Active control synthesis of nonlinear pitch-roll motions for marine vessels

Abstract This paper investigates the dynamical analysis and control synthesis for fractional-order pitch-roll system of marine vessels under regular waves. Suppression of the effects of roll and pitch motions is critical in improving maneuverability and stability of marine vessels with ensuring the safety of cargo and comfort to sailors. The pitch-roll mode shows complex behaviours such as period-2 motion, symmetry-breaking, torus attractor, and resonance depending on initial conditions, natural frequencies, wave frequencies, and wave amplitudes. Specifically, the nonlinear behaviours are characterized by phase portraits, bifurcation diagrams, and stability analysis. The nonlinear vibration patterns are observed even under regular waves because the pitch-roll motions are strongly coupled with two perpendicular directions. To secure the upright position of the vessels in heavy weather, adaptive fractional-order sliding mode control (AFOSMC) scheme has been employed to effectively regulate pitch-roll modes against extreme sea states. The closed stability of the ship pitch-roll system has been guaranteed by the Lyapunov theory. Numerical simulations have been extensively conducted to validate the effectiveness of the proposed control algorithms. To design more comfortable and safe vessels, this study presents pitch-roll resonance eliminations, stabilization and the challenges associated with robust vessel design.