1. Aulia SA ICTS 2009

ISSN 2085-1944 © 2009 ICTS

FUZZY LOGIC CONTROL SYSTEM IN SHIP MANEUVERING FOR

DEVELOPING EXPERT SEA TRANSPORTATION

Aulia Siti Aisjah 1, A A Masroeri

(2)

1 Engineering Physics Dept., Industrial Faculty of Technology, ITS

Jurusan Teknik Fisika , ITS, Gedung E Lantai II, 60111

[email protected] 2 Marine System Engineering Dept., Faculty of Marine Engineering

Jurusan Teknik Sistem Perkapalan, ITS, 60111

ABSTRACT

For achieving integrated modern sea

transportation, which is consist of rectifying of

shipping in according to traffic demand, regulate

of shipping management, saving in sea and also

expanding the industrial of designing of ship.

The one of this strategy is a designing ship

monitoring and control system for developing

safe in sea transportation. This paper propose a

designing expert control system which is

integrated with monitoring system for course,

position, tracking and ship maneuvering. The

system of controller is consist of controller

module, there are : (i) course controller, (ii)

position controller, (iii) speed controller, (iv)

control of avoiding collision, and (v) a controller

for rejection sea disturbance. In the early

research have done a designing module

controller for course keeping and tracking.

System designing base on fuzzy logical, in term

if ... then .... The module of fuzzy logic

controller (FLC) is composed some rules. These

rules are expressing the best rule, which is

achieved from the input and output another

controller that is LQG/LTR (Linear Quadratic

Regulator / Linear Transfer Recovery) controller

which is robustness performance. Composing

the rules are based from Sugeno Takagi

methods, in then ... action from least square

estimation. The good performance of FLC

design is showed in many simulations, like in

waves disturbance when the significant high is 3

meters, and the setting heading is 30o. The

response controller giving a settling time 279,34

seconds. Whereas in complex disturbance

(significant wave height is 3 meters), when

setting is fulfilling the dot point in early (0,0)

meter and target is (6000, 3465) meters, the path

error is 17,308 meters . The same strategy is

done at the controller proceed for the course

keeping in 30o (fulfilling the point (0,0) and

(6000, 3465) meters), the response of controller

giving the path error is 141,181 meters

Keywords: FLC, Sea Transportaion, course

keeping, maneuvering, monitoring,

tracking.

1 INTRODUCTION

Sea transportation needs of improving safe

in sea and efficiency of transportation, these are

most important. The program can be done for

increasing safety in sea and reducing sea

accidence, beside the regulation aspect, that is

the coordination for reducing accident, in writer

idea is “designing a control and monitoring

system in sea transportation. The integrated

monitoring and control system in ship, is needed

some unit controller, as a control of ship speed,

control of steering machine for course keeping

and track keeping, and also control for fulfilling

the trajectory and ship position. The monitoring

system have been doing from DGPS

(Differential Global Positioning System), this

component giving the information such as:

position and speed a ship in a few time, accurate,

cheap and in wherever, no depend on weather

season. The condition is needed for a good

controller is : (i) Having a stability

characteristics, a robustness performance and

giving response as desired (ii) Adaptive for the

changing the ship parameters and also from

disturbance environment (iii) Possibility

implementation in computer and other

supporting hardware.

mailto:[email protected]

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The weakness of former controller was

usually called a conventional system, in which

this system was coming from mathematical

models. The mathematical models is not capable

accommodate of all system condition is

controlled. In this matter, the controller is do

based on feedback information of sensors

(compass, gyrocompass), the specification

controller have not been doing in wide range,

especially in measurement variable is tend to

zero or tend to infinite. This condition is occur

when heading error, or path of error is least or

very big. But, this matter is surpass with a

controller that has been doing base on data base

management in real condition (the position,

heading, speed, ship trajectory), and data is

processed in numerically for construct the rules.

The rules are formed from real data, expertise, or

intuition of expertise. The output of controller

is a decision or action of controller such as the

position, speed, a path is recommended.

2. An Autopilot control system

An autopilot system in ship is occurring

when compass and gyrocompass is used in

maneuvering ship control. Some of invention the

models or control method in ship maneuvering,

as figure 1 below, that is classifying in four

methods : conventional, adaptive, modern and

expert methods.

