Reserach on Endocrine Compound Skyhook and Groundhook Control of Electro-magnetic Hybrid Active Suspension
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摘要: 为了改善汽车平顺性与操纵稳定性,且实现振动能量回收,设计了一种基于电磁直线混合作动器(EMLHA)的主动悬架系统。根据汽车行驶工况将悬架运动划分为经济、安全、舒适和综合这4种模式;将包含长反馈与短反馈的内分泌控制与天地棚控制相结合,提出了一种内分泌复合天地棚控制策略;采用加权优化函数与能耗最低优化函数确定了悬架不同模式下最优天地棚阻尼系数,并设计了内分泌控制规律,在随机路面进行时频域仿真分析。结果表明:相比天地棚控制,内分泌复合天地棚控制减振效果更优,对变化参数仿真具有较好的适应性,改善了汽车平顺性与操纵稳定性,且回收了部分振动能量。Abstract: In order to improve vehicle ride comfort and handling stability, also realize vibration energy recovery, an active suspension system based on electro-magnetic linear hybrid actuator (EMLHA) was designed in this study. The suspension motion was divided into four modes: economy, safety, comfort and comprehensive according to actual driving conditions of vehicles. An endocrine compound skyhook and groundhook control strategy was proposed, which combines endocrine control including long feedback and short feedback with skyhook and groundhook control. The weighted optimization function and the minimum energy consumption optimization function were used to determine the optimal skyhook and groundhook damping coefficients for different modes, and the endocrine control law was designed, the simulation analysis was carried out under random pavement. The results show that the control effect of endocrine compound skyhook and groundhook control is better than that of skyhook and groundhook control, which also has better adaptability to the simulation of changing parameters, improves vehicle ride comfort and handling stability, also recovers part of vibration energy.
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Key words:
- active suspension /
- multi-mode /
- endocrine control /
- skyhook and groundhook control
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表 1 参数辨识结果
$k$ 0 1 2 3 ${b_k}$ 9 614 8 905 −810 −11.45 ${c_k}$ 26 240 −18 980 −8 941 10.16 ${d_k}$ −95 216 17 288 24 203 1.86 表 2 各模式典型工况设计
行驶工况 模式划分 速度/$({\rm{km} }\cdot {\rm{h} }^{-1} )$ 路面 中低速平坦路面 经济模式 40 C 中高速粗糙路面 安全模式 80 D 中高速平坦路面 舒适模式 80 C 中低速粗糙路面 综合模式 40 D 表 3 车辆初始参数
参数 数值 簧载质量${m_s}/{\rm{kg}}$ 400 非簧载质量${m_u}/{\rm{kg}}$ 37 弹簧刚度${k_s}/{\rm{(N} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }{\rm{)} }$ 12 000 轮胎刚度${k_t}/({\rm{N} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } })$ 150 000 电磁阀减振器基值阻尼系数${c_0}/({\rm{N} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } })$ 580 直线电机推力系数${K_i}/({\rm{N}} \cdot {{\rm{A}}^{{\rm{ - 1}}}})$ 78.54 直线电机反电动势系数${K_e}/{\rm{(V}} \cdot {\rm{s}} \cdot {{\rm{m}}^{{\rm{ - 1}}}}{\rm{)}}$ 68.42 直线电机线圈内阻$R/\Omega $ 10 直线电机馈能回路内阻$r/\Omega $ 2 表 4 不同模式权重系数取值
工作模式 ${\lambda _1}$ ${\lambda _2}$ 经济模式 0.5 0.5 安全模式 0.3 0.7 舒适模式 0.7 0.3 综合模式 0.5 0.5 表 5 多模式参数优化结果
工作模式 天棚阻尼系数/$({\rm{N} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }) $ 地棚系数/$({\rm{N} } \cdot {\rm{s} } \cdot { {\rm{m} }^{ {\rm{ - 1} } } }) $ 经济模式 750 550 安全模式 650 950 舒适模式 1 550 450 综合模式 1 150 650 表 6 内分泌控制器参数
