FUNDAMENTAL PROPERTIES OF LINEAR SHIP STEERING DYNAMIC MODELS

線性船舶操縱模式特性分析

曾慶耀(Ching-Yaw Tzeng) ； 陳如芬(Ju-Fen Chen)

《Journal of Marine Science and Technology》 7卷2期 (1999/12) Pp. 79-88

https://doi.org/10.6119/JMST.199912_7(2).0002

摘要

船舶操縱運動包含複雜之流力作用現象，因此必須使用高階之非線性微分方程式方能完整描述其特性。然而就船舶自航器設計而言，多以較簡單之線性模式，如一階Nomoto模式爲設計依據。該模式具有架構簡單，且足以正確描述航向保持之小舵角船舶平擺動態之特性。經分析知，一階Nomoto轉移函數具有可鑑定性，而二階之Nomoto轉移函數亦爲可鑑定，但其零點與極點通常接近對消之狀況，因此實際計算時，會有數値不穩定現象。一階Nomoto模式所對應之狀態空間模式具有可控制性及可觀測，而二階之Nomoto模式對應之狀態空間模式為可觀測，但必須在橫移時間常數不等於平擺時間常數時，方為可控制。二階Nomoto轉移函數模式之零點及高頻之極點，乃源自橫移對平擺之耦合效應，且該零點將造成系統狀態之超射現象，因此對於在大舵角操縱時，平擺角速率之超射現象，須使用二階之Nomoto模式方足以描述之。另亦就一包含橫移、平擺及橫搖之狀態空間方程式，求出對應之四階轉移函數，並簡化成包含橫移、平擺之二階轉移函數及僅包含平擺這一階轉移函數。經由Bode頻率回應圖，可看出不同複雜程度模式造成之回應特性差異，該資料可提供使用者就其需求之模式需求精確度評估，進而選取簡單卻不失眞確度之模式。

並列摘要

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 modeled scribing 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 it self, 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.

並列關鍵字

Nomoto model ； Controllability and observability ； Identifiability ； Model reduction ； Overshoot ； Bode plot