On ship automation using computers

AFDELING DER SCHEEPSBOUW- EN SCHEEPVAARTKUNDE LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

Rapport No. 454.

ON SHIP AUTOMATION USING COMPUTERS.

M.Hirota

tJI

Deift University of Technology

Ship Hydromechanics Laboratory Mekeiweg 2

Deift 2208

Contents: _{page nr.}

o. Summary

I

I. Position Fix at Sea

J

1.1. Astro-fix, Statistical Test I

1.2. Accuracy of Astronomical Observations at Sea 2

On Ship Automation Using Computers

by

Minoru HirotaX

Ship's Motion under Steering ₃

2.1. Static Parameters (PAL-Test) ₃

2.2. Dynamics ₄

Optimal Steering

3.1. Course-Changing in Minimum Time (SHO-Method)

3.2. Course-Keeping by Minimum Time Loss or Minimum Fuel Consumption

Conclusion

References

Figures

X Kobe University of Mercantile

Marine

4 4 5 6 8 IO

)

)

o

O

o. Summary.

1. Position Fix at Sea.

This report consists mainly of an English translation of the author's work reported in Japanese. It contains (a) position fix at sea by using computers,

( b) automatic control of a ship's course, course-changing and course-keeping.

The report is not only theoretical but also practical, so all experiments are performed by an actual ship (a training ship m.v. Fukae Maru, 360 tons D.W.); the optimal controls are given by a feedback system. In this connection, a new method of the spiral test is described, as well as a practical algorithm for

optimal control, and some data obtained from actual ships, for instance, stan-dard deviation of error of astronomical observations at sea, and the ship's

static parameters and dynamics under steering.

We have many systems and apparatus to fix the ship's position at sea. In this paper, the use of the astronomical system is explained, because it is a typi-cal and basitypi-cal system at sea, and its extension can be applied to Decca,

Loran, Omega or Satelite system.

There are several spherical-trigonometrical formulae for astronomical position

fix which are well known to the navigators. 1, 2, 3 . The reduction of the

motion of celestial bodies is also formulated, so these are omitted in this report, and only statistical treatments are shown below. The accuracy of astronomical observation at sea is considered, because it is necessary to reject accidental errors by a statistical criterion. Some programs have been

used for computerization of the ship's position calculation.

The application of Kalman filter is omitted, because the estimated values of coveriance matrices are difficult to find and there is no theory of rejection

of erroneous data.

1.1. Astro-fix, Statistical Test 4, 5].

When the navigator observes the altitude of a star (a0 ), he measures also the

time of observation ( t0), and prepares a dead-reckoned position. Then he cal-culates a altitude (as) and an azimuth (Z) which are expected in t0 at the

dead-reckoned position withan aid of a navigational almanac. The difference between observed and calculated altitude (a0 - a) is called as an intercept

2

,dL

n-X E5iZCôsZ.

Yi coszZ.

We can estimate a2 _{as follows:}

Si;

Ast

Z2(N-2,

) 2

_<

X2N2

_jq)

where N

,

st

s

Degree of freedom = N 2m

i : number of position fix, _{m :}

total number of position fixes.

The value of o 1'O is obtained _{from about 800 observations of 13 ship's}

navigators after rejection of _{some data by statistical test.}

It may looks rather large compared with _{other results, but it is the}

ob-servation error of practical navigator's _{routine work at sea.}

n

=-!

IL:CÖsZL

(2)

The most probable position (X0 ,Y ) is obtained by solving egs (2). Let S

be the sum of squares of residuals,

z

S=et2 zfi

-

_{(x-X0)5ZL -(T-}

_Y)coZ}

(3)

Then S/a2has a X2-distribution of the degree of freedom n-2, where G

is the standard deviation of the errors of observations. We _{can reject an} unsuitable position fix which contains _{very large accidental error by the}

statistical test. According to _{my experience, the risk factor of first kind}

ç co is 5% for suitable rate of rejection which coincides with navigator's

practice 1

6]

1.2. Accuracy of Astronomical _{Observations at Sea.}

(4')

