基于分数阶PIλDμ的非线性分数阶主动控制悬架研究

Research on nonlinear fractional active control suspensionbased on fractional order PIλDμ

本文针对含非线性刚度和分数阶阻尼的悬架模型进行主动控制研究。在传统线性悬架模型的基础上进行改进,建立了含有三次方非线性刚度及分数阶阻尼的二自由度1/4车数学模型,并利用Oustaloup滤波器算法近似计算该模型中的分数阶微积分算子,然后分别设计分数阶PIλDμ控制器和整数阶PID控制器对该悬架系统进行主动控制研究。仿真结果表明,基于分数阶PIλDμ控制器的主动控制悬架和基于整数阶PID控制器的主动控制悬架都能够改善汽车悬架的平顺性和稳定性,但是分数阶PIλDμ主动控制效果明显优于整数阶PID控制,验证了非线性分数阶悬架模型的合理性和分数阶PIλDμ控制的有效性。

In this paper,the active control of suspension model with nonlinear stiffness and fractional damping is studied.Based on the improvement of the traditional linear suspension model,a two degree of freedom 1/4 vehicle mathematical model with cubic nonlinear stiffness and fractional damping is established,and the fractional calculus operator in the model is approximately calculated by the Oustaloup filter algorithm,then the fractional PIλDμcontroller and the integral PID controller are designed respectively to study the active control of the suspension system.The simulation results show that both the active control suspension based on fractional order PIλDμcontroller and the active control suspension based on integral order PID controller can improve the ride comfort and stability of automobile suspension,but the fractional order PIλDμactive control effect is obviously better than the integral order PID control,which proves the rationality of nonlinear fractional order suspension model and the effectiveness of fractional order PIλDμcontrol.