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.

本文研究了规则波浪作用下船舶分数阶俯仰侧倾系统的动力学分析和控制综合。抑制侧倾和俯仰运动的影响对于提高船舶的机动性和稳定性，同时确保货物的安全性和水手的舒适性至关重要。俯仰滚动模式根据初始条件，固有频率，波频率和波振幅显示出复杂的行为，例如周期2运动，对称破坏，圆环吸引器和共振。具体来说，非线性行为的特征在于相图，分叉图和稳定性分析。由于俯仰滚动运动与两个垂直方向强烈耦合，因此即使在规则波下也可以观察到非线性振动模式。为了确保在恶劣天气下船只的直立位置，已采用自适应分数阶滑模控制（AFOSMC）方案来针对极端海况有效调节俯仰模式。李雅普诺夫理论已保证了船舶俯仰系统的闭合稳定性。数值模拟已被广泛地进行，以验证所提出的控制算法的有效性。为了设计更加舒适和安全的船只，本研究提出了消除俯仰侧倾共振，稳定和坚固的船只设计所带来的挑战。李雅普诺夫理论已保证了船舶俯仰系统的闭合稳定性。数值模拟已被广泛地进行，以验证所提出的控制算法的有效性。为了设计更加舒适和安全的船只，本研究提出了消除俯仰侧倾共振，稳定和坚固的船只设计所带来的挑战。李雅普诺夫理论已保证了船舶俯仰系统的闭合稳定性。数值模拟已被广泛地进行，以验证所提出的控制算法的有效性。为了设计更加舒适和安全的船只，本研究提出了消除俯仰侧倾共振，稳定和坚固的船只设计所带来的挑战。