Dynamic analysis of the nonlinear fiber oscillator with fractional-order control in multi-filament fiber winding

Abstract

This work aims to investigate the dynamic behavior of the carbon fiber oscillator in the winding process of the novel multi-filament fiber winding equipment for high-pressure vessels, employing an improved fractional-order controller. Specifically, a coupling suppression fractional-order PD (CS-FOPD) control strategy is proposed for the two-degree-of-freedom carbon fiber oscillator. The multiple-scales method is employed to analyze the primary resonance of the system and derive the steady-state amplitude and phase solutions. The stability of the system is assessed using the Routh-Hurwitz criterion, and the analytical solutions are validated through numerical simulations. Furthermore, numerical simulations are conducted to investigate the effects of CS-FOPD control on the amplitude-frequency characteristics, controller performance, multi-stable phenomenon, attraction domain structure, and global bifurcation behavior of the system under varying system parameters. In the absence of coupling suppression strategy, the primary-superharmonic resonance characteristics are analyzed using the multiple-scales method, and stability is evaluated via Lyapunov's first method. The nonlinear dynamics of the system are further explored through amplitude-frequency response curves and attraction domain evolution. Finally, the Melnikov method is employed to calculate the distance between stable and unstable manifolds, providing an analytical prediction of the onset of chaos. The main obtained simulation results showed the excellent performance of the proposed control strategy and the evolution of the system's dynamic characteristics. By analyzing the nonlinear dynamics of the system under the proposed control strategy, this study provides key insights for optimizing the stability and performance of the novel multi-filament carbon fiber winding equipment.