Improvement of course stability by the subsidiary automatic control

Riport Ro1

317

Ligiist 1971

LABORATORIUM VOOR

SCHEEPSBOUWKUNDE

TECHNISCHE HOGESCHOOL DELFT

DPROVX OP COURSE STABILITY BY THE SUBSIDIARY AVPOMAIC

CONTROL

by

An jnv.itigation has been made to 1mpav. the course keeping qualities

of

.nitabis ship by adding a subsidiary automatic oontrol to the

manual steering.

Por this, us, has been mad. of .uult. of full sosie experiments vith a

200.000 Th'lT tarker sud a simulation etuy. Ooma instruotive resulte have

(i)

List of Tables.

List st ligures.

L Intisduetien.

The piseibility t. ohengs the ohaaetsristios by autemitto ontrol

3 Iasvt 5f aluns ksspiug tl2ality by ret. e.ntrel.

A reslisability oen.id.ssbi.n

Sisuistiest en an .na3.. ospitsr.

6

Onoluait.

List et Ta.bless

C.nditi.n f stebilLby

Ohsrsotuistiss o s 200.000 IMT t&nksr

31 Varisnel of 8 in wsv.s.

List of Figure.

Bleak diagram of the control system.

Gsneralizd feed-back sy.t.m.

Inspecting circuit.

Difference of stable and unstable ships in Nyquist plot. Nyquist plot of 200.000 IM1 tanker.

Characteristics et origina]. and apparent s3rstIms.

Transfer function â's-cS

andd..5

Diff.r.ntia] filter

Syn.try in phase oharacteristie.

Schematic sketch of Nyquist plot.

il. Nyquist plot with f iltex

squOncy rispan.. mirves of apparent systems, k - .-2/K.

Frequency response curves of apparent .stems, k 4/K.

Transfer function x

s-Spectrum of coure. deviation in ixrsgular wave..

Test input.

Transient nipona, to th. step input, without filter.

Transient response to the pulsiv. input, without filter.

Transient response te th. step input, with filt. k - -2/1:.

Traasi.nt response to the pulsive input, with filter k - s-2/1:.

ren.ient response to th. step input, with filt. k - .4/IC.

Transient response to the pulsive input, with filter k - -4/K.

Small oourse ohange by human operator A. Small course change by human operator B, Small course ohange by human operator 0. Hysteresis in feed-back loop.

Effect of hysteze.iu (Human op.rator B),

14

_{Intz'odupt4n,.}

Almost .!.ry super tanker whioh has been built nowsd&ys is oourie unatablef

and the sentrol of sush a ey*t.m has been a

_{ut oono.ru for us.}

Xt i. pur. that the mors maflsbls a skip: is, the urs. diffioult te stur.

Wasnaar et s.l

shovod .leazty

by simulator expsz!i.ents, that ther, was a

strong relation between the instability of ships and the dUtioulty to steer

using models with three

d.iffer.nt laysis of (Ln)sts.bility. They found also

that the d.iffioult3r was reduasd to & large extent when a helmsman was provided

with s rate Indicator or a osuno pre&Loton,

The author shoved in hie

papsr2)

_{that th. possibility to steer an unstable}

ship by manual ocntr.1 d..ply depends en the fast t, what extent s helmsman

sazi d.t.st a very small amount at rat. of turn and how h. can react to that

tim.].3r,

On th. ether hand, we eau see it easily that ib is not io d.iffieu3t to dssii

an snt.-pilot et an mstsble ship if enough rat. control Ls avLt1sb1.).

The abev. fasts suggest the vq te r.uea the ditfisulty

ta steer an unstable

ship. Fig i(e) shaw. the normal pattern of manual ..ntr,l, the h.lmw i.

in diffimilty b..aas. et leek of information according t. the d.ss of

instability. The first wy t. redue, the &tffioulty

i. te provid. a he1smsn

with th. additional information like Wsgmiaar

et al did (71g. 1(b) ). This

i. simply dependent en the f*.t that the difficulty is causad by the leek of

information, so the additional information is processed in the mind st the

helmsman..

On the ether hand, it is siso possible t. proses, the additional information

in an sutaumatiosi. way (Fig. 1(b) ), instead of giving that directly t. the

helaòisn. This is the seoand way to redues the difficulty and it i. the objec..

ti,. of this paper.

Vs can see it

more oleanly if ve rewrite that figure as shown in Fig. i(o). A

part of the

job of the helmsman L. replaced by

the subsidiary control or the

minor control _{and the helmsman will feil s. if he is steering}

_{a different}

apparent systam shown by the broken line instead of the ship it..1f. If that

The method t. reduce the &tffioulty by the subsidiary oontrol ha. been uad in the field of the manual control of airplanes but not for chipe. The author proposed tb. apliaation of that method in l964, but it has not

b..n used in praotioc partly because of the lack of investigation in how to

emsu the rate of turn of a chip aM how to reduce the ezoeuive rudder

moysment whioh will b. oau..d by waves.

Bo, in thi. paper, we will coniidir .in1y the low pase filter which vili

asks it easier to differentiate the oours. signai and to reduoe the _xoese

2

where

Tb. linear equation of motion of a ship S.s xpxeued as follows,

d V

M

r

EA%+BS

ali, _l2 (v\ (b1 I ¡

+1

&2l ₂₂ r/ b2

'y s drifting velocity of a ship

r s rate of turn of a ship

8s

ruddar angle of a ship

If ve choose

y

and z' as "the e4diticna1. inforsation" and introduce f..d back

iêops proportionsi. to them

8-

(pi, 2)() + (2)

3-where,

8*

ii th. helmsmen' e rudder angle (input to the apparent system).

