Effect of Delay on Control of Direct Resonance of Ships in Beam Waves Using a Proportional–Derivative Controller With Delay

Junaidvali Shaik, Thomas K. Uchida, and C. P. Vyasarayani
ASME. J. Comput. Nonlinear Dynam. June 2022; 17(6): 061004. https://doi.org/10.1115/1.4053561

Ships navigating heavy seas are susceptible to various types of wave excitation, which may lead to dynamic instabilities and, in the worst case, capsizing. Compared to the pitch and yaw motions, the roll motion of a ship has the least amount of damping. We study a harmonically excited, single-degree-of-freedom time-delay system with cubic and quintic nonlinearities. This system describes the direct resonance of a ship with an actively controlled anti-roll tank (ART) that is subjected to beam waves, or waves that are approximately perpendicular to the ship’s heading. A proportional–derivative (PD) controller with a constant time delay is assumed to operate the pump in the active ART system. A key result is obtained by deriving the stability boundary of the system, in the parametric space of the control gain and the delay, from the characteristic equation of the linearized system. As shown here, a smaller controller delay is not always better since, in some cases, reducing the delay will reduce the maximum controller gain for which the system is stable. We conduct further analyses using the spectral Tau method, the method of multiple scales, the method of harmonic balance, continuation techniques, and direct numerical simulation.
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