Fractional Order Linear Active Disturbance Rejection Control for Electro-hydrostatic Actuator of Ship Rudder

doi:10.12382/bgxb.2022.0922

Abstract

Abstract:

In order to improve the disturbance rejection performance of electro-hydrostatic actuator (EHA) of ship rudder, a fusion control method based on linear active disturbance rejection control (LADRC) and fractional order proportional derivative (FOPD) control is proposed. The mathematical models of the drive motor and hydraulic system are established, respectively. On this basis, a linear extended state observer (LESO) is employed to estimate the total disturbances of EHA, including internal and external disturbances, under different operating conditions. The bounded stability of LESO is also proved. Furthermore, the FOPD control is used as the control law to actively suppress the estimated total disturbance, and the control parameters are determined by frequency response indicators such as shear frequency and phase margin. The joint simulation analysis of EHA model based on AMESim and Simulink shows that the displacement control accuracy of the proposed control method based on LADRC and FOPD is about 1mm when the ship speed is 6kn or 8kn. The self-developed EHA is used to build a semi-physical testing device, on which the reverse rudder and sudden reversal tests are carried out. The results show that the proposed control method has high speed and stability in tracking steering commands under load disturbances and sudden reversal situations.

Key words: ship rudder, electro-hydrostatic actuator, linear active disturbance rejection, fractional order proportional derivative

CLC Number:

TP275

LÜ Mingming, XIE Huawei, ZHONG Wei, WAN Guolong, TU Chaofan. Fractional Order Linear Active Disturbance Rejection Control for Electro-hydrostatic Actuator of Ship Rudder[J]. Acta Armamentarii, 2024, 45(5): 1514-1522.

Figures/Tables 11

Fig.1 Schematic diagram of EHA

Fig.2 Simple model of EHA hydraulic system

Fig.3 Co-simulation model of EHA

Table 1 Key parameters of simulation model

部件	参数	数值
	观测器带宽/Hz	60
控制器	微分阶次μ	0.85
	比例增益k_p	8.1
	微分增益k_d	0.2
	额定功率/kW	6
电机	空载转速/(r·min^-1)	2086
	额定扭矩/(N·m)	38
	活塞直径/mm	160
	活塞杆直径/mm	90
	液压缸行程/mm	380
液压系统	液压缸最大工作压力/MPa	15
	液压泵1排量/(mL·r^-1)	19
	液压泵2排量/(mL·r^-1)	14
	液压泵最大转速/(r·min^-1)	3000

