Statistical Identification and Optimal Control of Marine Engine

Statistical Identification and Optimal Control of Marine Engine Kohei Ohtsu

Masanori Ishizuka

TOKYO UNIVERSITY OF MERCANTn..E MARINE

NYK LINE

2-1-6 Etchujima

2-3- 2 M arunouchi

Koto-ku Tokyo, Japan

Chiyoda-ku Tokyo, Japan

Abstract The authors presented a preliminary study on the optimal control of a marine engine in the last symposium . In this paper, they discuss some new results which were obtained after it. The first part of this paper is devoted to statistical identification problem of governor-propeller system . The identification is carried out to the data which was observed on a small training ship , using an auto regressive model. A salient feature of this data is that it was gained under almost no feedback control condition of marine diesel engine. Namely, the engine was controlled by a weak digital PI control, plus a strong random noise. They fit a statistical auto regressive model to this data and calculate a frequency response function, an impulse response function and a transfer function. The second part of this paper is devoted to an optimal control of the main engine. The authors has carried ou t m any actual experiments at sea using the theory which were proposed in the last symposium . In this part, they report some important results about the actual tests and propose an entirely new ship control system in which a marine engine control, ship's motions and steering motion are integrated.

1

Introduction

In a last paper, we made clear the main causes of fluctuations of rate of propeller revolution, using an actual control record observed at sea ( K.Ohtsu (1989) ). And we proposed one optimal control type of marine governor. However , we remained after the identifica.tion problem of governor - propeller system and its analysis . In the papers which has been published, many authors proposed the frequency response function of them . For examples, the frequency response function of a diesel engine was gained by Browns using a digital identification technique ( D. E. Browns (1971) ). However, the paper in which the dynamical properties of a marine engine were tested by using the records directly obtained at sea, is quite few. In the first part of this paper, we show the results of the statistical identification using a multivariate auto regressive model and demonstrate the impulse response function and the frequency response function from the ordered input signal in a governor system, to rate of propeller revolution ( M.lshizuka et al. (1991) ). In the second part , we propose two types of marine engine governors in which the first one aims to suppress fluctuations of rate of propeller revolution and the second one , to suppress not only

25

fluctuations of rate of propeller revolution but also propeller shaft torque. And we report the results of the actual experiments at sea using a small training ship ( M.lshizuka et al. (1992) ). Lastly, basing on the results of the actual sea experiments, we propose one entirely new governor system considering the relevant ship's motions.

2

lfp

~9 . 93

B.-u.

1000

DJ

2.80

RI

D
Experhnental System

The main engine used in the experiment is a middle type of marine diesel engine installed . in a small training ship SHIOJI MARU. The

Displooom_

717.52 """

Gross tollUlc


cpp

PropdIer

principal dimension is shown in Table 1 (

DJ

Bo-. lIIrus.er

2."

s..n. ...........

1.8"""

tom

Table 1 Principal Dimension of T.S. Shioji Maru

K.Ohtsu et al. (1989) ). Especially, we should take account of that this ship equips with a controllable pitch propeller (CPP). Furthermore, in order to regulate the revolution of the propeller, the conventional type of mechanical governor and the electronic one which is mainly operated under PID control law is installed in this ship. Vie developed a computer controlled system of Fig. 1

the governor for a direct digital controlling as shown in Fig. 1. In this system, the right of

Interface System between Computer System and Governor Actuator

control is completely transferred to the digital

~

8

g

~

to the computer's mode and the control signal from the computer is given to the actuator in

~

>:

>:8

. ~ ...,

:Z:@

Q.ljl

the governor to move position of the fuel pump rack bar. Fig.2 demonstrates the state of the rate of propeller revolution and the behavior

"'

0

8 g

of the posiotion of fuel pump rack bar in the

N

Propeller RPM

c

'"~

20 .00

40 . 00

"'+-~-'-'-4 -0.00

SEC

ship 's governor's mode to the computer's one.

Fig.2

It is seen that the switching is smoothly carried out.

FO Pump Racl< Bar

@

lIDo.oo

governor before and after swi tching from the

3.1

g

c

computer system when a switch is turned on

3

'C

...