)

)

I

position near the dead-reckoned position as follows:

X 5'vi Z

+ Y

c-os

ZL = r:

(L=

1,

2,

(1)

where -:

: number of observation. The total number of observations (n )

must be larger than 2, in order to _{get ship's position on the surface of the} earth and an evaluation of _{accuracy of observations.}

Cannonical equations _{are given by atplying the least square method}

to egs (1)

lt

,t

t't

X

s

4Z Z ¿

_{+ 'r'}

O

In recent years the ship becomes larger, but the _{number of crew is decreasing.} Consequently the importance of automatic control cannot be exaggerated. We must know the character of a ship in order to control its motion. _{There are} many results from model experiments, but full-scale data _{are rather scare.} Some full-scale measurements have been performed to determine drift angle or pivoting point, speed reduction under steady _{turning, and T , K for dynamics;}

then automatic control theory is applied _{to the actual ship's data. A new}

method of spiral test is explained in this connection.

2.1. Static Parameters

_7I

The frequency distribution of residuals is shown _{in Fig. 3. It is not}

Gaussian but of the 2-type.

For a detailed discussion the reader is referred to _{paper [5]}

2. Ship's Motion under Steering.

We have no reliable method to measure the drift angle ( ) and the tangent

speed ( V) of an actual ship _{even under steady turning conditions.}

A new method of PAL-test (Parallel Alignment Lines Test) and its full-scale

test are reported.

Suppose we have a transit line TL _{on the land, and a ship is steered in a} steady turning and crosses TL at P1 and P2 as shown in Fig. 4. The bearing

of the

TL is B

_{, and the perpendicular to TL has}

a direction

B + 900.

Then direction of the tangent at P1 is

B + 90° - Gt + 90°,

_{and it is equal} to O - , where , is the heading of the ship at P and is the drift angle of observer's position.

Similarly we can have the equation at P2

02 _ = B + 90° + + 9O

Therefore we get a measured drift angle by _{adding two directions of}

tangent.

F°2

-2

=: 28 ±(36o°,)x

i2Z

n= 0,1

p

=

(e,*o2)/z

-8 ±(/800»

¡p

-4-Now there are many pairs of two parallel transit lines, _{for instance, mile posts}

for speed test. If the same steady turning is proceeded _{crossing these two lines,}

we can get many data O, t1,O,t2. . . .., O , t. Applying the least square method,

we can determine many parameters less than n , for instance,

, V and other parameters with correction of wind and current effects. Shown in _{Figure 5.}

If two observers are on a ship, for instance, _{at the bridge ( B ) and at the stern} post ( s ), they can get two drift angles i ,

2 at each observation point.

Then we can easily find the pivoting point (P) and _{the drift angle at the center}

of the gravity ( _{), as shown in Figure 6.}

Some data obtained from m.v. Fukae Maru _{are shown in Fig. 7, 8, 9, 10 and Table 1,}

Fig. _{11 with her particulars. The data shows that the ship}

does not have a large nonlinearity in steering motion.

2.2. Dynamics

_181.

)

Dynamic qualities of the shipTs steering _{are obtained by Kempf' s zig-zag test and} Nomoto's analysis, as shown in Fig. 12.

3. Optimal Steering

_(8,

9, IO, I _{I )}

When a ship comes in a narrow channel _{or a harbour, a quarter-master steers her} under the order of a navigator, because _{automatic steering devices}

are mainly

used for a course-keeping. The time optimal _{control of course-changing is given} by a so-called bang-bang control, but _{the difficulties arise from the constraints} of a control and a state variable. The _{control is usually given as a time function,}

and not good for feedback control. _{The author introduces a}

new algorithm

(Successi-vely Heightening Order Method) _{to solve the control law in a simple form. For}

details of the theory the reader is referred to reference _L 9}.

As for the course-keeping, it is well known that the rudder action and the centrifu-gal force under yawing can be the cause of considerable speed loss or power loss. A reasonable performance index should be determined by experiments and the optimal

control is applied to it.

