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

Advances in Difference Equations

Amin Jajarmi¹  Samaneh Sadat Sajjadi²  Özlem Defterli³  Dumitru Baleanu⁴ 

[1] Department of Electrical Engineering, University of Bojnord, P.O. Box, 94531-1339, Bojnord, Iran;Department of Mathematics, Near East University TRNC, Mersin 10, Nicosia, Turkey;Department of Electrical and Computer Engineering, Hakim Sabzevari University, Sabzevar, Iran;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;Department of Mathematics, Faculty of Arts and Sciences, Cankaya University, 06530, Ankara, Turkey;Institute of Space Sciences, P.O. Box, MG-23, R 76900, Magurele-Bucharest, Romania;Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan;

关键词: Fractional calculus;    Exponential kernel;    Quarter-car suspension system;    Chaotic oscillation;    State-feedback control;    Optimal control;    34A08;    34C28;    49M05;    93B52;   

DOI  :  10.1186/s13662-021-03393-x

来源: Springer

【 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