Then we t

(.i + BP) % + B ₍₃₎

80 if th. helmsman seis the relation between

I

and % only, he will feel

if h s controlling a. system whose ohiraateristios are A + BP instead of

A.

As vs eau ohooss arbitrarily only two parameter. (9i' p2) in . 2, it is not

possibl. to chang. the oharsotsristios of s ship arbitrarily. But when another

controlling device which is ùraAtt of the rudder, for exampl, a bow thruster, is available, it i. possible (theoretically) to, change the

oharac-teristios oosir1.t1y, If the optimal oharsoteristice of a ship are known

('ve write that £0), the roots of the following equation

s4.

A° - A + BP + CQ ₍₄₎

give the est of preportional conetantu, p1, p2, and q2, of the subsidiary

ontrol (Q _{- t1,} q2) )'

But, in practise, is can hardly «st the informatien if y and it is also not usual t. use another oøntra1lizg devic, in add.iti.n to the rudder, so, our possibilities are r.stri.t.d. Nevertheless, sa w. will s.. later, even that rsstristsd possibility givs us a rather drastic ohnnge in the apparent

3

Improvement of course keeping quality bit rate

gntrol.

In this section, we consider the subsidiary control which io only proportio.'.

nel to the rate of turn,

vss't.

TI*P +(*4T) t + r

K(T38 +8 )

5)

Then w. consider tite control au follow. s

C')

Before going Into

detail, ist

ua recall the Nyquiet Criterion to u.. the

stability of th. feed b&ok ay.t.m.

When ve consider the genera ized f..d back .ystui (Pig. 2), the output of

that system i. .zpr.sued as follows,

x(s)

-+ aSGH o(e) + _{+ f3H} D(a)

as

(7)

Our concern is to know whether tit. characteristic function of EI.

₍₇₎

i + GG11 - O (8)

has any root. with a positiv, resi part or not, and it possible, without soi..

vliig that equatiols. The Nyquist Criterion claims that if we consider the

mapping of a circuit ('ig. 3), which covers sil, of the right half of th.

,sJ-plans, into the [GSGR) ¿plane, and if vs count the number of turne (N) of that

mapping

_{around tit. point (.1,}

o)

in [G5G).iplans Lu olook wies direction,

then N indicates tit. difference of the number of poles (P) and zeros (z) of

the function, i + G8G, in the right half plane, e.g

W. do not discuss her, to _{what extent ve should stabilize the ship, but the} eondit4on

(u)

viii giv, us a very good standard.

Fig. 5 shove the several Nyquist plots (o

+ joo only) of the 200.000 W1

tanker, whose oharaoterjetios are obtained

by full scale mea.urem.nt.6)(se.

Pable 2).

Ship

valueofk

P N

Unstable

k -1/K k -1/K 1

i

-'3. O 0 i stable unstable

Stable forsilk O O O stable

As P is known a priori, because the poleo of that function are the same as of 0H end G8, vo can see Z 4thout solving Eq. (8) d.traotly, and that i. the

nu*ber of characteristic riots with pooitiv. rea1 part et . (8).

Let us apply that criterion to our problem1 In our osso,

(T2s+lf

io)

and

GHk

(u)

Thou K, T1, T2 and T, a1warB r.m..in positive in oase of a stable ship

(ve use positive K to make our consideration en control easier), K and T1

become negative in ou. of an mutabl, ship. So, P - O when a ship is stable

and. P 1, when imitable. Conuquently, N should be O fer a stabi. ship and

should be -1 tor an -i*$Lab2,* ship to have a

stable appsrent systom.

The difference .f a stable and an unstable ship tn the Nyquist

put

(upping

of Pig. 3 ente [GSGH)..plan.) is eohenatioai]y shewn in Pig.

4.

Since the

point (o.ø) in [c)-plane i. aaped ante (kIC, Ø) in G5G)-plans, if we choose

k larger than -1/IC in osa, of an

unstable ship, its oharaoteri.tie nan be made

stable ( N -i)

as

leng au we ... it apparently (see Table 1).

Table 2. Characteristics of a 200,000 WI' tanker6

z _-269.3 sec Length s 310.00 a

T2 s _9'.5 seo Rreadth s 47,16 a

T3 s 200 u Draft s 18.90 a

s -O 0434/iso

£11 actual results praient.d here, apply to this ship.

We can see the affect of increasing the value of k from that figure. Fig. ₆

show, the fr.quency response of th. original uyetem (unstibi.) ant th. apparent system. who.. characteristic. are obtained by the mbsidisry oontröl. Thoui

the phase characteristic

of

th. original system starts from _l800 at low fr.-.

u.noy, thos, of the apparent systems start frem 0°, that asan., the apparent

system. b.eem. stable.

Next, vs hays t. lock at the characteristi, of the aebien of the ruddar,, because

if the ruddsr moves exaeuivsly by the subsidiary semtr,1, the apparent system

is of no USC SVSU if it ein make an unstable ship atable.

ma

transfer function of 8

¡

is shown in Pig. 7. Vs eau say that these

relations are moderate, because these ars O db sr

isa. In

the whole fremonoy

rang., which asanu that th, amplitude of the actual rudder anglet (J) is les.

than or equal to that of th. hlasms&e (J). The phase lead of ö to

S'

K,T

0 (1.4)

If vi consider the case of TL

-T, th. arguments of Eq. (3.3) and Ei. (14)

.e always tynnetrio along the line of ..90° (see Fig. 9), so the argumant

Of

i. always

4,

A r.alisabflity ,sidrdo.

To realise our' nisthod in praatise. it is necessary te measure the rat. of turn

of s ship in some way. In these days, wo can get a rate erro with very high

..n.itivi'by. 3ut va can not us. Lt in practice, bsos. it i. not reliable

nough for marine ussr the overhaul interval i. around 3. 000 houx'..

