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題 名 | 船舶操縱非線性動態分析=Analysis of Nonlinear Ship Steering Dynamics |
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作 者 | 曾慶耀; 林港富; | 書刊名 | 中國造船暨輪機工程學刊 |
卷 期 | 19:1 2000.02[民89.02] |
頁 次 | 頁47-59 |
分類號 | 444.8 |
關鍵詞 | 非線性操縱方程式; 分歧; 相位平面圖; 穩定平衡; 不穩定平衡; Nonlinear steering dynamics; Bifurication; Phase-plane plot; Stable equilibrium; Unstable equilibrium; |
語 文 | 中文(Chinese) |
中文摘要 | 本文以Norrbin非線性平擺方程式為基礎架構,探討不穩定船舶之動態特性。其中Norrbin 方程式係由一階 Nomoto 模式加以非線性項擴展形成。 透過調整 Norrbin 模式中之線性項係數可描述不同穩定程度之船舶操縱特性。例如舵角為零度,當線性項係數由正值變成負值時,則系統平衡狀況, 從原本一個舵角對應至一個平擺角速率之一對一關係,形成一個舵角對應至零、正、負值三個平擺角速率。此種不唯一之對應現象即為分歧(Bifurication),同時也是系統不穩定現象之徵兆。其中零平擺角速率對應至不穩定平衡點,而具正、負值之平擺角速率則為穩定平衡點。亦即船舶於零舵角時,實際上無法維持平擺角速率為零之直線運動,只要有微小干擾,則該不穩定船舶立即趨向正平擺之右迴旋,或負平擺之左迴旋,至於趨向何者則依干擾特性而定。另可藉由系統線性化並對平衡點展開,找出其對應之特徵值以驗證平衡點之穩定性。另亦說明,具逆螺旋試驗特性之穩態平擺及舵角關係圖,其中之不穩定迴圈寬度可用來描述船舶不穩定之程度。且可由不穩定迴圈寬度,界定出穩定住船舶航向所需之最小臨界舵角。上述推論將透過Z型測試驗證之,若使用小於臨界舵角值執行Z型測試,則方向角超射量將發散而無法控制船舶航向。而當使用超過臨界舵角值執行Z型測試,方足以抑制住船舶不穩定性控制船舶航向,而不致產生過大之方向超射角。另基於實際迴旋試驗時,平擺角速率及橫移速率呈現極其相近之變化趨勢之觀察,提出與Norrbin非線性模式相同架構之非線性橫移模式。 經結合本文提出之非線性橫移模式與Norrbin非線性平擺模式,可繪出v-r(橫移-平擺) 之相位平面圖,並藉以顯示船舶在給予不同初始狀況之收斂趨向,以進一步說明船舶動態在穩定平衡點與不穩定平衡點附近之行為。 |
英文摘要 | A simple nonlinear yaw equation proposed by Norrbin is employed in studying the steering dynamics of unstable vessels. The Norrbin model is a first order nonlinear differential equation describing the input-output relationship of the yaw rate and rudder angle. Specifically, a linear yaw rate term and a cubic yaw rate term appear in the model and it is indicated that the ship dynamics changes significantly due to variation of the coefficients α�� associated with the linear yaw rate term. As the α�� value varies from positive to negative, the unique mapping between the rudder angle and the yaw rate becomes the case that a rudder angle can give rise to three different equilibrium yaw rate conditions. This is an indication of system instability, known as the bifurication. Specifically, for zero rudder angle, the zero yaw straight line motion is an unstable equilibrium point and the positive yaw rate and negative yaw rate correspond to stable equlibrium points. This implies that with no rudder, the ship can hardly maintain a straight line motion and will either enter into a starboard or port turn, depending on the initial conditions or disturbance applied. Linearization technique is employed and the eigen values at the equilibrium points are computed to verify the stability condition of the equilibrium points. Moreover, the loop width that defines the degree of instability of a ship in the steady yaw-rudder plot that characterizes the reverse spiral maneuver is found to be closely related to the critical rudder angle required to stabilize the ship in a zig-zag maneuver. Simulations are provided to justify the above statements. Specifically, for unstable vessels, zig-zag maneuver. Simulations are provided to justify the above statements. Specifically, bound. However, the overshoot angle is reduced when a rudder angle larger than the ctitical value is applied. A nonlinear sway dynamics model of similar structure to the Norrbin yaw model is proposed, basing upon the observation of the similarity in the yaw and sway patterns in a turning maneuver. Finally by employing the Norrbin yaw model and the proposed sway model, sway-yaw phase plots that show the state trajectories from different initial conditions are provided to help identifying and explaining the location of the stable and unstable equilibrium points. |
本系統中英文摘要資訊取自各篇刊載內容。