Chaotic Behavior and Feedback Control of Magnetorheological Suspension System With Fractional-Order Derivative

The fractional differential equations of the single-degree-of-freedom (DOF) quarter vehicle with a magnetorheological (MR) suspension system under the excitation of sine are established, and the numerical solution is acquired based on the predictor–corrector method. The analysis of phase trajectory, time domain response, and Poincaré section shows that the nonlinear dynamic characteristics between fractional and integer-order suspension systems are quite different, which proves the superiority of using fractional order to describe the physical properties. By discussing the influence of each parameter on the vibration, the range of parameters to avoid the chaotic vibration is obtained. The variable feedback control is used to control the chaotic vibration effectively.