Th. alternativ. way te mensure the rate et turn ii to diff.r.ntist th. course

signal from the

ro compase. In that osa., vs can only us. s ditfer.nttatiug

filter with low pas. oharacteristio, Basana., if there is no low pass oharac.

tenuti., s very small nei.. if high fnetu.noy in the eaux'.. u4'l will mike

the sutptt st the filtix' very large

_{e Th.ref.r., vs need to asn.idr th. effect}

et that low pass ohsraotorishio t. the whel. iy.tsm Th black diagram of this

ay.tsm is sh.wn in Fig. 8, where ra i. th. rate of turn oMlssd by disturbances,

nd TL i. the tine constant of the low pasa filter. We san consider that

s'TLI+l - TLP+l

(13)

in this cas..

On thsòther hand, it ve oan use a rather' large T, vs ein expect a b.produot

to r.duU the ruddir angle against way... When w, recall Fig. 1, the gain

eharsoteristios of ra

is very larga. It i. known that th. rata of turn

cansad by waves can easily reach as much si 0,2 or 0.3 deg/eeo even in the

Oase of a. large super tankers so the actual rudder angl, will become 1.0° or

200

_{In that ose. We can see in the same figure that the phase ohaxaoteriat Loe}

f

S is almost 00 in the wave freunoy range. That

means, we need not

move th. rudder proportionally to the rate of turn in that fr.quanoy range.

Let us consider for a while the first order' syst.m in order to si*plity the

+ LH -

-1800

Va asnales seo that if T T, thsnLGG9 > -180e, and if T > -T, thon

¿GG

<-leo°. 8e the Jyij4.t plot can b. drawn sohematially as in Pig, 10

( w- O -joo). Thmtore, we can say that TL

should

be smaller than -T to maki th. system stabii.

Pig. 11 shw. the Nyquist plot of the resi. ship with several levels of low

pass filter (k - -4/IC). Thou&i the phase characteristic. are Improved a little

by the phas, lead .ff.ot of T3 f the ascend order syst.s, we eau see the asas

tendency ai we had seen in th. first order system. So, vo can tek. the require..

mont ocn&ttion

TL < _l (16)

as a standard in addition to the relation (12).

ma frequensy responso ohartotaristios cf qpar.nt systems with venous

aMkan..hmminFigo. 12aM13,

aathossfigor.e, wecan s.. that if

vs ehàses too largo, the apparent system ha.s a pair of oscillatory roots

(t. hs.ve m pak in the gain ohanactoriatto.). We better avoid that beesuse it is net our. at this moment whether w. may intreduc. it in the apparent system.

8e, TL should be less then the order .f ...T1/8 for k - -4/K end for k . .2/IC,

Next, ist us i.e the etf.ot of th. low pase filter t. reduce the ruddsr angle

einat waves. Pig. 14 shows the gain ehaz!setoriitios st the rd -

8

(k -2/K).

W. ein ese th. effect of the low pass filter le.r1y.

Vei4huy.en has osisulatod the spsstrmi (Pig. 15) of the cours. deviation of

the ship imder cousidoration, in the waves caused by winds of 3.sufert sosie e t 9 (samtag feas 45° in s head sea). So we can obtain the varianee of rudder angle against waves easily. If ve oonsidor the disturbanoss in the faim at course divistlçn

10

-6

ka2(Ts

+

l)20 + i)

-

+

l)11.

_{+ 1)(T25 + 1) + kKs(T3s + 1)}

and the sp.etrum aM the variance of ¿ san be obtained as follows I

'(5

¡2

= I-;I

Sçbç

C613 2

f Sçç aw

Tb. obtstn.d variances aecording t, filters are listed in rabel 3

Table 3.

Varisn..s cf S (in deg2)

(17)

(is)

110 ¿sg2

Vs eau s.. a drutio dorease of rudder angle by the lev pus filter (TL

O

zuna with.ut filter).

When we take an extreme va1u (w - ca ) of

,

(e), we get

J

k

(zo)

and as the frequency rangs of wave. can b. said t. b. in that range, w. may

say that if k eM TL are et the esas srder of nI1nItude, the angie .t the rudder

against wave. is as small s that et the yawing angi. of the chip caused by

wave, and remains modsrate

o

-T1/8

_T1/4 -2/IC -4/K 580.0 2340.0

2.08

8.50

0.52

206

0.12

0.52

.

sigsti.n on w snso

sceDutor.

In th. above &tsouasiono we restrioted ourselves in the fr.quenoy d-tn only.

But v swig, it better intuitiv.ly in

the tim.

dm4n. So the simulation

on the ama1e oodputer vs. osrri.d out.

Three sategories of experiment. have bien don without disturbanoss $

1, the transient rasponis to the itsp input (Pig.. 16(a)) 2. bbs transient response to the puisiv. input (Pig. 16(b))

3 s, 5.i.11 Gouri, ohangs (20) by human operator..

TbU

the huasn operators vere

not prof.uional

(the author aM hta ooll.agti.$),

vs may .zpeot scee important rimait..

In Fig.

17 and 18, the

response

te the step and pulsiv. inputs sr. shown

(with.ut low pas. filter). Vs can see that it ii possible to mak, an unstable

ship stable by increasing the valus of k larger than -1/K. It is interesting

to ses that when

8*

is kept cero after a oertala motien the sotual ruddix'

angle

8

becomu mero too at t - oO (Pig. 1g),

Th, effect. st the low pass filter are shown in Pigs. 19 to 22 fer th. saies

of k - -2/K sad -4/K rupsotivsly Prc those figures, we sen sec th it is

nsse35sxy

te shoese TL lees

than fer k - .2/K or less

than .-T1/$ for

k - .4/K to privant the oscillatory obarsoteristio.

