Ship propulsion modelling and optimisation in stern quartering seas

• Development of a 6-DoF time-domain simulation framework to study vessel propulsion dynamics and performance optimisation in stern-quartering seas with five state-of-the-art control algorithms. • Hydrodynamic and frequency-domain analyses are used to show that surge dynamics behave approximately as a linear low-pass filter, providing phase-lag and amplitude insights useful for Extremum Seeking Control (ESC) tuning and convergence. • Comparative evaluation of five control strategies shows that Model Predictive Control (MPC) achieves the highest mean propeller efficiency while keeping power variability limited. • A combined shaft speed and power control strategy creates favourable engine operating conditions, while a simpler power control method effectively reduces power oscillations under wave-induced disturbances. • Implementation of ESC to adjust propeller pitch in real time, enabling rapid convergence to near-optimal settings for efficiency and vessel speed while maintaining constant power. This paper investigates propulsion dynamics and performance optimisation for vessels operating in following seas using a 6-DoF time-domain simulation framework that combines a unified seakeeping and manoeuvring model with propulsion control. The work focuses on the behaviour of the propulsion system and the impact of wave disturbances, and studies propulsion controllers and the effect of thrust oscillations. Five control strategies are implemented, and shown that the combined shaft-speed/power scheme yields favourable engine operating points, while Model Predictive Control (MPC) attains the highest mean propeller efficiency with constrained power variability. For long-time-scale optimisation, a model-free Extremum Seeking Control (ESC) method is implemented to adjust the propeller pitch in real time. The results provide proof of concept that ESC converges to near-optimal operating conditions for propulsion efficiency and vessel speed within practical time scales. A novel approach is proposed to maximise the vessel speed while keeping the power constant, and we study how this approach is favourable relative to alternatives. Hydrodynamic analysis further shows that surge dynamics behave approximately as a linear low-pass filter at the investigated operating conditions, which explains the ESC convergence behaviour and links vessel dynamics to controller performance.