3.1. Course-changing in Minimum Time (SHO-method).

Ship's dynamics are:

iw

)

= Tw +/<T

where iji : ship's heading, w : turning rate, 5 : rudder angle, u : control, A : maximum turning rate of rudder.

The optimal control with state variable constraints is given as the function of time, but it is easily contaminated by noise and inaccuracy of parameters in dynamics giving unsatisfactory results. Now we have a control law for this problem and can compose a feedback system as shown in Fig. 13. The

control law is given as follows: Definitions:

6;:=srt(4j,

_6'z=srC4'1),

_63=5rlc:43')

where :

2

2/2AD

+/KD

if

?2O,

?=

_1S2/2

AR/K/A,

? = ?

/A

=

KAT(- 12

e2/T)(wk_

AT)61*?2)/T

if

2>

_û,

3=

/A

,

T,

13*

3 -

K- !+ e

Z3/T e12'3')/TJ

+(w -kS-

T)e+?2

Control Law: if if

j4S

1ifiIDtd3>0O

Íf34O

otherwise . - . . . - _ _j-. (if

(ífp-1

_{2 T -/} otherwise - - -if

_43=O

if..Off 4:',4o

. if

4, ;:.Q

(End of Control) - -

- o

Computer simulation and the actual ship's experiments by manual steering were reported, because it was not possible to construct the controller

using a computer at that time. Fig. 14,15,16.

3.2. Course-Keeping by Minimum Time Loss or Minimum Fuel Consumption (12

The performance index of a quadratic form is convenient to get the control

J

c

Zc'o

o

where (e)2/2

: distance loss caused by course error,

: speed loss or fuel consumption loss caused by steering, O : heading error frç _expected

course, : drift angle.

Dynamics for a ship are:

0=0)

=Tw

T'S

=T'p

KT'g

Then the control law is:

The experiments have been performed with m.v. Fukae Maru resulting in:

X 4 for speed lOss and X 6 for fuel consumption loss.

She ran along the speed test course under zig-zag manoeuvre to obtain _time

inter-val ( T) between two crossings of transit lines. Thenthe correct0 _factor

Jç__os

(e-3) dt

is calculated from recorded data to give rriean speed V

The speed loss factor k is given by the equation

_V

_{ho C} i

_-kr),

_where

V0 is the speed without steering and X 2k. Some data are s}c _in

Fig. 17, 18, 19.

The experiments have been carried out under strict regulation of _engine revolution, so the parameter A for speed loss is less than for ari

ordinary ship and the parameters ) for fuel consumption loss nay be larger thar

for an ordi-nary ship.

4. Conclusion.

This reort aims at getting a total control system of a ship's

_POSition

_and

has provided some theory and technique for this purpose. The work, _however, has not been finished completely.

The considered ship is a small training ship, and has a good

_stabi1t

_in

stee-ring. The problem of automatic control of an unstable ship is nowunder consi-deration. The performance index must be improved by additional term

but

the experiments needed is difficult and expensive. In fact a ship

position must be automatically controlled, but the higher order control _{5YStem is} difficult to solve. Kalman filters must also be studied.

6

íi2T

-

_11]

)

The author is grateful to Prof.ir. J. Gerritsma and Mr. W. Beukelman of the Deift University of Technology for having a chance to publish

this summary.

References:

8

.1

M. Hirota: The Logic of Position Fix; T.N.S.J., vol November 1968.

. 40, pp 71 - 78,

M. Hirota: Estimation and Representation of Ship's Position Error; Introduction of Statistical Hypothesis Test;

T.N.S.J.,, vol. 41, pp 97 102, May 1969.

Two-dimensional Joint Probability Density;

T.N.S..J., vol. 42, pp 85 - 90, October 1969rn

The Accuracy of Astro-Fix in Practice at Sea;

T.N.S.J., vol. 43, pp 121 - 130, May 1970.

Working Party : The Accuracy of Astronomical Observations

at Sea;

Journal of Royal Institute of Navigation, vol.X,

,

. 23, July 1957.