Figs. 25 to 25 show the risulti of a sash course chang. by

h,iii operators,

The upper parts of those figure. show the result. without f.ed..uk (original

iiip) and the lower pass, with filters, the value. f

whieb were k - -4/K sad

- -T1/$. ThoaØ the results are different fr.. sash ether dsp.n&thgmt the

hunan .perster we can sei clearly that the appssnt systom ves mad. sensidsrs,bly

easier to steer than the original .me.

V. are osn.id.ring to measure the rat. of turn of s iMp by differentiating

the semas .1&l from the gyro somps. In this regard

we must b. *sr. of

s. hysteresis sharact,rjstio in the course siguaJ, becaus, it

iS sade by tracking

the gyro compase with s servo mechanism. That should maki our method lees effective

A osspri..nvith and vithout hyatr.ui. oharut.riatia va. mada br two

husn oparator. using the hysteresis width of O,1

at both udii (Fig. 26)

vhr. k

i2/K, TL

-T1/8..Itesulte sr. shown in Fige. 27 and 28. Vi osu

net se. any ditferuna. train tho.. szperiente, at least

t first glana., or

w.

r synieaUy say tst thu )g1rn air hays felt ls.. diffis'lty when

the hysterssis was introduud.

13

-6.

Oon.1*tIen.

An inv..tl«stion to &ki an unstable chip stùls by the subsidiary oontrû

has

been aad. and ss instructive recuits vers dedueed

lt. steering of

en

unstable chip can be aids sailer by the subsidiary

s,itMLo rets control, the sftaoti',.nsss

of vhioh

s proved

to a certain

xtent by the simple simulator .xp.rim.nts with human operator..

Tb. proportional constant of rat. of turn fssd-back uhould be larger

thin .1/K to asks an unitabi. ship stabi. (relation (12) )

It i. possibl, to introduce s low pass filter in the feed-biok loop with

rather large tIns oonutant

(relation (16) ), and that fact asks. it suiez

to measur. th. rat, of turn of a .hlp by differentiating the acures .*gnsl

and also to r.duoe the rudder angle ageinat vives.

It was not possible to find a bad effect of hysteresis characteristics

1.Ws«.nur stai,

2. Es'sas, T.i

" A Prop..s1 te Define the P.xai..ibl. Orit.i.ta of Instability et Ships".

Shipbuilding Liborater3r of TR. Ditt, 1971. 2q

.

T.i

"Bets nets. _on tb. Auto.Pilot of an Unstabi. Ship".

Shipbuilding Laboratory of TR. Deift, 1971.

4 Motors, 8. and K.yaaa, ¶I.s

"Improv.a.nt eS Mmn..vrability by th. Autotati Control".

JSN.A. Japen Vol. 116, 1964. (Japan 8hipbui1diza & N.E. July 1968)

lIstet.,

Li

of Ketpfu Standird Manosiwrsr

ut

and Proposed Steering. Quality Indioie".

Firet Syaposium on Ship Maneou'ability, 1960.

Glan.dorp, 0.C.i

"3ia1stion of 7u11.Soale Result, of Manosuvring Trial, of _a 200.000 tone

Taxikor

vith

_a

Siapi.

Nathstatio.1

Model".

B.port

No 301,

Shipbuilding

Labøratory

of W,H. D.lft, Msroh 1971.

7

V.ldhnyun

W.s

"Ond.r.o.k

_nur

d.

Regelteo)thieohe Aspekten _van

hot

0.6mg

_van de Roerganger van

e.0

Supertanker".

Graduation

thesis,

T.H.

Deift,

April

1971

i (w&s 816)

Goal

lut way

Helmsman Helmsman (

a)

(b)

(o)

ig 1

Blook diagram of the oontrel eystem

Ship 2nd way

_L_i

.1

infornatien

F-Output >

J

_P!rL!Z5_

I A > Ship I

.

> I

j

Additional

I i

information

I

L

I

Helmsman Ship

Insufficient information

c(t)

Pig.3 Inspecting circuit

>

_Gs(s)

GH(S)

Fig.2 Generalized feed-back system

d(t)

(disturbance)

00

unstable stable

ig.4. _{Difference of stable and unstable ships}

in Nyquiet plot

m(t)

k .-_ 00

n.

uJ=-S

wo

s

Flg5 Ryquist plot

f 200.000 DW

tanker

ki_1e/K

w=.0006

3/1<

2/K

.1 3 .0019 et k .006L .0096 s .0043

IGl

db

-440

-60

Fig.6

Characteristics of original and apparent systems

II

ain

9',

Onginat

-2/1<

Ô

i

w

=r=

s

Gain

db

40

20

o

20

.005

foi

Pig.7

anafer functl. on

and 1'd &

.05

.1

.5

Phase

deg

. "1

na

-L s,g

-o

--->9

_{(lis-i-1 )(T2S+1)}

K(T3s+1)

ks

TLS+1

FLB.8 Differential filter Log u.) -. LG1 LGHGs

Fig.9 Symmetry in phase characteristic

rd

Fig.1O Schematic sketch of Nyquist plot

00

90°

?ig.11

Nyquist plot with

filter

IÍIrI

o

TL-2T1

_3

IGl

db

-40

-60

Flg.12

Frequency response curves of apparent systems, k -2/K

LG

s

i

TL41/2

-Ti//.

-Ti/8

0-1i=

o

-Ti/I.

-45----O

\

- P1.