2.1 Control System in Ship Maneuvering

A control system is used for moving the

ship steering as like as desire performance, and

many invention in this designing have been

trying in computer scale and also in minilab.

For example, is like tracking controller in un

predictable sea condition [Tee, Keng Peng, and

Ge, Shuzhi Sam, 2006, Velagic, J., et.al 2000].

This invention is conducted from former

researcher in expert autopilot.

Control systems at ship maneuvering based

on the technique designing, is distinguishable in

four methods (Aisjah, 2007). The conventional

method is a develop methods cause finding an

electrical gyroscope (Hopkins, 1980). And then

emerge a magnetic gyro compass which is

sensitive in magnetic noise. This founded is

support a close loop controller that is named

Metal Mike (Speery, 1911). Minorsky (1970)

was analyzing the PID controller, this invention

called the autopilot, whereas this designing

control system was SISO (Single Input Single

Output). The input of controller is deflection of

gyro compass and output is deflection of rudder.

The former researcher in Linear Steering

(Davidson and Schiff, 1946, Nomoto, 1957) and

Non Linear Steering (Abkowitz, 1964, Norrbin,

1970), have been given idea in SISO Minorsky

controllers.

Figure 1: The developing a system control design in ship

maneuvering [Aisjah, A.S, 2007].

The conventional designing was done by

some researchers simply meet many weaknesses.

It was not fully accommodate the existence of

high frequency disturbance, although it has been

adding band filter designed (Lozowicki and

Tiano, 2000). The environment disturbances

cause the changing of parameters controlled

system, and on this reason so appear an adaptive

controller. In the adaptive control system,

mathematical model like the one degraded in

modified, so the adaptive controller was

occurred. In this methods, the mathematics

models was modified from the conventional

method and becoming an equation with

accommodating the environment influence. This

modification mathematical model is expressed in

so many term, like MRAC (Model Reference

Adaptive Control) by Amorengen, V. (1970),

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Blanke, (1980) and ARMA (Auto Regressive

Moving Average) by Nejim (1998). The

proposed methods by Amorengen (1970)

showed non linear rudder by Amorengen, V

(1984) and he proposed a command generator

for obtained certainty model parameters. While

in Nejim structure showed the capability of

controller when the changing of service ship

speed.

The invention of computer, cause happen

the growth in designing of modern control

systems. Where in designing this modern control

systems, mathematical models of maneuvering

dynamics is expressed in the state space

equation. Modern technique was proposed by

Bertin (1980) with strategy ILQ (Inverse Linear

Quadratic) and Kijima (2003), H2 by Donha

(1998), LQG (Linear Quadratic Gaussian) by

Bertin (1998), H~ by Strand (1998) and also

Consegliere (2002), MPC (Model Predictive

Control) and LQR (Linear Quadratic Regulator)

by Wahl et al (1998).

2.2 Fuzzy Logic Controller in Ship

Maneuvering

Fuzzy logic theorem was found by Zadeh

in 1965. This theorem imitate logic of human

common sense in decision making at matters,

and simply can be applied in controller at

various households products for example

washing machines, room refrigerating machine,

rice cooker and others. The application of fuzzy

logic is not only growth in usage in this field, but

also at some industrial in Japan which have put it

from the beginning 1980’Th. And so do in

maneuvering system which have been proposed

by Noguchi and Mizoguchi (1998) from

Ishikawa Jima - Harima Heavy Industries, where

maneuvering is majored for safe path of ship.

The position variable and safe positions of ship

expressed as fuzzy variable. In the simulation is

shown of ship maneuver performance with fuzzy

logic can avoid existence of other ship.

Vukic et al (1998) designed of fuzzy logic

control at maneuvering system by two ways that

are using 2 fuzzy inputs and 3 fuzzy inputs. This

mechanism developed by Aisjah, et al (2004),

input of the FLC is 3 that is yaw and error yaw

divide in 7 areas of fuzzy membership function.

