A zig-zag test analyzer

(1)

N orno to

i. 1E?ACE

'there are a

number of

procedure8 of

analysing the

iig-Zag test

t

obt8ifl the

steering qualitY

8P5.-meters of a

ship in

aueßtiofl,

ranging from the simple

method of

the

rirat_order

(1 and T)-

equatiofl to 'the

phase plane

analysis

taking the higher order

puraiueters

and

o0_line'ar1tY into

5UOt.

lo spite

of the great

develoPments in tte

PM experiment plus

digitsl

sirnu.latiofl

technique, this

ot of aralYS

will keeP ita

role, in the

writer's

view,

or the

time being.

At least in

the analysiS

of actual

ship ttala we

have to

rely o

it

ar4y model

taaifl8 are,

at th

smfle time,

still

maiflg a good

deal of

fpee_ruflhltflg model

expertrfleflt8 as a quick

nieafls oX'

5va.l.Latiflg a hull

and/or rudder

onfigUXtt0fl5.

The ba8C

principle of the

analysiS flOW

ifl conßiderattofl

is

to define a

number of

parameters of a

mathematt0al model so

that

the model

fit with a

detected ship

motion and

rudder movement

as closelY

as

o5ib1e.

This may

lead us to a

simple simultaneOUs

equat1n8 or some kiad 01' the

least square

error method or

itoratlo

procCUre.

-A d1fftU1tY

ari8ifle at

thi8 point i

that the more

the 0iber

of pararueter$ to be

defined, the more

complicated the

omputattOfl

arid the more

errOr la

liable to be

introduced'

Rare is

another idea.

To make the

iteration on an

analogue

c.ompUter

adjust the

parameters

of the atheUiatt1 model

built la

the computer

merelY DY

turning a number

of knODs sod Iceep

one eye

to the

ptlaBe plane

trajeCtOrY

dlBPlSYSd o

a cathOdC''V

oaatllO-This note describes a

device of tbls

prtnAtplC and some

ot the

2.

BMA1'1CAL 14ODL

AND MSIC

SCHEME OF

MALYZßR

tical.mOdOls eplCY

arei

tor a ship

reaponaß

whore

.,Hrne5Urød

(nominal) rudder angle

:

x'esld*zal rudder

angle

àad tor s ateeri

getiIi

a

I

SZ

Onotes ttO

COtÑfld rudder

angle (nominal).

12)iLDPließ e

trat-ord

la

(exponetiSi lag)

with 5p.ed

aatur&

J , ...

-ThO matbe

C.-(1)

(2)

Qr$I=

/'C$

,.k7;S

i

a. v

ARC

(2)

tion which i the character of electra-hydraulic gears now in common use.

lt is possible to produce a certain sequence of rudder coTnrnand,

:wbieh follows the rudder command recorded at the test. Then

we-will geta

- P phase plane trajectory displayed on the oscillo

-scopé, _ç and signals being fed out from

the

circuit

simu-latirig

q. (1). Repeating the rudder command sequence signai at

a reasonably high frequency (the time scale in the simulation should

havebeen adjusted so as to fit this operation), the tra jectory

remains bright on the display.

Then we

could adjust the

para-meters of Eq. (1) by turning appropriate potentiometers so that

theisp1ayed tra

jectory

coincide with the actual one obtained from

the

test

reult. The latter trajectory is conveniently superimpose

:upon: the former by means of s transparent paper.

This

is the case.for zig-zag ±nanbeuvIe. in generai (in fact,

notniy zig-zag but any type of steering, in principle). However,

the procedure now in consideration beôomes

quite

plain in the

"limit-cycle" zig-zag manoeuvres, which means the zig-zag with a

fixed period and amplitude. For this type of zig-zag teats, we

need not input any rudder command signal. By adding an appropriate

switching element, which is usuallyvery simple, the analogue circut

sets in the limit cycle by itself, simulating the limit cycle

zig-zag motion of a ship.

Pig. 3. shows a scheme of an anblogue analyzer for yaw-rate zig-zag tests ( a typical limit cycle zig-zag ¡notion).

Switching Function :

F

reached _Ç switched to-,

/

¿:

Fig.. 1. Yaw-rate Zig-zag Analyzer - Schematic Diagram.

A limit cycle zig-zag test is particularly advantageous in the present type of analysis, because;

(i)

the pbase plane- trajectory

i.s a

closed curve and

thus visual

iteration is simple and accurate;

:(2)

the

-shlp's.phase plane trajectory is accute by averaging over

--

peiods.

cf. ano-ther paper presented at the same meeting.

(3)

3.

tUAL CIRCUIT AND PROCEDURE

: A picture

of the set-UP is

shown Ofl Fig. 2 and the

b].ock diagram of the circuit on Fig. 3.

All the operational

amp-lifiers and also the multiplders are of

module

type in the

market.

ina1reBdiflie

potentiometer setting, which gives parameter

figures, is oone by means

f

a reference

voltage and a digital-voltmeter, whiCh is not shown in the figure.

H.. .2. :.í....- 4_.

--h.?

i:

-3/ 7s.-7'

a/7,-/

",,

Actual

procedure

of

visual iteration

is:

ÏJ to

adjtst K

by the slope

of

the trajectory

at the

axis

(i.e.,

so as

to

fit

the displayed

slope to the one

obtained

from an actual

test),

T1

by the width

-of

thet.rajectOrY

along the

-

axis .

and

J1- by

parallel shifting

along the

₎

axis

Step

1,

Fig.L..

(4)

to acjast by curve fitting at the ist arid 3rd

quarters----step

2, and trien make some correction to step i if needed;

to

bd just T2 and T3 by curve fitting at 2nd and Lth quarters

and then make final touch-up ---Step

3.

Li.. S011E EXAlt[LES:

il) iathematicai Model: At first a mathematical model was emp-loyed to check the function of the

de-vice. The results are shown in Table 1.

7./e 2

11?17. I.".2./ ' _ps

tiiÁ

c64

/. 2/'2[ '. /C'/. 3'._

1<

-o32

-o.

_i'.af2

-?.2

-75

-2

-19g

-1*2

'1

,

73

2/.a

2

2f

33

in ttis case the error comes only from visual iteration since

the same type of mathematical model was used for giving the

tra-jec.ry in place of actual one.

(2) Actual Ship Results: Two examples are shown in Table 2 and on Figs. 5 and

6.

The car-ferry is a

prototype of course-stable ships and the results shows that the linear model is also consistent in this case.

The other is a 200,000 DW1T Class Tanker, representing unstdble giant snips. Trie parameter figures obtained look reasonable and the observed motion of the ship in the form of phase plane