-Ti /8

-______

..-.005

.01

_.05

IGl

db

-4

-60

.005

I

Fig. 13

Frequency response curves ot apparent systems, k 4/K

LG

d

ILT/

41/4

-Ti/8

__

TL= -Ti/2

Gain

-90

\

I

s

IS/rd I

db

40

20

Pig .14

fransfer tanction rd

-.0Q5

.01

.05

.1 . CL

TL=0

o

Fig.15

Spectrum of course deviation in irregular waves

o*l

o

Fig.16

Test input

(b) putsive input

t

(ci) step input

t

0.5 10 (L)

deg'sec

to

r

de,

4ec

0.8

0.4

O

-20 -0.4

Pig.17

Transient response to the step input,without filter

k=O 1/K

-2/K

r

a_e

__

--4/K

400_____600_____

- 4/K

_800____10

&

d eg

20

o

Fig.18

fr8nslentrespc*ee to the pulsive input,without riiter

r

8

1000

±sec

20-

0.4

0--20 0.4

r

deg d eg

0.8

r

deg sec

o

20-

-20-o.

0.4

o

-0.4

Fig.19

Transient response to the step input,with filter k.-2/K

r

TL=T1

-Ti/L

- -

-

- -

6*

--Ti/8

L

- - -

-b

400

-Ti

600

Ti/8

---TilL

--Ti/2

-800

101 SE

- - -

--r

deg

2

0-

s

r

deg deg sec

2s

0.4

o

0.4

10 deg

j

50 loo

U

300 sec 100 150 200 25 300 sec

2-

_with

_feedback

-lo

-Fig. 23

_{Small course change by human operator A}

150 200 250

original ship

deg lo

-lo

-lo -. 2 deg 50 150

with feed back

Fig. 24

SmaLl course change by human operator

B

loo 150 200 250 300 sec

original ship

50 loo 200 250 300 t sec - J-lo

-10

2

50 _iáo originaL shIp 150 ₂₀₀ with

_feedback

Fig. 25

_{SmalL course change by}

_{human operator}

C 250 300 sec t sec

s

Hysteresis

Fig.26

Hyateresis in feed-back loop

deg

lo

200 250 300 t sec sec with hysteresis

-lo ',8' c i _deg

-

lo * 50 100 150 200 250 without hysteresis 150

with hysteresis

200

Fig. 28

Effect of hysteresis

(Humòn

opetotor C)

250

Sec

824825

TECHNISCHE HOGESCHOOL DELFT

AFDELING DER MARITIEME TECHNIEK

LABORATORIUM VOOR SCHEEPSHYDROMECHANICA

IMPROVEMENT OF COURSE STABILITY BY

THE S UBS I DIARY AUTOMATI C CONTROL.

by T. Koyama Reportno. 317-P

August 1971

DeIft University of Technology

Ship Hydromechanics Laboratory Mekelweg2

2628 CD DELFT

The Netherlands Phone 015 -786882

126

1. Introduction.

Almost every super tanker which has been built

nowadays is course unstable, and the control of such a system has been a great concern for us.

It is sure that the more unstable a ship is, the more difficult to steer. Wagenaar et el. showed clearly [1] by simulator experiments, that there was a strong relation between the instability of

ships and the difficulty to steer using models with three different levels of (ln)stability. They found

also that the difficulty was reduced to a large

extentwhenahelmsmanwas provided with a rate Indicator or a course predictor.

The author showed in his paper [2] that the

possibility to steer an unstable ship by manual

control deeply depends on the fact to what extent

a helmsman can detect a very small amount of rate of turn and how he can react tothat timely.

On the other hand, we can see It easily that It is not so difficult to design an auto-pilot of an unstable ship if enough rate control Is available

[31

The above facts suggest the way to reduce the difficulty to steer an unstable ship. Figure i(a) shows the normal pattern of manual control, the helmsman is in difficulty because of lack of in -formation according to the degree of instability.

The first way to reduce the difficulty Is to provide

a helmsman with the additional Information like Wagenaaretal.did (Figure 1(b)). This is simply

dependent on the fact that the difficulty Is caused

by the lack of information, so the additional

in-formation is processed in

the mind of the

helmsman.

)Shipbuilding Laboratory of the Technological University Deift. The

Netherlands.

IÑPROVEMENT OF COURSE STABILITY

BY THE SUBSIDIARY AUTOMATIC CONTROL

by

T. Koyama)

Summary.

An investigation has been made to Improve the course keeping qualities of anunstable ship by adding

a subsidiary automatic control to the manual steering.

For this, use has been made of results of full scale experiments with a 200. 000 DWT tanker and

a simulation study. Some instructive results have been obtained.

On the other hand, it is also possible to process the additional information in an automatical way

(Figure 1(b)). Instead of giving that directly to the helmsman. This is the second way to reduce

the difficulty and it is the objective of this paper.

We can see it more clearly If we rewrite that figure as shown in Figure 1(c). A part of the job of the helmsman is replaced by the subsidiary control or the minor control and the helmsman

will feel as if he is steering a different apparent system shown by the broken line instead of the

Ooa -9---'I H.lmaaan BMp Outpwt Ie,ufftci.nt Lnforaation let way H.lmeaan Helsaeaan SMp 2nd way Additional _Lj

_otjo

F--Additional information

H

F-j

j

(o)

ship itself. If that subsidiary control is made correctly, his difficulty will be reduced very

much. The method to reduce the difficulty by the subsidiary control has been used in the field of the manual control of airplanes but not for ships. The author proposed the application of that method in

1964 [4], but it has not been used in practice partly because of the lack of investigation in how to

meas-ure the rate of turn of a ship and how to reduce the excessive rudder movementwhich will be caused by waves.