The FLC worked based on the output of PI

controller (Proportional - Integral). In the

simulation applied at Mariner class ship with

first order of Nomoto. Ability of Vukic FLC’s

by 3 inputs it was better in so many condition

compared with Aisjah , et al (2004). Based on

that performance the result hereinafter developed

by Aisjah, et al (2005a, 2005b, 2005c, 2006a) in

designing of robust controller, through model of

system in state space equation. This way apply

to get obtain detail analysis from internal

character of good ship dynamics controller in or

without disturbances. Lee, et al (2004) developed FAM (Fuzzy

Associate Memories) of FLC which compiled

based on expert information and experiment at

real condition. Fuzzy Controller is applied in

measuring of heading, yaw rate, relative speed’s

to desire ship position (location and heading) in

yield output control on the expected course.

Input controller is relative ship position offset to

expected, heading errors, yaw rate, projection of

vector distance’s from center gravity to expected

position, projection of relative speed to the

expected position. The developing of FAM in

FLC based on experiment result as have done by

Lee et al (2004), would affect to the capability of

control systems, when ship operating in other

condition. This problem is anticipated by Aisjah,

et al (2005c, 2006b, 2006c), developing of FAM

based on output of robustness control systems

that is a LQG/LTR controller. The LGQ/LTR

controller is capable to overcome the external

disturbances. A fuzzy control system’s is more simple in

rule base was proposed by Vukic, et al (1998), as

extending from FLC of Velagic, et al (1998).

This FLC uses 49 rules for output. The input of

controller is yaw error and yaw rate. The

membership function of error yaw and yaw rate

are triangular while output of signal of controller

(command rudder) is trapezoid function. And

then Omerdick, et al (2000) developed Vukic, et

al (1998) same in their rule base, whereas the

inference is Mamdani method’s and adding band

filter. The object of Omerdick, et al (2000) in

Mariner class ship, the length is 160.93 meters

ISSN 2085-1944 © 2009 ICTS

and service speed’s is 15 knots. The simulation

implemented by entering the environment

disturbances, the waves in Pierson - Moskowitz

spectrum, modal frequency is 1 rad/sec, and sea

current is 1’st order Gauss Markov. The Notch

filter is use for shafting waves. The performance

of control systems is settling time - Ts time is

less than 150 seconds, at the set point 10o and

30o. While in disturbances, the response of

Vukic FLC’s is fluctuations.

Development of rules using Sugeno-Takagi

algorithms, which are expressed in mathematic

equation as a function of all input variables. This

rule based is coming from least square

estimation from the relation of input and output

LQG/LTR as a reference control. The input of

LQG/LTR controller is yaw error and yaw rate,

while the output is signal command rudder. The

mechanism like this was designed by writer, and

simulation giving a good performance for

developing a module controller in “monitoring

and control transportation system”.

3. Fuzzy Logic Controller – FLC for

Developing Expert Sea Controller

Transportation.

3.1 The Development Sea Transporttion The sea models transportation is compose

with other system such as monitoring and

control system. This paper is proposes a

designing expert monitoring and control that is

integrated one and other. The expert system is

using fuzzy logic.

Designing a Monitoring system

In monitoring system, is a system is done as

a monitor for position, speed, course and the

trajectory of ship, in the specify shipping area.

The information is coming from monitor station

with GPS as a navigation system using satellite.

GPS receiver is obtained a signal from satellites

in earth orbiting. The mechanism of a system

designed is: GPS will give information about

position and the time. From two data can

calculate the speed and heading of ship, and then

continuing information to Monitor Station. The

data are storage in Monitor Station and then for

processing the controller.

Designing a Expert Controller

The second subsystem is a fuzzy logic

controller, the output this system is information

about the heading, position, trajectory and speed

of ship. These information as a recommended for

collision avoiding with other ship. This

information is send to Controller Station and can

access by user in ship.

Figure 2: Diagram block of Monitoring and Control System

The parameters are influence in designing

control system:

1. The architecture of control system

design.

2. Parameters in ship dynamic :

environmental disturbances (ocean)

The architecture of system will be design as

drawing in following figure.

Figure 3: Fuzzy Control system architecture

In the figure 3, is shown at Fuzzy Logic Control

architecture in this designing, there are

parameters are needed in this controller:

A. Information from sensors (heading / yaw

angle, yaw rate, position, ship speed)

ISSN 2085-1944 © 2009 ICTS

B. GPS Information (position of other ship

/ other foreign body)

C. Parameters for developing Fuzzy Logic

Controller.

a. Fuzzy Sets Classifying

The mechanism for classifying a danger area

(possibility collision) is done using grouping

horizontal zone as suitable with ship heading (o).

