Nonlinear Controller Design Of A Ship Autopilot

1. Nonlinear Controller Design Of A Ship Autopilot 指導老師：曾慶耀　教授 學 生：呂政倫 學 號：10267041

2. Out line • Introduction • Mathematical model of ship dynamics • Control system for ship course tracking • Simulation test • Conclusion

3. Introduction A conventional autopilot system used for controlling the ship motion is a PD controller with constant parameters values. These controllers can work properly in precisely defined operating conditions, but the quality of their work is worse when these conditions change. Ship dynamic characteristics can change as a consequence of changes of the ship speed, load, and external disturbances such as waves, wind, and/or sea currents.

4. Therefore a lot of research activities have been oriented to improving the quality of operation of these controllers using adaptive mechanisms which automatically change ship model parameters, depending on operating conditions. Controllers were tested in calm water and in the presence of sea waves . Compare the obtained results .

5. Mathematical model of ship dynamics Assuming a ship sailing on water surfaces which is stable in surge and sway directions and . we can neglect the dynamics of roll 、 pitch and heave.

6. The state variables describing the ship motion are collected in two vectors, and . R(ψ) is the rotation matrix, calculated from the formula

7. 2.1. Mathematical model of CyberShip II: Cybership II is a scale replica of a supply ship ,made at a scale of 1:70. Its mass is 23.8 kg, the overall length is 1.255 m, and the breadth is 0.29 m. The mathematical model of this ship: The system inertia matrix includes the rigid-body system inertia matrix ,and the hydrodynamic matrix included added mass coefficients .

8. The Coriolis-centripetal matrix C(ν) includes Coriolis and centripetal terms acting on the ship , as well as hydrodynamic Coriolis and centripetal terms connected with the fluid in which the ship moves .

9. The damping matrix which consists of the linear part , determined for a selected small and constant surge velocity , and nonlinear part , determine hydrodynamic damping forces at high velocities.

10. The vector of forces acting on the ship’s hull refers to the forces generated by the propellers and rudders and to the forces generated by acting disturbances: 2.2. Mathematical models of propellers and rudder blades For small speeds, the propeller/blade model can be divided into two parts, of which the first one describes the nominal thrust :

11. The second part refers to additional lift and drag forces the following surge and sway forces are obtained:

12. the vector of forces applied to the hull depending on the distribution of the propellers and rudder blades: where the matrix T is the actuator configuration matrix 2.3. Environmental disturbances (i) waves generated by the wind, (ii) ocean currents, (iii) the wind. which is directly added to the vector τ.

13. The wave slope can be related to the wave spectral density function .

14. Control system for ship course tracking The input signal in the examined control system was the desired course . To evaluate the quality of operation of the examined controllers, the cost function was defined as

15. 3.1. PD controller PD controller controls the rudder blade deflection depending on the values of the heading error and the yaw rate. 3.2. Sliding mode controller The output signal of the sliding mode controller, being the input signal for the controlled object, is composed of two terms (equivalent part and switching part.) 3.2.1. Equivalent part The manoeuvring model is obtained which consists of the surge dynamics

17. The parameters of the transfer function are related to the hydrodynamic coefficients

18. The Nomoto model can be reduced by determining the substitute time constant using the relation T = T1 + T2 − T3:

19. The sliding surface was definedas the equivalent part of the sliding mode controller following formula: where N is the gain to scale the commanded heading ,which is calculated from

20. 3.2.2. Switching part The switching part of sliding mode control takes the form 3.2.3. Complete form The control law of the sliding mode controller

21. Comparing Eq: (20) and (43) PD controller: The commanded rudder blade deflection only calculated from the heading error and the yaw rate . Sliding mode controller: The commanded rudder blade deflection is calculated from the course error, the yaw rate, the commanded yaw rate, and the commanded yaw acceleration.

22. Simulation tests

25. Conclusion The simulations made conclude that both controllers properly led the ship in calm water, and similar cost function values were obtained. The sliding mode controller better tracks the heading at the presence of waves than the PD controller. The advantage of the use of switching in the sliding algorithm that is helps to keep the current course by disturbances generated by an external environment .

26. THE END

27. 順滑模式:「t = 0，系統狀態X(t)在有限時間內，被外力所迫，推向順滑平面上(s(x) = 0)，且於後續時間內，系統不再脫離此順滑平面，並沿著順滑平面向平衡點移動，最終到達系統狀態的目標值」。 順滑模式的產生，可以歸納出兩個程序： 1.當系統在順滑面之外時，選定順滑函數，使所有軌跡在有限時間內接觸到順滑面，這個過程稱為迫近模式。 2.當系統進入後，應保證使系統不再離開並朝平衡點 x=0 逼近，這個過程稱為等效模式。

28. Switching:將狀態分成3個子空間s(x)>0 、 s(x)<0 和s(x)=0 ，設計就是要在s(x)=0 空間產生順滑模式。 科氏力:是因地球自轉，而對地表附近的運動（如風、飛彈、海流等等）所造成的一種偏向力。 向心力:物體做等速率圓周運動，加速度為向心加速度，方向指向圓心，依F＝ma，物體受力(F)方向必和加速度(a)方向相同，因此合力也指向圓心，稱為向心力(Fc)。