So, in this paper, we will consider mainly the low pass filter which will make it easier to

diff-erentiate the course signal and to reduce the

excess rudder movement against waves.

2. The possiblity to change the character. istics by automatic control.

The linear equation of pressed as follows:

d y

a11,a12 y dt = a21,a22 + S where X =

y: drifting velocity of a ship

r: rate of turn of a ship

s : rudder angle of a ship

If we choose y and r as 'the additional

informa-tion' and introduce feed back loops proportional

to them

5=(p1,p2) () +5*

PX 5* (2)

where, 5* is the helmsman's rudder angle (Input to the apparent system). Then we get

motion of a ship is

ex-(1)

b1

( )5

b2

(3)

So,if the helmsman sees the relation between 5*

and ' only, he will feel as If he Is controlling a system whose characteristics are A +BP instead

of A.

As we can choose arbitrarily only two

para-meters (p1,p2) In equation (2). it is not possible

to change the characteristics of a ship arbitrarily.

But when another controlling device which is independent of the rudder, for example a bow

thruster, is available, it is possible

(theoretic-ally) to change the characteristics completely.

If the optimal characteristics of a ship are known

(we write that A°) ,the roots of the following equa

-tion

A°=A+BP+CQ (4)

give the set of proportional constants, p1,p2,q1

and q2, of the subsidiary control (Q =(q1,q2)). But,in practice,we can hardly get the informa

-tion of y and it is also not usual to use another controlling device In addition to the rudder, so,

our possibilities are restricted. Nevertheless, aswe will see later, even that restricted possi-bility gives us a rather drastic change in the

apparent characteristics of a ship.

3. Improvement of course keeping quality

by rate control.

In this section. we consider the subsidiary

control which is only proportional to the rate of

turn.

Whenwe eliminate y from equation (1). we get the well -known second order equation of Nomoto

[5].

T1T2i(T1+T2)i+r=K(T3 +5)

(5)

Then we consider the control as follows:

(6)

Beforegoingindetail,let us recall the Nyquist

Criterion to see the stability of the feed back

system.

When we consider the generalized feed back system (Figure 2), the output of that system is expressed as follows: M(s) C(s)-f D(s) (7) l-FGSGH l+GSGH Gs i d(t) (dlsturbaiice) c(t) 2-

'

Os(s) I OH(S)

Figure 2. Generalized feed-back system. m(t)

128

Figure 3. Inspecung circuit.

Our concern is to know whether the character-istic equation of equation (7)

1+GSGH=O (8)

has any roots with a positive real párt or not, and

if possible. without solving that equation. The Nyquist Criterion claims that if we consider the

mapping of a circuit (Figure 3), which covers all of the right half of the[sI -plane, into the (GSGH)-plane,and If we count the number of turns (N) of that mapping around the point (-1,0) in

[GSGHI-plane in clock wise direction, then N indicates

the difference of the number of poles (P) and zeros

(Z) of the function. i +GSGH, in the right half

plane, e.g.

-As P is known a priori, because the poles of that function are the same as of 0H and G, we can see Z without solving equation (8) directly,

and that is the number of characteristic roots

with positive real part of equation (8).

Let us app'y that criterion to our problem. In our case,

K (T3s + 1)

°S(TS+1)

(T2s+1)

and

GH=k (11)

Though K, T1,T2 and T3 always remain positive in case of a stable ship (we use positive K to make

our consideration on control easier), K and T1

become negative in case of an unstable ship. So,

P =0 when a ship Is stable and P = 1, when unstable.

Consequently,Nshouldbe O for a stable ship and should be -1 for an unstable ship to have a stable

apparent system. The difference of a stable and

an unstable ship in the Nyquist plot (mapping of

Figure 3 onto [GSGHI -plane) is schematically shown in FIgure 4. Since the point (0. 0) in [s]

-plane is mapped onto (kK, 0) in [GSGH] -p1e, if

we choose k larger than-i/K in case of an

un-stable ship, its characteristic can be made un-stable

(Nr- -i) as long as we see it apparently (see Table

1).

We do not discuss here to what extent we should

stabilize the ship, but the condition

k>-1/K (12)

Figure 4. DIfference of stable and unstable ships In Nyquist plot.

(10)

Table 1.

Condition of stability.

Figure 5. Nyquist plot of 200. 000 DWT tanker.

Figure 5 shows the several Nyquist plots (0-'+

j only) of the 200. 000 DWT tanker, whose

characteristics are obtained by measurements [6J (see Table 2).

full scale Table 2 Characteristics of a 200. 000 DWT tanker [61 T1 : -269.3

sec Length :310.00m

T2 : 9.3 sec Breadth : 47.16m T3 : 20. 0 sec Draft : 18. 90m K -0. 0434/sec

All actual results presented here, apply to this

ship.

We can see the effect of Increasing the value of

kfrom that flgure.Figure 6 shows the frequency

response of the original system (unstable) and the

apparent systems whose characteristics are

obtained by the subsidiary control. Though the

phase characteristic of the original system

starts from-1800 at low frequency, those of the apparent systems start from 00, that means, the apparent systems became stable.

Next, we have to look at the characteristic of the motion of the rudder, because if the rudder

moves excessively by the subsidiary control, the

apparent system is of no use even if It can make an unstable ship stable.

ai

FIgure 6. Characteristics of original and apparent systems.

Figure 7. Transfer function -6 and r-&.

The transfer function of 6* 6 is shown in Figure

7.Wecan say that those relations are moderate, because those are O db or less in the whole

fre-quency range, which means that the amplitude of

the actual rudder angle (o) Is less than or equal to that of the helmsman's (5*). The phase lead

of O to 6* in the low frequency range contributes

to make a ship stable.