This grouping is like infollowing table.

Table 1: Description of grouping horizontal zone

Base on GPS information can taken to be

account for distance (d) between ships or to

other ship. The value of d in linguistic term,

there are: very close, close and far, or in other

term, such as: in front, behind, right and left. The

output of fuzzy I (figure 2) is a decision about a

possibility accident. In the logic value are : the

Front Zone Accident (FZA), Back Zone

Accident (BZA), Left Zone accident (LZA),

Right Zone Accident (RZA), and related with

confidence factor : Not possible (NP), Possible

(P) and most possible (MP). The confidence

factor is in a numerical value. The occurrence

accident is taken account in suitable rules, for

example in the following rule:

R: If di is (LD(k)

) Then cj is (LC(k)

) (1)

Where: k is amount of rules, di is a distance (is

accounted from GPS information), LD:

linguistic variable in the D set: (Very Close,

Close, and Far), ci: direction of accident (the

angle of heading collision, from compass

measurement), and LC is a C set variable = is

(Not Possibly, Possibly and Most possibly).

And then to grouping a danger zone

(possibly occur a collision), d is a distance to

other ship in fuzzy variables, and weighting

value of accident collision is determined from

result a verification data.

b. A module avoiding collision This module control is processes for

avoiding collision with other ship / other foreign

vessels, is navigation free of collision. The goal

of the controller design is a target course; this

course is a new course of ship. The rule is

needed in this module for reducing heading error

until to zero, which is the difference of target

and actual heading.

Variables Input module is:

(i). Possibility accident (LC) in linguistic

variable (NP – not possible, P – possible,

MP – most possible).

(ii). Error of yaw (Heading error) is

expressed in linguistic variable (LB –

Left Big, L – left, LS – left small, Ze –

zero, RS – right small, R – right, RB –

right big).

The output of module are two kinds, there are:

(i). The changing of heading / course (dψ) is

expressed in linguistic variable : (LF –

left fast, L – left, LS – left slow, Ze –

zero, RS – right slow, R – right, RF –

right fast).

(ii). Surge velocity (u) is expressed in

linguistic variable (S – slow, N – normal

F – fast).

The example of avoiding collision rule is

expressed:

If cj is LC(k)

And ψ is Lψ(k)

Then dψ is

LDψ(k)

and u is Ldu(k)

(2)

Where : k is amount of rules, cj is kind of j

accident, ψ is heading error, u is surge

velocity, LC, Lψ, LDψ and Ldu are

expressed in linguistic variables of cj, ψ, Dψ

and du. The k’th rule in mathematical

expressed is a relation fuzzy R(k) to C x ψ,

in domain fuzzy membership function :

µR(k)

(cj, ψ) = min[µLC(k)

(cj), µLψ (k)

(ψ)] (3)

The whole of rule base are expressed in a

union from all of individual rule:

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µR(cj, ψ,dψ, u) = K

k

j

k

R c1

)(),(

(4)

The output of navigation is expressed in

term:

),,,(

),,(minmax),(

*

,

*

udc

cud

jR

jAND

cNav

j

(5)

Where: ,*

jAND c is a combination from

input and output? udc jR ,,,

c. A Control module ship dynamics

In this module are composed two modules: there

speed control module and heading control

module.

Figure 4: Sub system a speed controller

Input speed control module are (i) a distance to

other ship (Zero, Close, Far, very far) , (ii) Surge

velocity (Slow, Normal, Fast), (iii) Surge

velocity target (Slow, Normal, Fast) and (iv)

Heading error ((Fast_Astern, Slow_Astern,

Dead, Slow_Ahead, Fast_Ahead).

One of those rules for speed controller is

expressed in this term:

If (distance is far) And (Surge_velocity is

Normal) And (Target_Surge_velocity is

Normal) And (Heading_error is Normal) Then

(RPM_of_propeller is Slow_Ahead)

(6)

d. Heading or Course Controller

In sub system heading controller, the input for

module is heading error (the difference of desire

heading to actual heading / yaw angle). The

environment factor as disturbance (wave, sea

current and wind) will influence heading error.

