Controlling period-doubling route to chaos phenomena of roll oscillations of a biased ship in regular sea waves

Dynamics, control, and stability of roll oscillations a biased ship in regular sea waves are investigated. The under oscillation is modelled as the classical Helmholtz–Duffing oscillator with strongly nonlinear asymmetric restoring moment characteristics. incremental harmonic balance method, amended pseudo-arc-length continuation approach, employed to obtain uncontrolled controlled frequency responses. primary subharmonic responses system examined through period-doubling route chaos path. same model then investigated state feedback control time delay. In scheme, moving weight actuated by delay controller generate anti-rolling moment. periodic studied using semi-discretization method extended Floquet theory. Bifurcation points on response branches identified from eigenvalue study. effect gains loop controlling Several chaotic obtained paths successfully controlled. Stable, periodic, steady-state solutions IHB verified numerical integration equation motion when applicable. Solutions aided phase portrait, Poincaré map, history, Fourier spectrum for better clarity. It shown that appropriate selections parameters can effectively reduce amplitude great extent improved measure stability.