模式 ${K_1}$ ${K_p}$ ${K_i}$ ${K_d}$ ${K_2}$ 经济 2.52 0.36 0.000 48 0.000 012 0.66 安全 2.65 0.36 0.000 68 0 1.52 舒适 2.56 0.358 0.000 8 0.000 01 0.78 综合 2.55 0.38 0.000 8 0 1.3 表 7 各悬架指标时域输出均方根值及控制效果
初始参数仿真 变化参数仿真 模式 性能指标 悬架类型 控制效果/% 悬架类型 控制效果/% 被动 天地棚
控制内分泌复合天地棚 天地棚
控制内分泌复合天地棚 被动 天地棚
控制内分泌复合天地棚 天地棚
控制内分泌复合天地棚 经济 $a/({\rm{m}} \cdot {{\rm{s}}^{ - 2}})$ 1.6933 1.444 1.3935 −14.7 −17.7 1.2470 1.0774 1.0387 −13.6 −16.7 ${f_{{d} } }/{\rm{m} }$ 0.0404 0.0377 0.0376 −6.7 −6.9 0.0448 0.0416 0.0415 −7.1 −7.4 ${F_{{d} } }/{\rm{N} }$ 751.9 666.9 644.4 −11.3 −14.3 737.8 652.9 629.3 −11.5 −14.7 安全 $a/({\rm{m}} \cdot {{\rm{s}}^{ - 2}})$ 4.7893 4.1858 4.0182 −12.6 −16.1 3.5203 3.0873 2.9605 −12.3 −15.9 ${f_{{d} } }/{\rm{m} }$ 0.1144 0.1076 0.1073 −5.9 −6.2 0.1266 0.1189 0.1187 −6.1 −6.2 ${F_{{d} } }/{\rm{N} }$ 2126.7 1726.9 1652.4 −18.8 −22.3 2083.4 1720.9 1643.8 −17.4 −21.1 舒适 $a/({\rm{m}} \cdot {{\rm{s}}^{ - 2}})$ 2.3945 1.8294 1.7073 −23.6 −28.7 1.7637 1.3827 1.3102 −21.6 −25.7 ${f_{{d} } }/{\rm{m} }$ 0.0572 0.0519 0.0517 −9.3 −9.6 0.0634 0.0574 0.0572 −9.5 −9.8 ${F_{{d} } }/{\rm{N} }$ 1063.4 929.4 906.0 −12.6 −14.8 1043.5 920.4 901.6 −11.8 −13.6 综合 $a/({\rm{m}} \cdot {{\rm{s}}^{ - 2}})$ 3.3862 2.7902 2.5904 −17.6 −23.5 2.4936 2.0772 1.9226 −16.7 −22.9 ${f_{{d} } }/{\rm{m} }$ 0.0809 0.0726 0.0725 −10.2 −10.3 0.0897 0.0792 0.0791 −11.7 −11.8 ${F_{{d} } }/{\rm{N} }$ 1503.8 1290.3 1260.2 −14.2 −16.2 1475.7 1270.6 1229.3 −13.9 −16.7 表 8 各悬架指标平均功率谱密度共振频段峰值量化及控制效果
类型 不同频段/Hz 性能指标 悬架类型 控制效果/% 被动 天地棚控制 内分泌复合天地棚 天地棚控制 内分泌复合天地棚 初始参数仿真 4 ~ 8 ${a^{APSD} }/({({\rm{m} } \cdot { {\rm{s} }^{ - 2} })^2} \cdot { {\rm{H} }_{\textit{z} } }^{ - 1})$ 2.417 1.616 1.318 −33.14 −45.47 $f^{APSD}_d/({ {\rm{m} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 1.96×10−3 1.57×10−3 1.56×10−3 −19.89 −20.41 $F^{APSD}_d/({ {\rm{N} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 4.78×105 2.41×105 2.16×105 −49.58 −54.81 8 ~ 12.5 ${a^{APSD}}/({({\rm{m} } \cdot { {\rm{s} }^{ - 2} })^2} \cdot { {\rm{H} }_{\textit{z} } }^{ - 1})$ 1.226 0.894 0.714 −27.08 −41.76 $f^{APSD}_d/({ {\rm{m} }^2} \cdot { {\rm{H} }_{\rm{ {\textit{z} } } } }^{ {\rm{ - 1} } })$ 6.7×10−4 5.2×10−4 4.7×10−4 −22.39 −29.85 $F^{APSD}_d/({ {\rm{N} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 2.34×105 1.07×105 1.06×105 −54.27 −54.70 变化参数仿真 4 ~ 8 ${a^{APSD} }/({({\rm{m} } \cdot { {\rm{s} }^{ - 2} })^2} \cdot { {\rm{H} }_{\textit{z} } }^{ - 1})$ 2.149 1.465 1.186 −31.83 −44.81 $f^{APSD}_d/({ {\rm{m} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 2.23×10−3 1.82×10−3 1.69×10−3 −18.39 −24.22 $F^{APSD}_d/({ {\rm{N} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 4.39×105 2.33×105 2.01×105 −46.92 −54.21 8 ~ 12.5 ${a^{APSD}}/({({\rm{m} } \cdot { {\rm{s} }^{ - 2} })^2} \cdot { {\rm{H} }_{\textit{z} } }^{ - 1})$ 1.262 0.8847 0.7094 −29.89 −43.79 $f^{APSD}_d/({ {\rm{m} }^2} \cdot { {\rm{H} }_{\rm{ {\textit{z} } } } }^{ {\rm{ - 1} } })$ 6.3×10−4 5.0×10−4 4.9×10−4 −20.63 −22.22 $F^{APSD}_d/({ {\rm{N} }^2} \cdot { {\rm{H} }_{\rm{z} } }^{ {\rm{ - 1} } })$ 2.59×105 1.47×105 1.31×105 −43.24 −49.42 -
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