20 .00

40 .00

SEC

Time History in Switching from Ship 's Governor to Computer Controlled One

Identification using an Auto Regressive Model Random Controlling of Marine Engine In this ch apter, it is sh own that the results of a statistical identification of the governor -

propeller revolu tion system in the marine diesel engine of Shioji M aru, using the records observed at sea ( M.lshizuka et al. (1991) ). It is well-known that the optimal input for such a statistical identification is the signal as random as possible, like white noise.

26

However, such a complete random input inGaussian

evitably gives large causes to plunge the main engine into dangerous state, because the engine

wbite noise

+

1f'JvJ"

+;) I

To Mw

I!~u..

Actuat.orf-?-

is su bstan tially unstahle in condition without any controlling. For this reason, we determined to input the signal which is added a white noise

Propeller nrM

?~~;;~~J

to the original PI controlling signal to cope with

L-..---n~

fluctuations of the rate of propeller revolution

( Fig.S).

+

Fig.4 shows the part of the PI

,f'

,"

,,' .. , '"

.•

random signal which is input into the main engine in operating at sea and the corresponding response of the rate of propeller revolution. It is seen that though fluctuations of the rate of propeller revolution are considerably large by such a signal, the main engine does not plunge into dangerous state. We observed the records which are composed of the rate of propeller revolution (rpm), the

Fig.4

Time Series of RPM , FO Pump Rack Bar and Ord erd Governor Signal

position of fuel pump rack bar in the governor and the ordered signal from the computer to the governor actuator under the above conditions. The data length were 10,000 points sampled at 0.1 sec. The spectra of these three signals are shown in Fig. 5. Fig .S

3.2

Power Spectra

Optimal Auto Regressive Model In the following , we fit an auto regressive model M

L

X(n) =

AM(m) X(n - m)

+

(1)

E(n)

m=l

to the observed data ,using the minimum Ale estimate method ( H.Akaike (1974) ) in which the state vector X (n) are composed of the rate of propeller revolution and the ordered signal from the computer to th e governor's actuator. Tabl e 2 shows the 6-th order auto regressive model fitted by this method . ,o,o:,.. ,,,on A. ( ,

, uuuo

,

-, .uuu.

I

.,

11111150

• unuo

TabJe 2 The Coefficients of Aut o Regressive Model

I

-f 14/"5 ..

, ,

-. HIltH}

• I.H \ I1,

-. IlltUU

I

-0 tUtU l l

I

- f'II 11I)O

I

· f . . . . UCI'

, ' ll tlU .

1)

!;ou.r •• r-'ropeller Sy.tem

· ..· ,

.1IUUI 1 1 1" Hl

lSu"n l'U01O ~

-.

• .~ 1 I ! 01 , UHOOOl

-. "U'U' -.

- , 'U1OHS

10U'"

0 ' ttI UO,

-.

·

"UUI,

.t'UUI

(Index l:RPM , 2:FO Pump Rack Bar)

27

Fig.6

Pole Positions of Governor-Propeller System in z-domain

Fig. 6 shows the location of the characteristic roots in the fitted AR model. It is seen that the model has one root in which the value locates on the real axis and nearly on the unit circle. It indicates that the system has l/s pole in the continuous domain ( K.J .Astrom et al. (1984) ). This is the reason why the system is unstable.

3.3

Frequency Response Function of the Governor-Propeller Revolution System

Using the-fitted auto Iegressive model, we obtain some useful tools for analysis of the system ( H.Akaike (1968) ). Let define firstly the cross spectrum between the i-th component and j-th one in the k-dimensional variable X(n ) by pi)(J) and the spectrum matrix by S(J). Then the 5(1) can be calculated by

(2) ,where LM denotes the variance and covariance matrix of E (n) and A(f), the Fourier transform of the autoregressive coefficient, A(m). The frequency response function Gij(f) of the i-th output from the j-th inpllt can be estimated by

(3)

Fig. 7 shows the frequency response function from the position of fuel oil pump rack bar to the rate of propeller revolution, illustrated by Bode plot style in which the solid line denotes the amplitude and the dot line phase shift. : " ::El • ...,., ,« c; .•

It is easily detected that the amplitude is decreasing in toward 4 Hz from lower frequency

has 90 degree's phase lag in zero frequency corresponding to the existence of the element l/s in Laplace domain. However in high frequency domain , the frequency response function associates with vibrations. This might be due to a non linear property like a time delay element in the system .

