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Influence of ship motion nonlinearities on the course controller design

Influence of ship motion nonlinearities on the course controller design. 指導 老師：曾慶耀　教授 學 生：呂政倫 學 號： 10267041. Outline. Abstract Introduction Maneuver prediction of ships Identification of a Linear Ship Model Investigation of the mariner class Mathematical Model

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Influence of ship motion nonlinearities on the course controller design

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  1. Influence of ship motion nonlinearities on the course controller design 指導老師：曾慶耀　教授 學 生：呂政倫 學 號：10267041

  2. Outline • Abstract • Introduction • Maneuver prediction of ships • Identification of a Linear Ship Model • Investigation of the mariner class • Mathematical Model • Analysis of the Turning Ability • PID-controller Design • Comparison of the Course Controllers • Conclusion

  3. Abstract • Since a ship yard usually provides insufficient data for developing a ship control system. • Controller design is based upon a Nomoto model determined with a Clarke estimation of hydrodynamic derivatives. • The steering quality of the Mariner class (ship) is discussed and linear model parameters are obtained by an interval approximation of Dieudonn´e’s spiral curve in the working range of the rudder.

  4. Introduction • In general, course and track controls of modernships are widely designed on the basis of linearNomoto models. • The linear velocity and acceleration derivatives of the mathematical model are usually estimated by the hull geometry. • Determiningthe hydrodynamic derivatives is to conduct experimental methods measuring forces and moments. • Differenttypes of ships in institute showing that nonlinearities of the plant are still problematic. • This may finally lead to inaccuracies in identifyingmathematical models, inefficient controllers, anda higher rate of wear of the rudder engine.

  5. Maneuver prediction of ships • The MAPSYS project (”Manoeuvre PredictionSystem for Ships”) aimed at improving the nautical safety of ships. • The prediction modelconsists of an adaptive linear time-variant dynamic model and a cascade control module withan inner course autopilot loop and an outer trajectory tracking control loop. • A nonlinear apriori model is usually determined requiring manyparameters obtained by measurements or designdrawings.

  6. Identification of a Linear Ship Model • The gathered data is used for determining parameters of, at first, the Nomoto coursemodel and, secondly, the track model applying theprediction-error identification method (PEM). • Nomoto’s 2nd-order model

  7. Investigation of the mariner class • Mathematical Model: 三自由度 surge(縱移), sway(橫移), yaw(平擺)非線性方程組

  8. Laplace transformation of Eq. (3) and somerearrangements yields the transfer function ofNomoto’s 3rd-order model: which can be simplified to the 2nd-order model,Eq. (1). Neglecting the influence of the rudder rate limiter

  9. Analysis of the Turning Ability

  10. Least-squares method is adopted inorder to determine the linear regression of thespiral curve in the defined rudder range where the regression coefficients are

  11. Using engineering judgment, the tangent slopeapproximates well the slope of the global rudderline.

  12. PID-controller Design • The controller design performed separately for each linearized system. Forsimplicity, Nomoto’s 2nd-order model is used forthe design process. • The root loci are reshaped by inserting a phase-lead compensator into the open loop so that two branches intersect a pair of dominant poles. • This pair of dominant complex-conjugate closed-loop poles is placed at the desired location specified by the damping ratio D and the natural frequency calculated.

  13. The transfer functions of the controllers are: • In order to compare both controller designs, themost important design criterion is

  14. The -controller cannot achieve the requested rudder angle criterion due to the small derivative time constant in conjunction with the required performance. Therefore, the settling time is increased to 150 s so that the specifications can now be fulfilled (Table 4).

  15. Comparison of the Course Controllers

  16. Conclusion • 本文主旨在設計一個影響船舶旋轉能力的非線性航向控制器。 • 線性控制器設計採用Dieudonn‘e螺旋的近似區間在舵的工作範圍內，以提供更好的成效。 • 由於船舶理論需要實際的論證是很困難的，因此造船場需要提供控制器設計的流體力學相關資料。 • 非線性控制器的設計概念需要對非線性螺旋曲線和自適應航向和追蹤控制參數做更多的實驗和理論研究。

  17. The End

  18. 1.預測誤差法(PEM): • 預測技術通常假設過去存在的系統未來將持續 • 誤差＝實際值－預測值 2.Dieudonn´e’sspiral test=DIRECT SPIRAL TEST : 評估船的動態穩定性及航向保持的能力

  19. 3.Nomoto 2nd-order model: 線性化的sway和yaw方程式取拉式轉換得平擺角速率對舵角的 轉移函數 4.regression coefficients(迴歸係數): 由最小平方法求得 5.least-squares method: 給定 n 個二維資料 (x1，y1)，(x2，y2)，(x3，y3)，.. (xn，yn) 得一條迴歸直線(最適合直線) y = a + bx， 6:Global ruddercharacteristic:須於舵工作範圍內複製一個真實的轉向行為 7.zig-zag maneuver: 為反覆執行固定大小值，但方向相反之舵令使船依所要求之航向旋轉，直到航向角與舵角值相同時在打反舵

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