M. Hirota: A New Method of Turning Circle Test and _{its Full-scale} Experiments; Transaction of Society of Naval Architects _{of Japan,} vol. 129, pp. 273 - 280, May 1971.

M. Hirota: Time Optimal Control Law to Alter Ship's _{Course and its} Manual Steering Experiments; T.S.N.A.J., vol. 131,

. 65 - 78, May 1972.

)

)

)

ti]

M. Hirota: Application of Digital Computer to Navigation, ii, _Great Circle Route by Rhumb-Line; Bulletin of Kobe University _of

Mercan-tile Marine, Part II, vol. 15, pp 39 48, March 1968.

M. Hirota: A Digital Computer for Training the Astro_fix _at Sea; Navigation (Journal of Nautical Society of Japan), _{no. 32,} pp 83 - 87, September 1970.

[31

M. Hirota: Astronomical Navigation with a Digital Computer; Spherical Trigonometry; Transaction of Nautical Society _of Japan, vol. 36, pp. 59 - 64, October 1966

Fourrier Series Interpolation of Nautical Almanac _Data, T.N.S.J., vol. 37, pp 29 34, May 1967.

Chebyshev Polynomical Interpolation of NautiQal _{Almanac Data,} T.N.S.J., vol. 38, pp 87 92, Ocotber 1967.

I9]

M. Hirota: Successively Heightening Order Method for Time Optimal Control Theory and its Application _{to Optimal Steering of a Ship;} Bulletin of Kobe University of Mercantile Marine, Vol. 20, Jan. 1973.

Iio]

M. Hirota: Determination of Time Optimal _{Control in Time Sequence}

(Successively Heightening Order Method) ; Transaction of Society

of Instruments and Control Engineers _{of Japan, vol. 7, no. 5,}

pp. 427 - 433, October 1971.

EiiI M. Hirota: Time Optimal Control of _{the Course of a Ship (Successively} Heightening Order Method); T.S.I.C.E.J., _{vol. 8, no. 2, pp 242 - 250,}

April 1972.

e

i: 121 M. Hirota: Performance Index for Course-Keeping (Part 1), Economic

I

Fig. 1. A line of position.

Fig. 2. Residuals of observations.

Fig. 3. Frequency distribution of

residuals of astronomical observations.

o 858 total number of observations

. 659 after rejection within group

+. 357 after rejection between groups

55 data are not shown in the figure, because their residuals exceed ±4'.

A curve shows N(-O. I , I .0)

D.R. position Y (North) o

(+ujc')

) X (East) O9.

t..

O/)

o58t

t

s é i-357 i1ttr

--

N(-o.1, s'o) 25' -4.' -3' -2' -1' 0' 1' 2' 3' 4'

drift angle. Fig. 5. PAL-test. ( a) approach perpendicular to transit line. (b) approach parallel to transit line. s

Fig. 6. Determination of nivoting

noínt and drift angle at center of gravity. c:' 't

tf\

,;-ífr6= (a)- (+XìA)

i

.Ij t., t, t t3 t4 ti, 00 o» e o e e,,

;o

a. X e 8j- _i

_{t, tatì}

_{4 ...} ;h aj e2 9 e ... -bjOac& ... _a.

f

12

-Fig 7 Response of angular velocity to the rudder

8ng es. MS Fukae Maru, V0 10 kuots, arid

engine rovolution WS kept constant. Spiral

test at speed 10. 6' and at speed O 9 . 6'.

Zig-zag test at speed +9. 6'. (These marks are common with Fig. 8 and B

Fig _{8 Speed reduction ratio due to steering.}

MS Fukae Maru, Vo:i:1O knots, Spiral

test (PAL-test).

Fig 9 udder angle versus turnirg radius of the center of wheel hcuse. MS Fukae Maru,

VO:1O knots, Spiral test (PAL-test).

Fig. O Drift angle

(PALtest).

(a)

o 2O0 tq

t

fo' 20'

8

pproacii speed s.8'O.2'

(a) at steering room.