I t.i

I1

j

I.

!:!

Illlli ~ "

I

domain. This fact clearly shows the low pass characteristics in the main engine. The phase

3.4

,i

=,

I I

" . "

." ."

i I

!i~:··· · '·.L; "'" l: I ) i !. " ,.. ~

Ill!;"

I 11 IIHI,

I I

Frequ~ncy R~'$p~ns~

'I

l!

~i'

"TV

10 Pump Rotk Sor 10 Prope ll l r RPM

I! .I:!' I! lJj:j,~ '-{ I I 'll;! , I Ill!,,' 1\: I ii"

I i III!II' I I! 11111; .' I: ':'1, I I I:!II, !':! Il,!l I I 11,'1,

Funct'i on ' I,:

fro m

,i i I::!!' I I! I'il'

,

I

I

1,1 1'11' ~ I );,!, ! i ' 1111' I} !f", . I !iI·'

' ! !Iii:!:

! II!III

o le

11 !~!

'. 00

10 . 00

I I II!L~

-se

i 1: I ~:"

i

i I I i!

I

I ,,!

I

I ;

I

IHIi' I III!IP! .,.IIll!:

I

!'il"

I! I!!",

I

1CC' .OO

·ne

1111I1! .~

11: '000

-

11 !lIil

""

11 1111 I I!II: I!!! 1 !l'" ." _ _,..;.;"",, :.,'- +I ++r; 1·1,;;;. 11"-++1 l lmml,,_++ I rnl+I,i",i,l'- ++rn";'"I.n'- I-+1'-++nt I'" ." '
C

oc

Fig. 7 Frequency Response Function from FO Pump Rack Bar to Propeller RPM

Impulse Response Function of the Governor-Propeller Revolution System The physical response of the i-th output from the impulsive input of the j-th variable

hi)

can be represented by k

Xi(n)

=L

M

L

hi)(m) Xj(n - m)

+

Ui(n)

(4)

j=l m=l

where we assume that h .. = 0, but the u(n) is generally coloured noise. This model is called by impulse response model.

28

Then, the unbiased estimate of hi) is given by using the fitted auto regressive model. ~

Fig. 8 shows the impulse response function from

Impuls~

Respons. Function rrom FO Pump Rock Bor 10 Propeller RPM

the position of fuel pump rack bar. to fluctiuation of the rate of propeller revolution. Obo

served the shape of this impulse response func-

dl ~O----;:-O' ' - - 0 5

0 .'

I 0

1. 2

2.1

2 S

10'

tion, it can be pointed out that

Fig.8

Impulse Response Function

1. High frequency vibration does not exists in the system due to the impulsive change of the

input in the governor and the response of the rate of propeller revolution resembles the system having the property with the third order poles including l/s. 2. Stationary bias remains in the impulse response of the rate of propeller revolution .

3.5

The Form of Transfer Function

Generally, the transfer function from position of fuel pump rack bar to rate of propeller revolution is given by 1 D(s) -(Me(s) - M/(s)) s

=

where, s is Laplace operator , Me(s) denotes propeller shaft torque by a main engine, M (s), the loading torqu e by sea disturbances and so on.

Horigome et al. (1990) proposed that the transfer function from the input signal to the actuator in the governor to the rate of propeller revolution has a form represented by

K --~ - s (Ts + 1)

D(s)-

(5)

. analysing a simple step response test under proportional control. However infered the results 1. and 2. in the last section, it may be suggested that the transfer function has the form given by,

K D(s)- ---..,-------- S (T}s + 1) (T2S + 1)

4

(6)

Optilnal Control of Marine Engine The main aim of the conventional governor is put on regulating only fluctuation s of th e rate

of propeller revolution from the required one. However, in rough sea, marine engineers might require to furnish with the ability to regulate also propeller torqu e, taking care of torque rich , propeller racing and turbo charger's surging of a main engine . Considering these requirements , we developed two type of main engine governors ( M.lshizuka et

al. (1992) ) . The first one aims at regulating only fl uct uations of the rate of propeller revolu tion from the required value. In the following chapter , this will be called by Type I governor. The second one aims at regulating not only rate of propeller revolution but also propeller shaft torque . This will b e called by Type II governor. The basic concept for such regulator problem using a multi-variate auto regressive model has already been discussed in the paper of the last symposium ( K.Ohtsu et al. (1989) ).

