A new fractional study on the chaotic vibration and state-feedback control of a nonlinear suspension system

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. (C) 2019 Elsevier Ltd. All rights reserved.