_{(b) at stern post.}

o. O. Z 0.3 o 0.1

(b)

M.S FUKAE MARU

GENERAL ARRAtGEMEN1

(a) Side 'iew and top view.

a,

11h::

:L

f

G/

ji

3.00

- o. w. L

li

'2. ¿ 5

-.---(b) Body plan.

Fig. i i Flans of the experimental ship.

nl

'GT 361.71

750PS/72Orpm (Experi ment condi ti ons)

ì. E i L 37.00rn

ìth

2.18 Propeller 285-3ISrpm

--tA'

B 7.80m 12.8knots Speed 9. 6-10. 9 knots

JI?

410m IMJ:! 1/35.8

*d

2.684m t. 'J.A 0.871m Draft d1 =2. 16, d=2.71 Deadweight 365 ton

ì<;ít

'D0.61m

Cb 0. 555, C =0. 647 Pitch angle 20 (fixed)

Co

Computer

14

-u K' 1.0 00 o -.0

-70 tS.69

-S -Ll -30 -20

s Zig- zig test

o Zig-zag test _{ehe se}

ç day + Spiral test J s

z

o .

o f _$_

Io

20 30 K

sT +

Fig.

13. Feedback control loop of ship's course-changing.

w

lo 20

s

Fig. 1'- Trajectories and rudder angle response of the time optimal steering obtained by thgiia computer

simulation and drawn by an XY-plotter. (Steering indices are rounded off.)

is

Figj 12 Steering indices of the experimenta' ship.

MS Fukae Maru, zig-zag test. Nondimenstonal

T=TV/Lpp, K'KLpp/V; where V(8'11') is approaching speed. T' 1.0 0.5 * . s .8 %

;

O . o o ..,

_,,,,7

,

_N \

\\

';

/ s

,.. io 15 20

"v,;,

40 +S'

//

TIHE OPTIMAL 5TEERIN

r4

INPICES T4 sec- K=o.is/sec ,=4dei/sec DISde&

(0) (b) (C) (d)

Ï

10 20

\

K= 0.075. 0.15 , 0.30 (1/sec) -20 -4Ö -60 -O 30 2 , 4 S (dei/sec) D IO, 15. 25 (de) 50

'\60

65 4

-I

)(. 4- 0

Fig.( i 5 The effect of parameter variation on the retponse of rudder angle. (Except one varied parameter,

the remainder is fixed as follows : A = 4

/sec, D15', T

5 sec, K0. 15/sec. Initial conditions

are common o= O , = O '/sec, *.s=-60. )

40

\

60

(a) Starboard, Or right turn. (b) Port, or left turn.

Fi 1. Records of hand steering experiments. (Dotted lines are calculated responses. Although experimentalists steered partly by feedback according to the method (ffl), they could meet her on the new course by i

error.)

A

r

/1

=i::

!I:11

t(sec) IO 2O T= 2.5, , IO (sec) ;o

'

20

o

60 O. 20 -Ic

Fig. i 7 Speed reduction ratio

I

and solid line are obtained

by steady turning,

X

by zig-zag test,

A

by modified zig-zag test. These symbols are common in Fig.

18 and 19.

Fig. i 8 Fuel cons::mption (Clean bottom)

Fig. i 9 Fuel ccnsumption (Fouled bottor)

300 750 ç7O0 - £SO-0O 750 goo- 750- 700-2cf

i«

o /o' 20 I

:

-20°

-ib'

Tt c:';tin. cc/3Osac. (Heavy oJ. P

cçrcaç. s;el 9.96 3ft rev. 2)O rp ¡it,:t angle 20.0 Cil temp. 35C r

:.

Gert1etrCeZe

s

/o

20'

ie1conSptiOfl, cc/3Osec.

\

roah5pe 9.05 ': 5hat rev . 7S itc ig1e 19. oil tp. 35C ted ca1i ApPrc&ch'.çeed 9.02 ;ft . 25 ZlT v;1e :o.c o ternp. 34C :-Ocad 2:0. ./0O 00 /7° O ISpiral test, y Zg-zgtest, difie zig-zag test

-to L

-20

A