4. A realizability consideration.

To realize our methodinpractice, it Is

neces-sary to measure the rate of turn of a ship in some

way. In these days, we can get a rate gyro with

very high sensitivity. But we can not use it In practice, because It is not reliable enough for marine use; the overhaul interval is around

1. 000 hours.

The alternative way to measure the rate of turn is to differentiate the course signal from the gyro

compass. In that case, we can only use a

dif-ferentiating filter with low pass characteristic.

I

I

IL

Ship

value of k P N Z=N+P

Unstable k>-1/K 1 -1 0 stable k>-1/K 1 0 1 unstable

Stable for all k O O O stable

- -. -r k -UK -3/K

L

-2/K .1

L

1/2

'

a!, 20 o--20 m I/r.I

T

,.

---

¿ ¡/1' -I0I db £0 -60 129 w

130

Because, if there is no low pass characteristic,

a very small noise of high frequency in the course signal will make the output of the filter very large.

Therefore, we need to consider the effect of that

low pass characteristic to the whole system. The

block diagram of this system is shown in Figure

8, where rd is the rate of turn caused by disturb

-'9

(T1S+1)(T2s+1)K(T3s+1) ks ILS + i C

i-S

Figure 8. DIfferential filter.

ances, and TL is the time constant of the low

pass filter. \Ve can consider that

GH-'

_{Ts+l TL5+l}

ks k

in this case.

On the other hand, if we can use a rather large

TL, we can expect a by-product to reduce the rudder angle against waves. When we recall

FIgure 7, the gain characteristics of r - o is very large. It is known that the rate of turn caused by waves can easily reach as much as 0. 2 or 0. 3 deg/sec even in the case of a large super tanker;

sothe actual rudder angle will become 100 or 200

In that case. We can see in the same figure that

the phase characteristics of 55 is almost 00

in the wave frequency range. That means we need not move the rudder proportionally to the rate of

turn in that frequency range.

Let us consider for a while the first order

system in order to simplify the problem, e.g.:

rd

(13)

Figure 10. Schematic sketch of Nyquist p'ot.

If we consider the case of T1 = -T, the

argu-ments of equation (13) and equation (14) are always

symmetric along the line of -90° (see Figure 9,

so the argument of GHGS is always

LGHGS=LGS+LGII=_1800 (15)

We can also see that if TL <-T, then LGHGS> -180°,andifTL> -T, then LGHGS< -180°. So the

Nyquist plot can be drawn schematically as in

Figure 10 (c= 0-'joo). Therefore, we can say that TL should be smaller than -T to make the system

stable.

Figure 11 shows the Nyquist plot of the real

ship with several levels of low pass filter (k= -4/K). Though the phase characteristics are

improved a little by the phase lead effect of T3 of

the second order system, we can see the same

tendency as we had seen in the first ,order system.

So, we can take the requirement condition

TL< -T1 (16)

Figure 9. Symmetry In phase characteristic, _{as a standard in addition to the relation (12).}

K,T O (14) FIgure 11. Nyquist plot with filter.

tog u)

L6

_900

B m -e n' s# dig' sec 1.0 0.5 o 0.5

Figure 14. Transfer function rd-6.

w

lo u)

Figure 15. Spectrum of course deviation in irregular

waves.

The frequency response characteristics of

ap-parent systems with various TL and k are shown In Figures 12 and 13. From those figures, we can

see that if we choose TL too large, the apparent

system has a pair of oscillatory roots (to have a

peak in the gain characteristics). We better avoid that because it is not sure at this moment whether

we may Introduce it in the apparent system. So,

TL shouldbe less than'the order of -T1/8 for k=

-4/K and -T1/4 for k=-2/K.

Next, let us see the effect of the low pass filter to reduce the rudder angle against waves. Figure 14 shows the gain characteristics of the rd-B (k= -2/K). We can see the effect of the low pass filter

clearly.

Veldhuysen [71 has calculated the spectrum (Figure 15) of the course deviation of the ship

under consideration, in the waves causedby winds

of Beaufort scale 8 to 9 (comIng from 450 in a head see). Sowe can obtain the variance of rudder

angle against waves easily. If we consider the

disturbances In the form of course deviation Yd'

the transfer function '+'d B can be described as

follows:

s ks2(T1s+1) (T2s+1)

'pd- S(TLS+l) (T1s+1) (T2s+1) +kKs(T3s+1)

(17)

and the spectrum and the variance of S can be

obtained as follows: S55=I 2 (18) 'Pd Do E1621=21 S58 dcù (19) o

The obtained variances according to filters are

listed in Table 3.

Table 3.

Variances of 5 (in deg2)

E(yd21 1. lOdeg2

We can see a drastic decrease of rudder angle

by the low pass filter (TL = O means without

filteri. '3' -T

0-90 -1.-T/2 4,,'

:

-.5 IO T, .0 20 T,. -T,/2 -T'I' O O -T1/8 -T1/4 -T1/2 -2/K -4/K 580.0 2340.0 2.08 8.30 0.52 2.08 0.12 0.52

Figure 12. Frequency response curves of apparent

systems, k -2/K.

Figure 13. Frequency response curves of apparent

systems, k=-4/K. 5 w IO db .0 IO' £0

132

When we take an extreme value (c.-' of

ecuat1on (8), we get

6 k

d TL

and as the frequency range of waves can be said to be In that range, we may say that if k and TL are of the same order of magnitude, the angle of

the rudder against waves is as small as that of

the yawing angle of the ship caused by waves and

remains moderate.

5. Simulation on an analoque computer. In the above discussions we restricted

our-selves In the frequency domain only. But we can see It better intuitively in the time domain. So the

simulation on the analogue computer was carried

out.

