Ship track-keeping: experiments with a physical tanker model

1. Ship track-keeping:experiments with a physical tanker model 指導教授:曾慶耀 學生:曾彥翔 學號:10253081

2. Outline • Introduction • Model • Controler design • Experiment • Conclusion

3. Introduction • For economic and safety reasons, experiments with ship-tracking algorithms, and maneuvering workshops for ship captains and harbor pilots are often carried out using computer simulators, or small-scale material models ,the results of experiments can easily be recalculated to refer to real objects, using well-known relations

4. Model broken line:desiredtrajectory K,L:turningpoints :earth-fixed clock-wise Cartesian frame :frame related to the current segment of the trajectory :moving frame :osition coordinates :longitudinal and transverse components of the ship’s speed vector :heading angle :turning rate

5. a simple dynamic linear model In order to determine the control law, the actual values of and should be known. However,only be record directly at The plant out

6. The variables can be indirectly estimated on the basis of measured position coordinates heading and rudder angle These measurements can be proved to fulfill the conditions of full observability of the system A simple and well-known decomposition method was used in the above estimation. First, the values of and defined in the fixed frame, are, generally, calculated, and then and . The estimated values of and derivatives are reconstructed in a steady-state Kalman filter

7. (1) Where is the sampling period, is the vector of measurement noise, and is the disturbance vector which respects the random movements of the ship

8. Verification of fault-tolerance is used before the filtering, as impulse noises and fading may be possible sources of large errors at the filter output

9. The longitudinal and transverse speed components are determined using At the next step, the variables , and are filtered and calculated. After that, , and are determined equation(1) can be transformed to the state where the state and the output vectors are:

10. The steady-state Kalmanfilter for estimating is given by where Now is defined as the state vector, and the expression is the single input vector. The transverse deviation is an output vector and is calculated from the following

11. When the ship approaches its next way point at a distance known as ‘the advance way of the maneuver’, the coordinate frame fixed to the actual segment of the trajectory suddenly changes. That causes a transition change of the desired direction and the sway position . Therefore, to ensure undisturbed working of the filter, the change in the estimator is applied at this moment

12. control design The output feedback controller which stabilizes the transverse deviation is designed to minimize the quadratic cost function Coefficients were chosen for the tests on the basis of an assumption that the control system should guarantee good stability over a wide range of operating conditions and provide good controllability both during maneuvers and on straight sections of the trajectory.

13. The optimal control signal is generated from a Kalman filter, cascaded with a control gain matrix The control gain factors ki can be calculated from the steady- state Riccati equation in the usual way

14. Correct steering of the ship during a change from one trajectory segment to another requires the maneuver to begin precisely at an estimated instant. Any delay in the beginning of the maneuver will usually lead to large overshoots. The time instant at which the step change takes place, and at which the measurement of the transverse deviation from the new segment of the set trajectory begins, can be most conventionally transformed into a proper advance distance.

15. The proposed robust autopilot is a cascade controller. The superior controller sets a desired course, to follow the defined route. The subordinate controller is designed using an standard optimization technique. Its task is to keep the ship on the course set by the superior controller.

16. Direction controller

17. Course-keeping robust controller :linear mathematical model V, W : the measurement noise :The course error :the weighted rudder motion :the weighted course error

18. The feedback control system can be transformed to the standard problem where define

19. the standard plant in this case is given by The standard design problem is to find a real rational proper K to stabilize the plant G and minimize the norm of the transfer matrix from v to z

20. and are chosen to compromise between the robustness and the fundamental dynamic properties of the closed loop (a settling time, a damping ratio, etc.). For disturbance rejection and steady-state course keeping properties, the function , which penalizes the error signal, was kept high at low frequencies. The robustness stability constraints are more important at higher frequencies and is constructed in a such a way that , where is the nominal model response at each frequency and is the actual (or expected) system respons

23. Both trajectory keeping algorithms have successfully controlled the material tanker model. Since the time passes on the model about five times faster than in the modeled process, the implementation of the control system on real objects would not involve any computational difficulties. Changes to the model speed (engine commands) had little influence on the real path. Big rudder angles were caused by the inertial properties of the tanker and the shapes of the desired trajectory, which were limited by the range of the positioning system. What is more, the concentration of turns caused permanent departures from the given trajectory; therefore no integral measures of performance were applied. Instead, the maximum trajectory departure and the maximum rudder action amplitude at a given straight trajectory section were applied as evaluation parameters, along with the scale of overshooting during the turns.