29

In here, we briefly review it. The model for prediction of governor - propeller revolution system is given by M

X(n)

= L a(i)

M

X(n - i)

+L

;=1

b(i) Y(n - i)

+ U(n)

(7)

;=1

, where X (n) denotes the state vector . In the Type I governor, it is composed of a single variable , rate of propeller revolution , whereas in the Type Il, rate of propeller revolu tion and propeller shaft torque. And Y (n) denotes order signal to an actuator in a governor system from the con troller . Using the representation of the model of main engine system, we can designed the optimal control law given by a stationary feedback law

Y(n)

= G Z(n)

(8)

under a quadratic performan ce function ,

E[ p

Jp

= E[

X(n)t Q X(n)

+ Y(n - I)t

R Y(n - 1)

1]

(9)

where G denotes the optimal gains obtained by solving a Riccatti equation, and Z(n) , the appropriate state variable composed of the past and the present value of X(n) ( K.Ohtsu et al. (1989) ). Summarizing the procedure, 1. Observe the records about rate of propeller revolution, propeller shaft torque and ordered

signal to an actuator in a governor system driven by noise as random as possible. 2. Fit a control type of auto regressive model (7) by the minimum AlC estimate method. 3. Calculate the optimal gain by solving a Ricatti equation. 4. Implement a digital white noise simulation using the equation given by

Z(n) { Y(n)*

= =

cl> Z(n - 1)

+r

Y(n - 1)*

+ W(n)

G Z(n)

( 10)

where cl> and r are given in K.Ohtsu et al. (1989). where W (n) denotes white noise with appropriate variance. 5. Repeat from 3. to 5., changing weighting factor in performance function to various values, until a designer obtains a satisfactory result.

5 5.1

Silnulations and Actual Sea Experiments The Procedure of the Actual Experimenj The ship used for the actual experiments was the same ship with the one in Chapter 3 .

The sampling period was fixed on 0.1 sec by taking account of the results of identification. And

30

we gathered the original record which were composed of the rate of propeller revolution, the propeller shaft torque and the ordered signal to the actuator, generated by PI plus white noise control law. The original weighting factor matrix Q and R were determined by the following procedures: 1. As Q , take the diagonal matrix with the diagonal elements defined by the reciprocals of the corresponding diagonal elements of the estimate of the variance-covariance matrix of U (n) which has still remained after fitting a multivariate AR model to the record of observations X(n), 2. As R , take the diagonal matrix with the diagonal elements set equal to the reciprocals of the allowable limits of the variances of the ordered signal to the actuator , Y(n) 3. With the gain calculated by the above weights, perform a simulation using (10) and compute the variances of X(n) , Y(n ). 4 . If the variance of the ordered signal to the actuator is above the allowable limit, increase the value of the weight to the ordered signal to the actuator , R. If, below the allowable limit , decrease it . 5. Repeat the procedure 3.,4. until the satisfactory result in the simulation is obtained . The actual experiments of th e optimal controlling were carried by the following procedure: 1. Switch from the ship's governor to the digital PI controlling for a moment , 2. After propeller revolution is sufficiently settled , switch to the optimal controlling .

Type J governor

5.2 5.2.1

Construction of the system

The Type I governor consists of the following variables.

X (n), the state vector:

the rate of propeller revolution

Y ( n), the control vector:

the ordered signal to the actuator

Based on the original record , a control type of auto regressive model with 6-th order was obtain ed 0 by the MAICE method. ~

5.2.2

Simulation :r:

~ ~

CL

Fig. 9 and Table 3 show the relationship of w th e variances of th e rate of propeller revolu tion u z a and th e ordered signal to the actuator , with 0:: various Q/R ratios in the simulation . Fig. 1 0 a > demonstrates a typical exam pIe of the time history of the simulation . The left half part of the figure shows the optimal controlling with the Q/R ratio= 0. 001/1 . 0, the right one, the time Fig.9 history of the original data. From these figures, the following results were obtained ;

31

a::

~ IJ)

0 . 001

GlE. 0

ON

W

a:: w o a:: o

0

.

