. Adaptive fuzzy hierarchical sliding-mode control for the trajectory tracking of uncertain underactuated nonlinear dynamic systems[J]. IEEE Transactions on Fuzzy Systems, 2014, 22 (2): 286-299.
|
| [15] |
RAYGOSA-BARHONA R, PARRA-VEGA V, OLGUIN-DIAZ E, et al. A model-freebackstepping with integral sliding mode control for underactuated ROVs[C]//IEEE. 8th International Conference on Electrical Engineering, Computing Science and Automatic Control. New York: IEEE, 2011: 1-7.
|
| [16] |
LIU Chun-mei, YEH Chih-ping, CHEN Wen. Robust iterative learning control for output tracking via chatteringfree sliding mode control technique[C]//IEEE. 8th IEEE International Conference on Control and Automation. New York: IEEE, 2010: 241-246.
|
| [17] |
ZHAO Guo-liang, ZHAO Can, WANG De-gang. Tensor product model transformation based integral sliding mode control with reinforcement learning strategy[C]//IEEE. Proceedings of the 33rd Chinese Control Conference. New York: IEEE, 2014: 77-82.
|
| [18] |
HE Xiong-xiong, ZHUANG Hua-liang, ZHUANG Duan, et al. Pulse neural network-based adaptive iterative learning control for uncertain robots[J]. Neural Computing and Applications, 2013, 23 (7/8): 1885-1890.
|
| [19] |
HUANG Zheng-yu, EDWARDS R M, LEE K Y. Fuzzyadapted recursive sliding-mode controller design for a nuclear power plant control[J]. IEEE Transactions on Nuclear Science, 2004, 51 (1): 256-266.
|
| [20] |
JIA He-ming, ZHANG Li-jun, CHENG Xiang-qin, et al. Three-dimensional path following control for an underactuated UUV based on nonlinear iterative sliding mode[J]. Acta Automatica Sinica, 2012, 38 (2): 308-314. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-MOTO201202019.htm
|
| [21] |
BU Ren-xiang, LIU Zheng-jiang, LI Tie-shan. Iterative sliding mode based increment feedback control and its application to ship autopilot[J]. Journal of Harbin Engineering University, 2007, 28 (3): 268-272. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG200703004.htm
|
| [22] |
BIAN Xin-qian, CHENG Xiang-qin, JIA He-ming, et al. A bottom-following controller for underactuated AUV based on iterative sliding and increment feedback[J]. Control and Decision, 2011, 26 (2): 289-292, 296. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-KZYC201102025.htm
|
| [23] |
SHEN Zhi-peng, JIANG Zhong-hao, WANG Guo-feng, et al. Fuzzy-adapted iterative sliding mode control for sail-assisted ship motion[J]. Journal of Harbin Engineering University, 2016, 37 (5): 634-639. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201605002.htm
|
| [24] |
SHEN Zhi-peng, DAI Chang-sheng. Iterative sliding mode control based on reinforced learning and used for path tracking of under-actuated ship[J]. Journal of Harbin Engineering University, 2017, 38 (5): 697-704. (in Chinese). https://www.cnki.com.cn/Article/CJFDTOTAL-HEBG201705007.htm
|
| [25] |
SHEN Zhi-peng, GUO Chen, ZHANG Ning. A general fuzzified CMAC based reinforcement learning control for ship steering using recursive least-squares algorithm[J]. Neurocomputing, 2010, 73 (4-6): 700-706.
|
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SHEN Zhi-peng, DAI Chang-sheng, ZHANG Ning. Trajectory tracking control of underactuated ship based on adaptive iterative sliding mode[J]. Journal of Traffic and Transportation Engineering, 2017, 17(6): 125-134.
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