The third disturbance factor will be modified

heading error, the changing of yaw rate and

distance to target point. The third inputs module

are expressed in linguistic variables : _Heading

error (NB - Negative Big, N – Negative, Z –

Zero, P – Positive, PB – Positive Big), Yaw rate

(Ne - Negative, No - Normal, Po - Positive), and

distance (Z – Zero, C – Close, F - Far).

Output of heading controller is two kinds, there

are: the voltage of thruster and rudder angle, are

expressed in linguistic variable (B – Negative

Big, N – Negative, Z – Zero, P – Positive, PB –

Positive Big). And rule of two inputs in this

module is shown by:

If (Heading_Error is Positive) And (Yaw rate is

Normal) And (distance is Far) Then

(Thruster_Voltage is Positive) And

(Rudder_Angle is Positive).

(7)

Figure 5. Structure of diagram block a Monitoring and Control

system for designing expert transportation

e. Control for reducing disturbance The disturbances are commonly from

environment will be considered: wind, ocean

current and waves. In general the third

disturbances will influence heading of ship.

Analyzing those disturbances is derived in value

and angle of coming from every disturbance

[Aisjah, A.S, 2007]. In the assumption that

waves is wind generated, so in the future module

design just on two disturbances, there are wind

and ocean current. In these control modules,

there are two position fuzzy controller, target to

Xo and Yo. Inputs of controller are ship

position, target position, Euler angle, wind

speed, wind angle, velocity current and current

angle. Projection of current and wind will

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influence of dynamic and surge velocity and also

drag effect. The output of this controller is rpm

propeller and thruster voltage.

3.2 Designing a Course and Path Control

Module.

Mechanism of FLC designing

The mechanism in fuzzy logic control

systems yielding a decision (signal controlled)

through some steps, which are fuzzification,

mechanism in inference engine, and

defuzzification (Jamshidi, 1993. In

defuzzification is a function to change a crisp

variable becomes fuzzy variable by expressing in

the membership function. This membership

function of universe discourse is analogous to

level of probability marginal from the variable

(Aisjah, et al, 2005d). Many researches in

designing a fuzzy control systems use triangular

function, because a simple easy to represent in

numerical variable (Kosko, 1997).

In Fig.7, Fij is fuzzy set, ci is real

parameter, yk

is output of systems in rule R(l)

, M

is amount of fuzzy rules. From those rules, in

the part of IF in the form of fuzzy set, while part

of THEN is crisp value, is linear combination of

input variable. Sugeno - Takagi fuzzy control

systems is shown in Figure 7. The x is input

variable, y is output variable that is result of

Sugeno - Takagi inference, w is available

weighting factor from iteration of simulation.

L(1) : IF x1

is F11 and … and … x

n is F

n1 THEN

y1 = c01 + c

11 x

1 + … +c

n1 x

n

LM) : IF x1

is F1

Mand … and … xn is F

nM THEN

yM = c0

M + c1

M x1 + … +c

nM x

n

Weighting

averageUx Vxy )(

w1, y1

wm,ym

Figure 6. Configuration of Sugeno-Takagi Fuzzy Logic Systems

(Wang, 1994).

Model reference (LQG/LTR) is applied to

derive and evaluate of FLC performance. Input

of LQG/LTR controller as a reference controller

is yaw error and yaw rate is applied to obtain

unknown parameters cij1 and cij

2 which for rule

base at FLC. At early model reference is

implemented beforehand precede KLF, to obtain

the both value cij through least square estimation,

and then FLC is implemented separately without

LQG/LTR.

Structure of FLC controller device consist

of two units, in first unit based on yaw error (e)

and yaw rate (r) input, second FLC unit working

based on normalization of path error. FLC

structure in this research is different from other

structure when it is used a Mamdani inference

function. At the time Mamdani inference is

applied, some robustness parameters of

controllers are not met. When simulation is done

in some condition like as such as circle

maneuver, the fluctuations is appear in complex

environment condition. The error of radius circle

maneuvering is ±20% and tends to not

convergent (Aisjah et al, 2006d).

