### Adaptive fuzzy ship autopilot for track

```Adaptive fuzzy ship autopilot for
track-keeping

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Outline
1. Introduction
2. System description
4. Simulation results
5. Conclusion
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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.
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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.
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• The position and orientation of the ship are described
relative to the inertial reference frame OE-xEyEzE (Earthfixed reference frame).
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• The general ship equations of motion can be expressed
in compact form as
• M is the inertia matrix, C ( v ) is a matrix of Coriolis and
centripetal terms , v   u , v , w , p , q , r  is the body-fixed (ship)
linear and angular velocities vector and    X , Y , Z , K , M , N 
is a generalized vector of external forces and moments.
T
T
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• Due to that 6DOF model is simplified and reduced to 3DOF
model (Fig. 3).
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• For this ship the nonlinear mathematical model which
relates the yaw (Ψ) with the rudder angle (δ) is described
by the following equations:
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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).
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• The desired way point is ( x , y )  ( x , y ) Hence, the
desired heading angle can be obtained from the
expression:
d
d
i
i
• The distance d between the current ship position and
the desired way point can be calculated from
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• 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
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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.
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• 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).
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• This controller consists of if-then rules of the form
• Inference with rules defined in (14) and given in
Table2 is done as follows.
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• 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.
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• Shapes of membership functions of input variables
and output variable are shown in Figs. 10–12.
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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:
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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).
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• Fig. 14 shows the time responses of heading , commanded
rudder angle (δc) and rudder angle (δ) during a coursechanging maneuver . The heading time response is without
overshoot and oscillation during transient response. The
response of the rudder is rather smooth.
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• 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.
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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).
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THE END