(T)

o

.

Simulation 's Results of the Type I Governor by Various Gains with different Q/R Weights

1. As Q/R increases, the variance of the rate of propeller revolution decreases, 2. But Q/R increases too large, the variance of the rate of propeller revolution approaches a constant value. 3. The ordered signal to the actuator is smooth and the movement of it are not so quick as the actuator in the actual system can not follow it.

r~~~~ll{~M\~,KV: I

Fig .lO

5.2.3

'

I

V";-x

(rpm )

0<1 .1) I R(I . I)

AOOOI

0001 I 10

AOOOS

0 ,00:5 I

AOOI AOOS

V.--,c

( ........ noc.t )

13 5190

O.GOIS.

1.0

7 .9187

0019:51

0010 I

1.0

!1i.I2~

0 .04375

O.oso

10

10251

0 , 13902

AOI

0100 I 10

0 .9199

O. IW!

OrCiMI

-

109110

O,:znJ6

D. . far AA · Model

I

-

'1""

G.i.tI Flk

TabJe 3

I

Optimal Gains and Simulation Results of the Type I Governor

Time History of Simulation by Gain with Q/R (0 .01/1.0)

Actual Experiments and its Analysis

Table 4 shows the results of the full-scale experiments at sea. The experiments in the table were successively h..._ _ _ . T y p e Type I . eo.m.o.. , 7 05. 1 5 0 703 . 3 I 2 implemented. The time length of each ex......... 6 9 6, 6 2 5 11 9 7. 250 periment has about 5 or 6 minutes. The ex7 00. • 36 100 . 9 7 • 3 , 302 I, 22 5 -wa periments by the conventional ship's governor I I 2 r a c 26, 6 I 2 ......... 2 " was continued soon after the optimal governor's 2 . , .81 ......... 2 5 , 050 26 , 01 9 25, 101 control was finished. The wind scale was the I 51 0, o 1 3 0 -wa 2nd class in Beaufort scale and the ship reTabJe 4 Statistics on the Series Experiments ceived it from the port beam direction during of the Type I governor the experiments. The table shows the following results :

... ........

~eo..mo.

-

11.

1. The variance of the fluctuations of the rate of propeller revolution in the ' optimal governor

are smaller than that in the conventional one except for in the case of the optimal one with the weakest gain. 2. The variance of the position of fuel oil rack bar in the optimal governor is also very smaller than that in the case of the conventional one . Fig.11 shows a typical of the time histories of the rate of propeller revolution and the position of

fuel oil rack in the optimal governor. And Fig. 12 shows those in the conventional one performed soon after the first one. We can observe that the long period vibration of t~e rate of propeller revolution diminishes in the experiments by the optimal governor. Fig .13 shows the power spectra of the rate of propeller revolution and the position of fuel oil pump rack bar in the case of the optimal one with Q/H gain=O.OOl/l(A001 gain) and Fig. 14 the power spectra in the case of the conventional governor.

32

o

0

A1 ;~~.-----------.,~

+~

' .co! . - - - - - - - - - - - - - - - - - : - : - : - - : - : - : : - - - - '

lo o

to 0

LO. t

" .0

ra

.0 . 0

'"mp

10 . 0

10 0

lII,et"

'JO 0

1e ::O

to 0

. 1); I)

" I itl on

." Fig.12

Fig.II

Time History of the Actual Experiment of the Type I Governor by Gain with Q/R (0.01/1.0)

Time History of the Actual Experiment of the Conventional Governor

~T""-----"'" o

m

(1)0

o (1)0

O~

00 :E ::J 0::

...

00

::EO :::J

:J

1-0

I-

:E

0::

0::

UN w

U

WO

U

WO

0

n. N

Q.

(/)0

Q.