To determine rule base of fuzzy controller

which applied is as follows:

21 duduu d (8)

in which

krckecdu ijijij

211 (9)

δd is a command signal rudder, cij1 is a gain

signal controller that is based on change of error

yaw, cij2 is gain a signal controller that is based

on yaw rate, du2 is output of controller that is

based on normalization path error η. To obtain

the gain in equation of (9), it is done using estimation least square.

Input of 2’nd FLC unit is normalization of

path error d, and output of controller is du2.

When d is negative hence du2 is negative, and so

do on the contrary if d is positive, the value of

du2 is positive. The available rule for this logic

can be expressed as a form (10).

.tanh2 sdu (10)

S is sensitivity of FLC in which its input is η.

In Figure of (8) is showing a diagram

block of controller structures which is designed

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in this research. Mechanism of FLC that is input

is yaw error (e) and yaw rate (r). In the course

keeping simulation, output of FLC signal control

is du1 feeding to steering machine and steering

machine is moving ship as according to heading

setting. If simulation is done by setting heading

from position objects, hence FLC works with

input yaw error ( e), yaw rate (r) and path error

and output of FLC signal controller is du1 + du2.

This signal is moving steering machine and then

the rudder will move ships towards the expected

position.

Way

point

desire

(xd, yd)

Course

desire

Offset from

desire path

Yd

Fuzzy

Autopilot

Offset Path

Autopilot

du1 = c1 e + c

2 r

du2 = tanh

(s)

Steering

Machine

Ship

Dynamics

c

LQG/LTR

Controller

Ship Dynamics

Compas

Giro

CompasGPS

Yd+

-

Yr

Y

r

x,y

Disturbance

FLC Based LQG/LTR

Figure 7. Diagram block of Sugeno – Takagi FLC with LQG/LTR as a model reference for heading and tracking control

Table 2 Range of error yaw, yaw rate, path of error and output of

controller.

Table 3 Notation usage in gain FLC controller

The value of cij, i = 1 … 5 and j = 1..5 are

obtained from least square estimation from

output of LQG/LTR controller.

4. Simulation

4.1 Course Keeping Simulation At accomplishment of course keeping

(heading is constant), controller will work if d ~

0, here just 2’nd FLC unit is active. The goal of

fuzzy controller is bring a ship to the desire

angle of yaw / heading the expected, in this

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case when Δψ = ψd – ψ = 0. 1’st unit of FLC is

active with input e and r, 2’nd unit of FLC is

off, and then action of controller is du1 which is

signal of command rudder δc = du1. At course

keeping simulation is done by giving signal

testing in the form of step function as an input

of control systems. The first simulation, set

point of heading is 30o and done at UN

disturbance condition. The result of simulation

like seen at Figure of 9 for Mariner class and

Figure 10 for Tanker (100000 - 350000 dwt).

Seen at both, the settling time (Ts) when set

point heading is 30o in LQG/LTR controller is

141.3 second and 117.8 second in FLC. While

Ts of Tanker (100000 - 350000 dwt) is 379.3

second (FLC) and 410.9 second (LQG/LTR).

This value is better than result of LQR

controller ( Aisjah, et al, 2006b).

The performance of controller in time

domain, in general marked in parameters:

maximum overshoot (mov), settling time (Ts),

rise time (Rs), steady state error (ess). These

parameters give a stability character of a

controller. Though those parameter are not one

kindness of a controller performance. To get a

stability parameter like those, by the way of

through giving a certain testing signal and

comparing the result of the response to this

signal testing. With test signal can be analyzed

mathematically and experimental from a

control systems.

Heading Response Mariner Class Ship

___ LQG/LTR

___ FLC

Figure 8. Heading response of Mariner class ship when setting

point is 30o in UN disturbance condition

Figure 9. Heading response of Tanker (100 000 – 350 000 dwt)

when setting point is 30o in UN disturbance condition

A first system order is expressed in the

transfer function as following:

Ts

K

sR

sC

1)(

)( (11)

Which is K is gain of system, T: time constant

of system, C: output of system and R: input of

system (Ogata, 1992). The response of control

systems in some vessel types of level could be

determined of time constants system. The way

for finding this time constant by when it

reached 63.2 % from heading target, this time is

a time constant of system (Ogata, 1992). For

Mariner class ship, the length is 161.9 meters,

and service speed is 7.72 m/sec and Tanker

(190000 dwt) is 304.65 meters , 8.24 m/sec, the

time constant of both type vessels are 107,89

seconds and 289.82 seconds.

