考虑一类非线性船舶横摇动力学模型，采用数值方法求解其运动微分方程，通过分岔图、相轨线图和吸引域揭示了系统的多稳态动力学。利用间歇控制方法，实现系统在不同的稳态之间切换。进一步考虑间歇控制力的强度，研究约束控制力对控制效果的影响。含约束的间歇控制方法，在限制了最大控制信号的情况下，先将当前系统的轨迹控制到一个暂态的轨迹上，再通过间歇控制进行不断的调整，使其最终稳定到期望周期解的轨迹上。数值研究结果表明：含约束的间歇性控制方法的整个控制过程相对平缓，同时又可以控制单次输入信号的强度大小，更适用于实际的多稳态动力系统。
关键词：船舶横摇系统；多稳态动力学；吸引域；间歇控制方法
Abstract
Considering a class of ship’s nonlinear rolling dynamics model, numerical methods are used to solve the established differential equations of motion, and multistable dynamics are uncovered by bifurcation diagram, phase trajectory diagram and attraction basins research system. Intermittent controlling method is used to enable the system to switch between different steady states. The strength of the intermittent control force is further considered, and the effect of limited control force on the efficiency of the control effect is investigate. The intermittent controlling method with constraints, in the case of limiting the maximum control signal, controls the current trajectory to a transient one first, then adjusts continuously through intermittent controlling to stabilize the dynamics to the trajectory of the desired periodic solution. The numerical results show that the whole control process of the intermittent controlling method with constraints is relatively flat, and at the same time it can control the strength of a single input signal, which is more suitable for the practical dynamics system.
Key words: Ship’s rolling system; Multistable dynamics; Basins of attraction; Intermittent controlling method
关键词
船舶横摇系统 /
多稳态动力学 /
吸引域 /
间歇控制方法
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Key words
Ship’s rolling system /
Multistable dynamics /
Basins of attraction /
Intermittent controlling method
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