The use of transfer functions for the improvement of the first-order linear Nomoto model solution

Abstract

This study investigates the application of the grey-box system identification method for estimating the parameters of the first-order linear Nomoto mathematical model, a well-established approach in naval architecture and marine engineering for representing ship manoeuvring dynamics. The primary objective is to assess the Nomoto model's predictive capability for yaw motion behaviour (1) simulated data from a full-scale model of a Marinerclass cargo vessel and (2) experimental free-running data from a scaled car carrier model. A key focus of the research is the investigation of 'adjustment intervals' within the grey-box identification method and their impact on the estimation accuracy of Nomoto model parameters and subsequent manoeuvring characteristics. Model performance is evaluated using statistical metrics for both turning circle and zigzag manoeuvres. In addition, a parametric sensitivity analysis is conducted to quantify the influence of the Nomoto time constant on the turning performance of the car carrier model. The results show that the predicted advance is highly sensitive to variations in the time constant, with larger values leading to increased 'Advance' due to slower yaw response. Overall, the first-order Nomoto model demonstrates reliable prediction of turning circle dynamics for the Mariner benchmark case, whereas for the car carrier case, it captures the overall turning circle and zigzag behaviour satisfactorily but shows limitations in reproducing turning circle characteristics with zigzag-trained models, particularly with respect to 'yaw-rate peaks' and 'Advance' prediction. These findings confirm the practical suitability of the firstorder Nomoto for real-time implementation, control system design, and computationally efficient simulation frameworks, while also highlighting the limitations of zigzag-trained linear models in representing the dynamics of directionally unstable vessels.