Adaptive fuzzy ship autopilot for track-keeping

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Adaptive fuzzy ship autopilot for track-keeping. 指導教授 : 曾 慶 耀 學 號 :10267036 學 生 : 潘 維 剛. Outline. 1. Introduction 2. System description 3. Adaptive fuzzy track-keeping autopilot 4. Simulation results 5. Conclusion. 1. Introduction.

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### Adaptive fuzzy ship autopilot for track-keeping

Outline

1. Introduction

2. System description

4. Simulation results

5. Conclusion

1. Introduction
• The approach taken in this paper tries to overcome the need for ship’s mathematical model(s) by using the fuzzy logic autopilot which is augmented by the

capability of adjustment of its scaling factors.

• The proposed adaptive fuzzy autopilot emerges as a viable practical alternative for coastal sailing where the track-keeping is of vital importance in all circumstances.
2. System description

2.1. Ship dynamics

• The block diagram of the proposed adaptive fuzzy control system for the ship track-keeping is shown in Fig.1.

The position and orientation of the ship are described relative to the inertial reference frame OE-xEyEzE (Earth-fixed reference frame).

The general ship equations of motion can be expressed in compact form as

• M is the inertia matrix, is a matrix of Coriolis and centripetal terms , is the body-fixed (ship) linear and angular velocities vector and

is a generalized vector of external forces and moments.

For this ship the nonlinear mathematical model which relates the yaw (Ψ) with the rudder angle (δ) is described by the following equations:

2.2. The steering gear servo system

• The steering gear servo system consists of two

electrohydraulic steering subsystems: telemotor position servo and rudder servo actuator (Fig. 4).

• The input of the steering gear servosystem originates from the autopilot and is called the commanded rudder angle(δc). The output is the actual rudder angle (δ).

The desired way point is Hence, the desired heading angle can be obtained from the expression:

• The distance d between the current ship position and

the desired way point can be calculated from

• Fig. 7 shows a simple block diagram of this autopilot. The range of values for a given autopilot inputs and output are normalized to the interval [-3 3] by scaling factors in “conditioning” blocks.
• The course-keeping fuzzy autopilot (FLC) contains two control inputs: heading error e=Ψd-Ψ and yaw rate r=dΨ/dt: The control action generated by the autopilot is the command rudder angle δc.

The output variable y of type autopilot obtained constant values (NB→-3,NM → -2, . . . ,PM → 2, PB → 3).

Shapes of membership functions of input variables are shown in Fig. 8. Labels for the membership functions are given in Table 1.

These rules contain the input/output relationships that define the control strategy. The fuzzy autopilot uses 49 rules, corresponding to 7*7 different combinations of the two input fuzzy sets. (Table 2).

This controller consists of if-then rules of the form

• Inference with rules defined in (14) and given in Table2 is done as follows.

Fig. 9 shows the basic configuration of the FGC structure.

• The main part of this mechanism is a Mamdani type fuzzy controller (FGC) with two inputs: distance d and yaw angle

Ψ and one output: gain k: In this section, a fuzzy tuning method for the gain of FLC variables is presented.

Shapes of membership functions of input variables

and output variable are shown in Figs. 10–12.

The overall control rule set for the FGC, is defined as the

following:

IF d is NE and Ψ is PS then ki is PS

IF d is NE and Ψ is PM then ki is PM

IF d is NE and Ψ is PB then ki is PB

IF d is ZE and Ψ is PS then ki is PB

IF d is ZE and Ψ is PM then ki is PM

IF d is ZE and Ψ is PB then ki is PS

IF d is PE and Ψ is PS then ki is PS

IF d is PE and Ψ is PM then ki is PB

IF d is PE and Ψ is PB then ki is PM

This set of rules is the same for the ke ; kr and ky:

4. Simulation results
• In the first case the desired path is given with six way points P1,P2, . . . ,P6 . From the simulation results obtained(Fig.13).

Fig. 14 shows the time responses of heading , commanded rudder angle (δc) and rudder angle (δ) during a course-changing maneuver . The heading time response is without overshoot and oscillation during transient response. The response of the rudder is rather smooth.

In Fig. 17, the comparison between adaptive fuzzy

and standard fuzzy autopilots is presented.

The results of the comparative performance test showed that adaptive fuzzy autopilot has shown much better performance in comparison with the standard fuzzy type autopilot.

5. Conclusion
• A standard fuzzy control system and an adaptive fuzzy control system for the ship track-keeping are developed and compared. Simulations suggest that, in the case without influence of the sea currents, the standard fuzzy type (Sugeno) autopilot is robust and has good performance.
• Simulation results has shown that this adaptive fuzzy autopilot have better performance in comparison with standard fuzzy type autopilot especially in the presence of environmental disturbances (sea currents and waves).