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摘要:
为提高钢轨打磨车打磨钢轨的平顺性及稳定性,提出以电动静液作动器(EHA)代替传统液压作动系统作为钢轨打磨车的专用执行器,考虑柱塞泵的总效率波动和液压缸动静摩擦差异大2个非线性因素,建立非线性数学模型;建立EHA的MATLAB、AMESim联合仿真模型,对PID控制、滑模变结构控制、反演控制进行控制策略对比研究,仿真分析验证反演控制在响应快速性及稳定性方面具有良好的表现。搭建四象限平台对EHA进行反演控制负载试验,结果表明:其位移控制精度达0.21 mm,具有较好的控制性能。
Abstract:In order to improve the smoothness and stability of rail grinding by the rail grinding vehicle, an electric hydrostatic actuator (EHA) was proposed to replace the traditional hydraulic system as the special actuator of the rail grinding vehicle. By considering the nonlinear factors including the total efficiency fluctuation of the plunger pump and the large difference between the dynamic and static friction of the hydraulic cylinder, a nonlinear mathematical model was established. The MATLAB and AMESim joint simulation model of EHA was established, and the control strategies of PID control, sliding mode variable structure control, and backstepping control were compared. The simulation analysis verified that the backstepping control had good performance in response speed and stability. The four quadrant platform was built to carry out the backstepping control load test of EHA. The results show that its displacement control accuracy reaches 0.21 mm, indicating good control performance.
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表 1 EHA设计指标
Table 1. Design indexes of EHA
行程/mm 负载力/KN 速度/(mm·s−1) 位移全尺寸精度/% 100 ≤10 ≥20 ≤0.77 表 2 摩擦模型相关参数
Table 2. Relevant parameters of friction model
${{{\sigma _0}} / ({{\mathrm{N}} \cdot {\mathrm{m}}}})$ ${{{\sigma _1}} /( {{\mathrm{N}} \cdot {\mathrm{m}}}} \cdot {{\mathrm{s}}^{ - 1}})$ ${{{\sigma _2}} /( {{\mathrm{N}} \cdot {\mathrm{m}} \cdot {{\mathrm{s}}^{ - 1}}}})$ ${{{v_{\mathrm{s}}}} /({{\mathrm{N}} \cdot {\mathrm{m}} \cdot {{\mathrm{s}}^{ - 1}}}})$ ${{ {{f_{\mathrm{c}}}} } /{{\mathrm{kN}}}}$ ${{ {{f_{\mathrm{s}}}} }/ {{\mathrm{kN}}}}$ $ 2.1\times {10}^{7} $ 0.1 150 0.1 142 12 表 3 EHA仿真参数
Table 3. Simulation parameters of EHA
参数 数值 油缸有效行程/mm 100 油缸直径/mm 63 活塞杆直径/mm 35 泵额定转速/(r·min−1) 3000 泵排量/(ml·r−1) 1 溢流压力/MPa 8 转子惯量/($ \mathrm{k}\mathrm{g}\cdot{{\mathrm{m}}}^{2} $) $ 2.7\times {10}^{-5} $ 线电阻/Ω 5.5 线电感/H $ 9.6\times {10}^{-3} $ 反电势常数/($ \mathrm{V}\cdot \mathrm{m}\cdot {{\mathrm{r}}}^{-1} $) $ 3.2\times {10}^{-2} $ 表 4 不同控制策略仿真数据
Table 4. Simulation data of different control strategies
控制策略 上升时间/s 控制精度/mm 最大超调量占比/% PID控制 4.97 0.037 0.08 滑模变结构控制 2.74 0.642 1.28 反演控制 3.56 0.035 0.07 表 5 反演控制试验数据
Table 5. Backstepping control test data
反演代表参数 上升时间/s 控制精度/mm 最大超调量占比/% $ {k}_{1}=200 $ 8.49 0.09 0.18 $ {k}_{1}=300 $ 5.54 0.72 1.43 $ {k}_{1}=350 $ 4.62 0.65 1.31 $ {k}_{1}=400 $ 4.12 0.77 1.54 -
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