中文摘要：

为研究分数阶微积分在汽车空气悬架半主动控制中的应用效果，建立了4自由度半主动空气悬架非线性动力学模型。采用改进的Oustaloup滤波器算法来模拟分数阶微积分，进而建立分数阶天棚阻尼半主动悬架的仿真模型，将仿真结果与被动悬架和整数阶天棚阻尼半主动悬架进行对比分析。分析结果表明：当汽车以20m／s的速度行驶在B级路面时，与被动悬架相比，整数阶和分数阶天棚阻尼半主动悬架的车身垂向加权加速度均方根值分别减小了31．9％和43．9％，车身俯仰角加速度均方根值分别减小了23．1％和30．7％；基于分数阶微积分的天棚阻尼控制策略能更有效地抑制车身共振，改善乘坐舒适性。

英文摘要：

In order to study the application of fractional calculus in the control of semi-active air suspensions, a 4-DOF nonlinear dynamic model of semi-active air suspension system was built. A modified Oustaloup filter algorithm was adopted to simulate fractional calculus. The simulation model of semi-active suspension with fractional-order sky-hook damping was developed. And its simulation results were compared with those of passive suspension and semi-active suspension with integral-order sky-hook damping. The comparison results indicate that in contrast to passive suspension, when the car is running at the speed of 20 m/s on grade B road, the integral-order and fractional-order sky-hook damping control strategies reduce weighted RMS （root-mean-square） values of vehicle body vertical acceleration by 31.9% and 43.9% , and decrease RMS values of pitching angular acceleration by 23.1% and 30.7%. The results further show that the semi-active control based on fractional calculus could suppress vehicle body resonance more effectively.