基于微分几何法的非线性分数阶悬架主动控制

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摘要现有主动悬架的研究主要以线性弹簧和线性阻尼组成的悬架系统为研究背景，但油气悬架、空气悬架和磁流变悬架等实际悬架不仅具有非线性特性，而且同时具有粘弹性材料的特点。因此含有非线性刚度和分数阶阻尼的悬架模型能更准确的描述悬架的动力学性能。本文针对含有三次方非线性刚度及分数阶阻尼的二自由度1/4汽车悬架模型进行研究，利用Oustaloup滤波器算法对悬架系统中的分数阶微分进行近似计算，分别采用PID控制器和基于微分几何理论反馈线性化的LQR控制器对该悬架系统进行主动控制。结果表明，基于PID控制器的主动悬架和基于反馈线性化LQR控制器的主动悬架都能有效提高汽车悬架的舒适性和稳定性，其中反馈线性化LQR主动控制效果明显优于PID控制。

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	常宇健1
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	陈恩利1
	李韶华1

关键词 ：非线性, 分数阶阻尼, Oustaloup滤波器算法, 微分几何法, LQR控制

Abstract：Current research of active suspension is mainly based on the suspension system composed of linear spring and linear damping, but the actual suspension, such as hydro pneumatic suspension, air suspension and magnetorheological suspension, not only has nonlinear characteristics, but also has the characteristics of viscoelastic materials.Therefore, the suspension model with nonlinear stiffness and fractional damping can more accurately describe the dynamic performance of suspension.In this paper, a two-degree of freedom 1 / 4 vehicle model with cubic nonlinear stiffness and fractional damping was studied.The fractional differential in the suspension system was approximately calculated by the oustaloup filter algorithm.The active control of the suspension system was carried out by a PID controller and a LQR controller based on the feedback linearization of differential geometry theory.The results show that the active suspension based on the PID controller and the active suspension based on the feedback linearization LQR controller can effectively improve the comfort and stability of automobile suspension, and the effect of feedback linearization LQR active control is obviously better than PID control.

Key words： non-linear fractional differential damping Oustaloup filter algorithm differential geometry method LQR control

收稿日期: 2019-09-09 出版日期: 2021-02-28

引用本文:

常宇健1,2，田沃沃2，金格2，陈恩利1，李韶华1. 基于微分几何法的非线性分数阶悬架主动控制[J]. 振动与冲击, 2021, 40(4): 270-276.
CHANG Yujian1,2, TIAN Wowo2, JIN Ge2, CHEN Enli1, LI Shaohua1. Active control of nonlinear suspension with fractional order based on a differential geometry method. JOURNAL OF VIBRATION AND SHOCK, 2021, 40(4): 270-276.

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http://jvs.sjtu.edu.cn/CN/ 或 http://jvs.sjtu.edu.cn/CN/Y2021/V40/I4/270

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