Fig.4 Load curve of EHA

Fig.5 EHA displacement tracking curve of ship at 6kn

Fig.6 Displacement tracking curve of EHA during sudden load change

Fig.7 EHA displacement tracking curve of sinusoidal input

Fig.8 Test bench of EHA

Fig.9 Test curves of EHA at 8kn and 6kn

Fig.10 Displacement tracking curve of EHA at sudden reversing

References 27

[1]	徐巧宁, 艾青林, 杜学文, 等. 模型-数据联合驱动的船舶舵机电液伺服系统早期故障检测[J]. 上海交通大学学报, 2020, 54(5):451-464.
	XU Q N, AI Q L, DU X W, et al. An integrated model-based and data-driven method for early fault detection of a ship rudder electro-hydraulic servo system[J]. Journal of Shanghai Jiao Tong University, 2020, 54(5):451-464. (in Chinese)
[2]	LIANG L H, WANG L Y, WANG J F. The compensation for nonlinear friction of DDVC flange-type rotary vane steering gear[J]. Plos One, 2018, 13(11):1-21.
[3]	GU W W, YAO J Y, YAO Z K, et al. Output feedback model predictive control of hydraulic systems with disturbances compensation[J]. ISA Transactions, 2018, 88:216-224.
[4]	黄超群, 赵玉刚, 魏栋, 等. 船舶舵机负载模拟系统位置与力跟踪控制特性研究[J]. 液压与气动, 2019(4):74-78.
	HUANG C Q, ZHAO Y G, WEI D, et al. Position and force tracking control characteristics of ship steering gear load simulation system[J]. Chinese Hydraulics & Pneumatics, 2019 (4): 74-78. (in Chinese)
[5]	王明康, 付永领, 赵江澳, 等. 电动静液作动器的新型变阻尼级联滑模控制[J]. 北京航空航天大学学报, 2021, 47(8):1612-1618.
	WANG M K, FU Y L, ZHAO J A, et al. Novel damping- variable sliding mode cascade control for electro- hydrostatic actuator[J]. Journal of Beijing University of Aeronautics and Astronautics, 2021, 47(8):1612-1618. (in Chinese)
[6]	陈宗斌, 廖健, 刘帮会. 新型电液舵机的自抗扰控制算法及试验研究[J]. 中国舰船研究, 2022, 17(1):166-175.
	CHEN Z B, LIAO J, LIU B H. Application research on active disturbance rejection control algorithm and test electro- hydraulic steering gear[J]. Chinese Journal of Ship Research, 2022, 17(1):166-175. (in Chinese)
[7]	付永领, 李宇鹏, 王明康, 等. 电动静液作动器的自适应变阻尼滑模控制[J]. 北京理工大学学报, 2021, 41(11):1171-1178.
	FU Y L, LI Y P, WANG M K, et al. Novel cascade control based on damp variable sliding mode control for electro-hydrostatic actuator[J]. Transactions of Beijing Institute of Technology, 2021, 41(11):1171-1178. (in Chinese)
[8]	李阁强, 赵文奎, 毛波, 等. 转叶舵机用复式摆动缸操舵原理[J]. 工程科学与技术, 2021, 53(5):175-182.
	LI G Q, ZHAO W K, MAO B, et al. Steering principle of compound swing cylinder for rotary vane steering gear[J]. Advanced Engineering Sciences, 2021, 53(5):175-182. (in Chinese)
[9]	曹洪涛, 陈锋, 陈佳. 集成一体化舵机技术研究综述[J]. 舰船科学技术, 2017, 39(7):1-7.
	CAO H T, CHEN F, CHEN J. Review of the research on integrated steering gear technology[J]. Ship Science and Technology, 2017, 39(7):1-7. (in Chinese)
[10]	陈宗斌, 何琳, 廖健, 等. 双泵源电液舵机线谱噪声控制[J]. 国防科技大学学报, 2019, 41(2):170-175.
	CHEN Z B, HE L, LIAO J, et al. Linear spectrum noise control of electro-hydraulic steering gear with dual pump source[J]. Journal of National University of Defense Technology, 2019, 41(2):170-175. (in Chinese)
[11]	李婷, 王新民, 杨婷, 等. 基于速度观测的双余度电液舵机系统容错同步控制[J]. 北京航空航天大学学报, 2020, 46(10):1929-1940.
	LI T, WANG X M, YANG T, et al. Fault-tolerant synchr- onization control for a dual redundant electro-hydraulic actuator system based on velocity estimation[J]. Journal of Beijing University of Aeronautics and Astronautics, 2020, 46(10):1929-1940. (in Chinese).
[12]	董胜, 袁朝辉. 基于LMI方法的电液舵机动刚度H∞控制器分析与设计[J]. 振动与冲击, 2019, 38(4): 229-236,249.
