Effect of Delay on Control of Direct Resonance of Ships in Beam Waves Using a Proportional–Derivative Controller With Delay
Bibliographic record
Abstract
Abstract A harmonically excited, single-degree-of-freedom time-delay system with cubic and quintic nonlinearities is studied. This system describes the direct resonance of a ship with an actively controlled antiroll tank (ART) that is subjected to beam waves. We consider low-, medium-, and high-freeboard ship models. A proportional–derivative (PD) controller with a constant time delay is assumed to operate the pump in the active ART system. The delay originates from the time required to pump fluid from one container to another, the inertia of large impeller blades and linkages, and the measurement and processing time of the roll-sensing unit. The stability boundary of the system, in the parametric space of the control gain and the delay, is derived analytically from the characteristic equation of the linearized system. We show that the area of the zero equilibrium region is inversely related to the derivative time constant of the PD controller; thus, we focus on a strictly proportional-gain controller. The spectral Tau method is used to identify the eigenvalues associated with the zero equilibrium since the rightmost eigenvalues determine the system's robustness to perturbations in the initial conditions. We use the method of multiple scales and harmonic balance to obtain the global bifurcation diagram in the space of the applied frequency and the amplitude of the response. Numerical simulations verify our analytical expressions. Study of the dynamics, stability, and control of the roll motion of ships is critical to avoid dynamic instabilities and capsizing.
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How this classification was reachedexpand
Full frame machine prediction
Teacher imitationNot calibrated prevalence, not ground truth. Human validation pending. The Gemma side is a direct model label for every work in the frame, read from the title-only record. The Codex side is a classifier learned from the 10,348 direct Codex labels and calibrated to design-weighted sample rates; fields without enough sample support carry no Codex call. Candidate is the union of the two sides; consensus is their intersection. These outputs are machine_predicted_unvalidated and are not human labels.
Distilled classifier scores by category (both heads)
| Category | Codex | Gemma |
|---|---|---|
| Metaresearch | 0.000 | 0.001 |
| Meta-epidemiology (narrow) | 0.000 | 0.000 |
| Meta-epidemiology (broad) | 0.000 | 0.000 |
| Bibliometrics | 0.000 | 0.000 |
| Science and technology studies | 0.000 | 0.001 |
| Scholarly communication | 0.001 | 0.000 |
| Open science | 0.000 | 0.000 |
| Research integrity | 0.000 | 0.000 |
| Insufficient payload (model declined to judge) | 0.001 | 0.000 |
Machine scores (provisional)
The two teacher heads of the student model, read on this work. A score orders the frame for review; it never asserts a category, and the validation status ships verbatim with every row.
Baseline scores from an immature model (maturity gate not passed, 7 training rounds). Scores rank; they never assert a category.
score_only:v0-immature-baseline · verbatim from the scoring run: score_only means the number may rank works, and no category label ships from itClassification
machine, unvalidatedMachine predicted; a candidate call from one source (direct Gemma or distilled Codex), not a consensus.
How this classification was reached, model by model and score by score, is at the end of the page under "How this classification was reached".