基于并联机构的多维隔振系统振动鲁棒最优半主动控制

doi:10.16183/j.cnki.jsjtu.2023.230

摘要/Abstract

摘要：

为隔离车载精密仪器所承受的多维振动,提出基于2-RPC/2-SPC并联机构和磁流变 (MR) 阻尼器的多维半主动隔振系统.通过几何关系和Lagrange方程分别建立多维隔振系统运动学和动力学模型,分别考虑质量、刚度和阻尼不确定因子,提出多维隔振系统鲁棒最优半主动控制策略,在随机路面激励下,研究多维隔振系统频域隔振能力和不确定因子变化对隔振性能的影响规律,与具有相同不确定因子的线性二次型调节器 (LQR) 半主动控制策略在阶跃激励下进行对比分析.研究表明:多维隔振系统可实现沿 x、 y、 z轴和绕y 轴的多维振动有效隔离;质量不确定因子变化对隔振性能影响最显著;存在不确定因素时,鲁棒最优半主动控制策略的隔振能力显著优于LQR半主动策略的隔振能力.

关键词: 并联机构, 多维隔振系统, 磁流变阻尼器, 半主动控制

Abstract:

In order to isolate multi-dimensional vibration experienced by vehicle-mounted precise instrument, a novel multi-dimensional vibration isolator is proposed based on 2-RPC/2-SPC parallel mechanism and the magneto-rheological (MR) damper. The kinematic and dynamic models are established by geometric relation and the Lagrange approach respectively. The robust optimal semi-active control algorithm is obtained by deducing linear matrix inequality. The vibration isolation capability is addressed in time and frequency domain under stochastic road excitation with mass, stiffness, and damping coefficient uncertain factors respectively. Meanwhile, the relation between isolation performance and uncertain factors is explored. The isolation capability is compared with the linear quadratic regulator (LQR) semi-active control algorithm with the same uncertain factors under step excitation. The results demonstrate that the proposed isolator inhibit the vibration in the x, y, z axes and around the y axis significantly. The isolation performance is affected by mass uncertain factor most obviously. The robust optimal semi-active control algorithm is more effective than the LQR algorithm with uncertain factors.

Key words: parallel mechanism, multi-dimensional vibration isolator, magneto-rheological (MR) damper, semi-active control

中图分类号:

TB535
TH113

高翔, 牛军川, 贺磊, 秦榛, 王忠龙. 基于并联机构的多维隔振系统振动鲁棒最优半主动控制[J]. 上海交通大学学报, 2025, 59(5): 648-656.

GAO Xiang, NIU Junchuan, HE Lei, QIN Zhen, WANG Zhonglong. Vibration Robust Optimal Semi-Active Control of Multi-Dimensional Vibration Isolator Based on Parallel Mechanism[J]. Journal of Shanghai Jiao Tong University, 2025, 59(5): 648-656.

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参数	取值
活塞有效面积,A_p/mm²	0.6
磁流变液黏度,η/(Pa·s)	0.15
阻尼通道长度,L/mm	25
阻尼器内外壳间隙,h/mm	1.5
阻尼器内壳外径,r/mm	1.2
拟合系数,a₄/(kPa·T^-3)	-1 090
拟合系数,a₃/(kPa·T^-2)	718.2
拟合系数,a₂/(kPa·T^-1)	11.4
拟合系数,a₁/kPa	0.271
拟合系数,a₀/(kPa·T^-4)	389.7

参数	取值
动平台质量,m_p/kg	25
动平台绕y轴转动惯量,I_y/(kg·m²)	0.67
弹簧刚度,k/(N·m^-1)	15 000
定平台边长,d/m	0.35
定平台边长,c/m	0.40
动平台边长,b/m	0.16
动平台边长,a/m	0.15
权重系数,α_K	70
权重系数,α_M	80
权重系数,β_M	6×10^-3
下截止频率,n₀/m^-1	0.012
参考空间频率,n₁/m^-1	0.1
路面不平度系数,G_q/m³	6.4×10^-5
车速,v_e/(m·s^-1)	16.7

控制策略	沿x轴/ (m·s^-1)	沿y轴/ (m·s^-1)	沿z轴/ (m·s^-1)	绕y轴/ (rad·s^-1)
被动	5.01×10^-3	5.78×10^-3	2.09×10^-3	7.00×10^-3
半主动	2.50×10^-3	2.06×10^-3	1.02×10^-3	2.20×10^-3
主动	5.48×10^-5	8.84×10^-4	5.77×10^-4	2.11×10^-5