On a nonlinear dynamical system with both chaotic and nonchaotic behaviors: a new fractional analysis and control

Advances in Difference Equations

article

Baleanu, Dumitru¹  Sajjadi, Samaneh Sadat⁴  Jajarmi, Amin⁵  Defterli, Özlem¹ 

[1] Department of Mathematics, Faculty of Arts and Sciences, Cankaya University;Institute of Space Sciences;Department of Medical Research, China Medical University Hospital, China Medical University;Department of Electrical and Computer Engineering, Hakim Sabzevari University;Department of Electrical Engineering, University of Bojnord;Department of Mathematics, Near East University TRNC

关键词: Fractional calculus;    Exponential kernel;    Quarter-car suspension system;    Chaotic oscillation;    State-feedback control;    Optimal control;   

DOI  :  10.1186/s13662-021-03393-x

学科分类：航空航天科学

来源: SpringerOpen

【 摘 要 】

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.

【 授权许可】

CC BY