	DONG S, YUAN Z H. Analysis and design of a stiffness H∞ controller of electro-hydraulic rudder based on the LMI method[J]. Journal of Vibration and Shock, 2019, 38(4):229-236,249. (in Chinese)
[13]	王永宾, 林辉. 基于滑模控制的机载作动器摩擦转矩补偿研究[J]. 中国机械工程, 2010, 21(7):809-814.
	WANG Y B, LIN H. Friction compensation of aircraft actuator based on soliding modeI control[J]. China Mechanical Engineering, 2010, 21(7):809-814. (in Chinese)
[14]	韩小霞, 冯永保, 谢建, 等. 考虑油液黏温特性的电静液作动器流量死区动态逆补偿方法[J]. 兵工学报, 2022, 43(2):316-327. doi: 10.3969/j.issn.1000-1093.2022.02.009
	HAN X X, FENG Y B, XIE J, et al. Dynamic inverse compensation method of flow rate dead-zone of electro-hydrostatic actuator considering viscosity-temperature characteristics of oil[J]. Acta Armamentarii, 2022, 43(2):316-327. (in Chinese)
[15]	朱斌. 自抗扰控制入门[M]. 北京: 北京航空航天大学出版社, 2017.
	ZHU B. Introduction to active disturbance rejection control[M]. Beijing: Beihang University Press, 2017. (in Chinese)
[16]	GAO B W, SHAO J P, YANG X D. A compound control strategy combining velocity compensation with ADRC of electro-hydraulic position servo control system[J]. ISA Transactions, 2014, 53(6):1910-1918. doi: 10.1016/j.isatra.2014.06.011 pmid: 25085480
[17]	HAMID R, GIANLUCA P, MORAD N. Disturbance observer-based nonlinear feedback control for position tracking of electro-hydraulic systems in a finite time[J]. European Journal of Control, 2022, 67(Sep.):100659.
[18]	MIAO J G, WANG J Y, WANG D, et al. Experimental investigation on electro-hydraulic actuator fault diagnosis with multi-channel residuals[J]. Measurement, 2022, 180: 109544.
[19]	付永领, 陈辉, 刘和松, 等. 基于自抗扰控制的导弹电液舵机系统研究[J]. 宇航学报, 2010, 31(4):1051-1055.
	FU Y L, CHEN H, LIU H S, et al. Study on missile electro- hydraulic actuator system based on active disturbance rejection control method[J]. Journal of Astronautics, 2010, 31(4):1051-1055. (in Chinese)
[20]	高志强. 自抗扰控制思想探究[J]. 控制理论与应用, 2013, 30(12):1498-1510.
	GAO Z Q. On the foundation of active disturbance rejection control[J]. Control Theory & Applications, 2013, 30(12): 1498-1510. (in Chinese)
[21]	MONJE C A, VINAGRE B M, FELIU F, et al. Tuning and auto-tuning of fractional order controllers for industry applications[J]. Control Engineering Practice, 2008, 16(7): 798-812.
[22]	王荣林, 陆宝春, 侯润民, 等. 交流伺服系统分数阶PID改进型自抗扰控制[J]. 中国机械工程, 2019, 30(16): 1989-1995.
	WANG R L, LU B C, HOU R M, et al. FOPID improved ADRC in AC servo systems[J]. China Mechanical Engineering, 2019, 30(16): 1989-1995. (in Chinese)
[23]	杨钟鼎, 周洁敏, 郑罡, 等. 基于滑模变结构控制的EHA系统仿真研究[J]. 测控技术, 2017, 36(4):61-65,69.
	YANG Z D, ZHOU J M, ZHENG G, et al. Simulation research on EHA system based on sliding mode variable structure control[J]. Measurement & Control Technology, 2017, 36(4): 61-65,69. (in Chinese)
[24]	MA L L, WANG F X, WANG J Z. Fault-tolerant control of PMSM based on NTSMC and NLFO[J]. Asian Journal of Control, 2022, 24(4):1928-1941.
[25]	LIN P, WU Z, FEI Z Y, et al. A generalized PID interpretation for high-order LADRC and cascade LADRC for servo systems[J]. IEEE Transactions on Industrial Electronics, 2022, 69(5):5207-5214.
[26]	FATEME D, HAMED M. An ADRC-based backstepping control design for a class of fractional-order systems[J]. ISA Transactions, 2022, 121:140-146.
[27]	王婉婷. 基于高精度辨识的复合轴控制策略研究[D]. 北京: 中国科学院大学, 2016.
	WANG W T. Research on composite control strategy based on high precision identification[D]. Beijing: University of Chinese Academy of Sciences, 2016. (in Chinese)