基于音圈电机的柔性杆自抗扰LQR抑振控制算法研究

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振动与冲击 ›› 2023, Vol. 42 ›› Issue (22) : 283-292.

论文

朱泳廷，张泽

作者信息 +

Algorithm for the LQR active disturbance rejection control of a flexible beam for vibration suppression based on voice coil motors

ZHU Yongting, ZHANG Ze

Author information +

文章历史 +

摘要

本文将音圈电机作动的二重动力吸振器应用于柔性杆端部来实现振动抑制。为克服柔性杆本身容易受扰和动力吸振器抑振带宽不足的问题，采用两个小型音圈电机构成主动式二重动力吸振器，针对该动力吸振器设计主动振动控制方法。首先，基于柔性杆的动力学等效建立了状态空间模型，在分析音圈电机的驱动特性后，采用LQR反馈控制器最小化扰动通道的传递函数增益，结合非线性跟踪微分器同时滤波和提取微分信号；在此基础上，引入时变增益的扩张状态观测器对模型不确定性、高阶模态以及未知扰动进行补偿。对抑振效果进行仿真分析，结果表明基于音圈电机的二重动力吸振器与自抗扰LQR控制器相结合，抑制柔性杆端残余振动，兼有强鲁棒性和抗扰能力。

Abstract

In this paper, a double Dynamic Vibration Absorber (DVA) actuated by two voice coil motors is applied to the end of a flexible beam to achieve vibration suppression. In order to overcome the problems of flexible arm’s susceptible characteristic and insufficient vibration suppression bandwidth of the DVA, two small voice coil motors are used to form the active double DVA, and an active vibration control method is designed. Firstly, the state space model is established based on the dynamic equivalent model of flexible beam. After analyzing the driving characteristics, LQR controller is used to minimize the transfer function gain of disturbance channel, in which nonlinear Tracking Differentiator (TD) is used to filter and extract differential signals; On this basis, the time-Varying Gain Extended State Observer (VGESO) is introduced to compensate for model uncertainty, high-order modes and unknown disturbances. Finally, the numerical simulation evaluation of vibration suppression effect has been carried out. The results show that when the double DVA based on voice coil motor is combined with the LQR Active Disturbance Rejection Controller, the residual vibration at the end of the flexible beam can be suppressed while it has strong robustness and disturbance rejection capability.

导出引用

朱泳廷，张泽. 基于音圈电机的柔性杆自抗扰LQR抑振控制算法研究[J]. 振动与冲击, 2023, 42(22): 283-292

ZHU Yongting, ZHANG Ze. Algorithm for the LQR active disturbance rejection control of a flexible beam for vibration suppression based on voice coil motors[J]. Journal of Vibration and Shock, 2023, 42(22): 283-292