Three categories of experiments have been

0.4

0

¿f

step input

(b) putsive input

Figure 16. Teat input.

(20)

t

-20 -0.4

Figure 17. Transientresponseto the step Input, without filter.

r

-2' -0.4

Figure 18. Transient response to the pulsive input, with-out filter.

-20 0.4

Figure 19. Transient response to the step nput, with filterk=-2/K.

0.9

-20 -0.4

Figure 20. Translentresponseto the pulsive input, with filterk=-2/K.

o

-0h

Figure 21. Transient response to the step input, with filter k=-4/K.

_

vA

r

-1K _.__600--900

r

10

t

2 ' 400

_A- .

_{_____}

_-

_{___}

2 400 1,/2

:'

10

-8 00 ¿00

_. ''

SI r

-UK 2 __..._.._6OO---- uu lLlII -1,/2 1,/ 1,/8 ,%. O'

''

S -It -1,/2 20 0.4 o a'a r d. d. 0.4 20 o o ß r 0.9 0.4 20 O o

r

Figure 22. Transient response to filter k= -4/K.

done without disturbances:

The transient response to the step input

(Figure 16(a)).

The transient response to the pulsive Input

(FIgure 16(b)).

A small course

change (20) by human

operators.

Though the human operators were not profes-sional (the author and his colleagues), we may expect some important results.

In Figures 17 and 18, the response to the step and pulsive Inputs are shown (without low pass fllter).We can see that It is possible to make an unstable ship stable by Increasing the value of k

larger than -1/K. It is Interesting to see that when

5* is kept zero after a certain motion, the actual rudderanglesbecomes zero too at t-. (Figure

18).

The effects of the low pass filter are shown in

Figures 19 to 22 for the cases of k= -2/K and

-4/K respectively. From those figures, we can

see that It Is necessary to choose TL less than

-T1/4 for k = -2/K or less than -T1/8 for k -4/K

to prevent the oscillatory characteristic.

Figures 23 to 25 show the results of a small

course change by human operators. The upper parts of those figures show the results without

feed-back (original ship) and the lower parts, with

filters, the values of which were k=-4/K and

TL= -T1/8. Though the results are different from each other depending on the human operator, we can see clearly that the apparent system was made considerably easier to steer than the original one.

We are considering to measure the rate of turn

of a ship by differentiating the course signal from

the gyro compass. In this regard we must be

aware of a hysteresis characteristic in the course signal because it. Is made by tracking the gyro

compass with a servo mechanism. That should make our method less effective.

A comparison with and without hysteresis

characteristic was made by two human operators

using the hysteresis width of 0. lo at both sides (Figure 26) where k= -2/K, TL= -T1/8. Results are shown In Figures 27 and 28. We can not see any difference from those experiments, at least at first glance, or we may cynically say that the

helmsman may have felt less difficulty when the

hysteresis was introduced. 6. Conclusion.

An investigation to make an unstable ship stable by the subsidiary control has been made, arid some

instructive results were deduced.

The steering of an unstable ship can be made easier by the subsidiary automatic rate control,

the effectiveness of which was proved to a certain

extent by the simple simulator experiments with human operators.

The proportional constant of rate of turn feed

-back should be larger than -1/K to muke an un-stable ship un-stable (relation (12)).

It is possible to introduce a low pass filter in

the feed -back loop with rather large time constant

(relation(16)), and that fact makes it easier to

measure the rate of turn of a ship by differentiat -ing the course signal and also to reduce the rudder angle against waves.

It was not possible to find a bad effect of hysteresis characteristics in the course signal

at least from the present experiments (+0. 1°of

width).

133

Ti.-Ti

2

2 o.'

the pulsive input, with

o

-134 ar # lo -de0 10

-IO IO 10 ot b io ..di0 'o2 So 100

j

originaL ship 100 ISO

n

with feed-bock

Figure 23. Small course change by human operator A.

loo

with teed - back

700 750

150 200 200

Figure 24. Small course change by human operator B.

'st

300

'st

s

lo

Figure 25. Small course change by human operator C.

deg -lo -7-50 151 loo mo originaL _shil ISO 200 250 300 150 251 750

with feed -back

without hysteresis

ISO

with hysteresis

ks

Figure 27. Effect of hysteresis (Human operator B).

s

Hysteresis

Figure 26. Hysteresis in feed-back loop.

250 200 250 sec "e 300 lee 135

136

-Io

-3-without hysteresis

Wagenaar, et al.

Koyama, T., 'A proposal to define the permissible criteria of instability of ships', Shipbuilding

Laboratory of T. H. Delft, No. 299, 1971. Koyama. T., 'Some notes on the auto-pilot of an

un-stable ohtp', Shipbuilding Laboratory ofT. H. Deift,

1971.

Motora, S. and Koyama, T., 'Improvement of ma-noeuvrabiiity by the automatic control', J. S. N.A.

Japan, Vol. 116, 1964. (Japan Shipbuilding & M. E. July 1968)

with hysteresis

Figure 28. Effect of hysteresis (Human operator C).

References.

Nomoto, K. , 'Analysis of Kempf's standard manoeuvre

test and proposed steering quality indices', First

Symposium on Ship Manoeuvrability, 1960.

Glansdorp,C. C., 'Simulation of full-scale results of manoeuvring trials of a 200. 000 tons tanker with a simple mathematical model', fleport No. 301,

Shipbuilding Laboratory of T. II. DeIft, March 1971.

VeLdhu,sen, W. , 'Onderzoeknaarde regeltechnische aspekten van het gedrag van de roerganger vaneen supertanker ',Graduation thesis, T. H. Delft, April

1971.

300

lic