In this paper, we aim to analyze the complicated dynamical motion of a quarter-car suspension system with a sinusoidal road excitation force. First, we consider a new mathematical model in the form of fractional-order differential equations. In the proposed model, we apply the Caputo–Fabrizio fractional operator with exponential kernel. Then to solve the related equations, we suggest a quadratic numerical method and prove its stability and convergence. A deep investigation in the framework of time-domain response and phase-portrait shows that both the chaotic and nonchaotic behaviors of the considered system can be identified by the fractional-order mathematical model. Finally, we present a state-feedback controller and a chaos optimal control to overcome the system chaotic oscillations. Simulation results demonstrate the effectiveness of the proposed modeling and control strategies.

在本文中，我们旨在分析具有正弦道路激励力的四分之一汽车悬架系统的复杂动力学运动。首先，我们考虑分数阶微分方程形式的新数学模型。在提出的模型中，我们将Caputo–Fabrizio分数运算符与指数核一起应用。然后，为了解决相关方程，我们提出了一种二次数值方法，并证明了其稳定性和收敛性。在时域响应和相像框架内的深入研究表明，所考虑系统的混沌和非混沌行为都可以通过分数阶数学模型来识别。最后，我们提出了一个状态反馈控制器和一个混沌最优控制来克服系统混沌振荡。