4.2 Track keeping Simulation At track keeping simulation (path

accomplishing), the goal of fuzzy logic control

systems is bring ship from actual position

towards to path desired.

If the ship in left side from the path

expected that is the value of η > 0. This

means required a signal command rudder is

positive yielding transformation of positive

direction. Signal of du2 will have + and will

boost up a signal command rudder, and then

cause ship direction (angle of yaw) is bigger

than which expected for a few moment. At

this impulse of ship towards to the expected

orbit, so that d will go down towards 0.

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a

Mov = 31.4o Steady 29. 65 - 30. 34o

b

Mov = 39 . 7o

Muv = 27 . 3o Steady 28 . 75 - 31 . 8o

c

Figure 10. The response of Mariner class ship, in setting heading is 30o in wave disturbance wind generated, (a) Hs = 1 m

(b) Hs = 2 m (c) Hs = 3 mIn the opposite, when the

value of η < 0, in which the ship in the right

side of desired path, with symmetrically in the

rule at η > 0, so the value of du2 is negative and

reduce to a signal command rudder, so be

reducing the course of ship.

If ship in desired path the value of η = 0, in

this case du2 = 0, fuzzy autopilot will active

in such yaw error and yaw rate. This

mechanism is called course keeping

controller...

The input of control system is dot series

of desired position (xi,yi). In simulation in

which is input is (0,0) meters and (3465, 6000)

meters in where this point as a linear tracking

is suitable with heading is -30o. In below figure

is shown a position of actual and desired path

ship, when in complex disturbances. The value

of significant height wave are 1,2 and 3 meters,

velocity of sea current is 1 – 3 m/sec.

(3465,6000)

(0,0)

desire

actual a

a

bc=30o, gw=30

o

Figure 11 Trajectory of Mariner Class in complex disturbances,

setting point position is initial is (0,0) meters and target (3465, 6000) meters, Hs = 1 meters.

desire

actual (3465,6000)

(0,0)

a

ab

b

bc=30o, gw=30

o

Figure 12 Trajectory of Mariner Class in complex disturbances,

setting point position is initial is (0,0) meters and target (3465,

6000) meters, Hs = 2 meters.

desire

actual

Yd

a

a

b

b

bc=30o, gw=30

o

Figure 13 Trajectory of Mariner Class in complex disturbances, setting heading is -30o Hs = 1 meters.

In their two different mechanism in course

control and tracking control, in which

trajectory of ship moving as shown in fourth

above figures. If the setting of controller is

heading target, the 1’st unit of FLC is active,

whereas setting of controller is position of

desired path, 1’st and 2’nd units of FLC are

active. The different of those mechanism

proceeds error of the actual positions to

desired target. In figure of 11 and 13, zoom of

a and b location, the distinct of path when

ISSN 2085-1944 © 2009 ICTS

setting in controller is heading -30o, result of

error bigger than in which is setting controller

is point target. The error when just 1’st unit of

FLC is active and the both are active is shown

in table of 4.

desire

actual

Yd

a

b

a

b

bc=30o, gw=30

o

Figure 13 Trajectory of Mariner Class in complex disturbances, setting heading is -30o, Hs = 2 meters.

Table 4 Error performance of FLC result at the heading and tracking set point.

5. THE CONCLUSION From result of simulation, are result

conclusions

The developing an expert control system in

sea transportation is is done for fulfilling

trajectory, position and avoiding collision.

The Sugeno – Takagi FLC controller giving

good performance at turning, this is marked

by gain of Nomoto from simulation result is

tend to same with result from the

calculation.

FLC controller with Sugeno- Takagi

consequence function giving good

performance when turning and tracking in

wave disturbance.

The Sugeno Takagi FLC is follow a

LQG/LTR robust controller, this is could be

seen in trajectory response in turning and

also tracking.

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Documents

1. Aulia SA ICTS 2009