This paper is concerned with the fundamental properties associated with the Nomoto models. Specifically, the state space model associated with the first order Nomoto model is both observable and controllable. The state space model associated with the second order Nomoto model is also observable; however, it is controllable only if the effective sway time constant is different from the effective yaw time constant. The zero appearing in the transfer function model is found responsible for the overshoot behaviors, which are typical in the yaw rate for large rudder angle steering. This suggests that a second order Nomoto model is more appropriate if the overshoot feature is to be properly modeled. Both the first and second order Nomoto transfer function models are identifiable, with an ill-conditioning problem associated the latter. This makes the first order Nomoto model very popular in the adaptive autopilot applications. Model reduction for a fourth order transfer function ship model describing the sway-yaw-roll dynamics is conducted to reach the second order Nomoto model describing the sway-yaw dynamics and the first order Nomoto model describing the yaw dynamics itself, and the Bode plots for these models are given to show the changes in system frequency response caused by model simplification. Thus, appropriate model structures can be selected according to the intended frequency range of application to meet the modeling accuracy requirements.
Tzeng, Ching-Yaw and Chen, Ju-Fen
"Fundamental Properties of Linear Ship Steering Dynamic Models,"
Journal of Marine Science and Technology: Vol. 7:
2, Article 2.
Available at: https://jmstt.ntou.edu.tw/journal/vol7/iss2/2