Abstract
•The complex behavior of a magnetorheological suspension system is studied.•A new fractional model with Mittag–Leffler non-singular kernel is introduced.•The analysis of the time-domain responses and the phase trajectories are employed.•The new fractional model is able to identify both chaotic and nonchaotic behaviors.•A state-feedback controller is designed to avoid the chaotic vibration.
This paper aims to establish a new fractional model to identify the complex behaviors of a magnetorheological suspension system under the road excitation of sinusoidal function. In the new model, we employ a recently introduced fractional operator with Mittag–Leffler kernel. To implement the model, we develop an efficient approximation scheme and discuss its stability and convergence analysis. We identify the complex behaviors by using the analysis of time-domain responses and phase portraits. The results show that the new fractional model has a strong capability to identify different characteristics of the system under investigation, including chaotic and nonchaotic behaviors. Finally, to avoid the chaotic vibration, a state-feedback controller is designed and its efficiency is proved by some simulation experiments.