参考文献

[1] 邱志成. 柔性机械臂的振动测量和控制研究进展综述[J]. 信息与控制，2021, 50(2):141-161.
QIU Zhicheng. Review on research progress in vibration measurement and control of flexible manipulators [J]. Information and Control, 2021, 50(2): 141-161.
[2] KIANG C T, SPOWAGE A, YOONG C K. Review of control and sensor system of flexible manipulator[J]. Journal of Intelligent & Robotic Systems, 2015, 77: 187-213.
[3] 潘昌忠, 罗晶, 李智靖, 等. 平面欠驱动柔性机械臂的PSO轨迹优化与自抗扰振动抑制[J]. 振动与冲击，2022, 41(14):181-189.
PAN Changzhong, LUO Jing, LI Zhijing, et al. PSO-based trajectory optimization and active disturbance rejection vibration suppression of a planar underactuated flexible manipulator [J]. Journal of vibration and shock, 2022, 41(14): 181-189.
[4] 孟庆鑫, 赖旭芝, 闫泽, 等. 双连杆刚柔机械臂无残余振动位置控制[J]. 控制理论与应用，2020, 37(3):620-628.
MENG Qingxin, LAI Xuzhi, YAN Ze, et al. Position control without residual vibration for a two-link rigid-flexible manipulator [J]. Journal of Control Theory& Applications, 2020, 37(3): 620-628.
[5] MENG Q X, LAI X Z, WANG Y W, et al. A fast stable control strategy based on system energy for a planar single-link flexible manipulator[J]. Nonlinear Dynamics, 2018, 94: 615-626.
[6] LIU Z, LIU J. Boundary control of a flexible robotic manipulator with output constraints[J]. Asian Journal of Control, 2017, 19(1): 332-345.
[7] 邱志成, 韩建达, 王越超. 基于复合喷气压电驱动器的柔性机械臂振动控制[J]. 机械工程学报，2009, 45(5):184-192.
QIU Zhicheng, HAN Jianda, WANG Yuechao. Vibration control for flexible manipulator based on the combining of jet thruster and piezoelectric actuators [J]. Journal of Machanical engineering, 2009, 45(5): 184-192.
[8] 娄军强, 廖江江, 李国平, 等. 压电柔性机械臂的实验辨识及最优极点配置抑振控制[J]. 振动与冲击，2017, 36(16):18-25.
LOU Junqiang, LIAO Jiangjiang, LI Guoping, et al. Experimental identification and vibration suppression of a piezoelectric flexible manipulator using an optimal poles-Assignment method [J]. Journal of vibration and shock, 2017, 36(16): 18-25.
[9] SETHI V, FRANCHEK M A, SONG G. Active multimodal vibration suppression of a flexible structure with piezoceramic sensor and actuator by using loop shaping[J]. Journal of Vibration and Control, 2011, 17(13): 1994-2006.
[10] 王兴松. 带载柔性机械臂固有频率确定及其减振器设计[J]. 东南大学学报，1997, 27(5):8-12.
WANG Xingsong. Calculation of the eigen-frequences and designing of the absorbers of a flexible beam with tip mass [J]. Journal of Southeast University, 1997, 27(5): 8-12.
[11] KARIMPOUR H, EFTEKHARI M. Exploiting internal resonance for vibration suppression and energy harvesting from structures using an inner mounted oscillator[J]. Nonlinear Dynamics, 2014, 77: 699-727.
[12] YONG C, ZIMCIK D G, WICKRAMASINGHE V K, et al. Research of an active tunable vibration absorber for helicopter vibration control[J]. Chinese Journal of Aeronautics, 2003, 16(4): 203-211.
[13] 张洪田, 李玩幽, 刘志刚. 电动式主动吸振技术研究[J]. 振动工程学报，2001, 14(01):117-121.
ZHANG Hongtian, LI Wanyou, LIU Zhigang. Study on active electro-dynamic vibration absorber [J]. Journal of Vibration Engineering, 2001, 14(01): 117-121.
[14] 杨恺, 崔龙, 黄海. 主被动电磁式动力吸振器及其在桁架振动控制中的应用[J]. 振动与冲击，2012, 31(18):14-19.
YANG Kai, CUI Long, HUANG Hai. An active-passive electromagnetic dynamic vibration absorber and its application in vibration control of trusses [J]. Journal of Vibration and Shock, 2012, 31 (18): 14-19.
[15] TARANTI C G R. A computationally efficient algorithm for disturbance cancellation to meet the requirements for optical payloads in satellites [D]. California: Naval Postgraduate School, 2001.
[16] 柴嘉伟, 贵献国. 音圈电机结构优化及应用综述[J]. 电工技术学报，2021, 36(6):1113-1125.
CHAI Jiawei, GUI Xianguo. Overview of structure optimization and application of voice coil motor [J]. Journal of China Electrotechnical Society, 2021, 36(6): 1113-1125.
[17] PATELSKI R, DUTKIEWICZ P. On the stability of ADRC for manipulators with modelling uncertainties[J]. ISA transactions, 2020, 102: 295-303.
[18] ZHONG S, HUANG Y, CHEN S, et al. A novel ADRC-based design for a kind of flexible aerocraft[J]. Control Theory and Technology, 2021, 19: 35-48.
[19] RAMIREZ-NERIA M, MORALES-VALDEZ J, Yu W. Active vibration control of building structure using active disturbance rejection control[J]. Journal of Vibration and Control, 2022, 28(17-18): 2171-2186.
[20] PREUMONT A. Vibration control of active structures: an introduction (4th Edition) [M]. Cham (Switzerland): Springer, 2018: 89-91.
[21] 刘建英, 王效岳, 宫金良. 考虑不同边界条件悬臂梁的模态研究[J]. 振动与冲击，2017, 36(19):221-226.
LIU Jianying, WANG Xiaoyue, GONG Jinliang. Modal analysis of cantilever beams with different boundary conditions [J]. Journal of Vibration and Shock, 2017, 36(19): 221-226.
[22] 滕青芳, 佐俊, 潘浩, 等. 基于时变增益扩张状态观测器的逆变器系统自适应super-twisting电压鲁棒控制[J]. 控制理论与应用，2020, 37(9):1880-1894.
TENG Qingfang, ZUO Jun, PAN Hao, et al. Robust voltage control for inverter system using time-varying gain extended state observer-based adaptive super-twisting algorithm [J]. Journal of Control Theory&Applications, 2020, 37(9): 1880-1894.
[23] 王越, 刘夫云, 邓聚才, 等. 半主动悬架SH-LQR阻尼控制策略仿真研究[J]. 噪声与振动控制，2022, 42(3):68-72+79.
WANG Yue, LIU Fuyun, DENG Jucai, et al. Simulation analysis of SH-LQR damping control strategy for semi-active suspensions [J]. Journal of Noise and Vibration Control, 2022, 42(3): 68-72+79.
[24] 韩京清. 自抗扰控制技术―估计补偿不确定因素的控制技术[M]. 北京：国防工业出版社，2008.
HAN Jingqing. Active Disturbance Rejection Control Technique― The Technique for Estimating and Compensating the Uncertainties [M]. Beijing: National Defense Industry Press, 2008.
[25] 史中权, 叶文华. 基于音圈电机作动器的主轴振动LQG控制研究[J]. 中国机械工程，2016, 27(10):1308-1314.
SHI Zhongquan, YE Wenhua. Research on LQG control of spindle vibration based on voice coil motor actuator [J]. Journal of China Mechanical Engineering, 2016, 27(10): 1308-1314.