Ul

N

(/)0

o

"I

~-'------

~ ~

-'-

,,-'-------'

_ _ _ _---J

0 .00 1 .0) l .oo 1 .00 " .00 • . 00

H2

Fig.13

5.3

~

H2

4-------' I co l co :1 . 00 • . 00 • • m

, 0 .00

• 0 . 00 1.00 l . aD , 00 • . 00 • . 00

HZ

H2

Power Spectrum of the Type I Governor

Fig .14

Power Spectrum of the Conventional Governor

Type 11 governor

5.3.1

Construction of the system

The Type II governor consists of the following variables

X {n), the state vector:

the rate of propeller revolution and the propeller torqu e.

Y (n), the control vector

the ordered signal to the actuator.

Based on the original record , a control type of auto regressive model with 9-th order was obtained by the MAICE method.

"""

....... ..a

S 10

oS

10 001 1 30 0

2 ?OH

o 004}04J7

00&09 15

S09

1 010007 / ) 00

2.<4 129

o O()41.S90

o 089H4

S08

12 100( 7/ ) 00

12192

0(04)77 1

O_

S 0 7

1•

2...,

00043946

o 10)050

15 6707

000>6299

o 45032.5

v...n Fur

5.3.2

Simulation

Table 5 shows the results of the simulations. The table indicates that the optimal gover[lor designed in here has the ability to suppress not only the fluctuations of the rate of propeller revolution but also those of propeller ;haft torque .

33

V W'\&ftO!(rpn)

V.,..or (

~.,

0<1 . I)IQ(2 .2)11«I . I)

1 0007 1 10 0

)

v~

( or1kn:cI ,..a )

()r"c..-lO . .

r", AR ·Mockl

Table 5

-

Optimal Gains and Simulation Rfsults of the Type 11 Governor

5.3.3

Actual Experiments and its Analysis ~=---------~----------r----------'

Table 6 shows the results of the actual experiments by the gains in the last table. The wind force was the 2nd class in Beaufort scale and the ship navigated in oblique sea condition . Fig.15 demonstrates a typical of the time history of the rate of propeller revolution, the propeller shaft torque aILd the position of fuel oil rack in controlling by the optimal governor with the gain 508 in Table 5 whereas Fig. 1 6, those by the conventional governor in the ship.

Table 6 Statistics on the Series Experiments of the Type II Governor

The tables and figures show that:

1. The variance of the rate of propeller revolution in the optimal governor is larger than that of the conventional one, 2. But the variance of propeller torque in the optimal governor reduces to 1/2 of the one in the conventional one, 3. The variance of necessary motions of the posItIOn of fuel oil pump rack in the optimal governor to realize the above results are smaller than those in the conventional one. 1'. OIlt'IIt'1

flf' M

o

· ~ rV\~~J~W'v~~"t\'W :0 ,)

,: p~~~~~.+~

0

,0 0

2'0 0

310 0

..0 ()

!oO 0

T.rque

T. r Cl u e

toe "

'1tJ 0

100 "

~ C

.. , , ()(\

(>

_ 1 _ _ _ _ _ __ _ _ _ _ _ _ _ _ _

Fig.l5

Time History of the Actual Experiment of the Type II Governor by Gain with Q/R (1.2/0 .007/30.0)

Fig.16

Time History of the Actual Experiment of the Conventional Governor

In particular, the last conclusion is important in meaning that further movement of the position of fuel pump rack bar might be utilized for reducing fluctuations of the rate of propeller revolution. Fig.17 shows the power spectra of three variables in controlling by the optimal governor and Fig.1B, those by the conventional governor. In particular, we can see that the power spectrum of the propeller torque in controlling by the optimal governor reduces in low frequency domain, comparing with the one by the conventional one.

34

I'rop"',r

Ill' ....

r

TorQ""

0,--_ _ _ _-,

6,-------,

c

o

Cl

Cl

(I)

o

00

.:;

5~ a:: ~

a:: >-

Ion

0

[)j

CL

o

'?

'? 0-'---_ _ _ _---'

o -'--_ _ _ _--' 0 . 00 I 00

1. 00 Z . OO lOO 4 . 00 ' . 00

HZ

Proptr !! er

.. 0 , I I

w '

lJlo

zoo,

o

00 4 . CXi ' .00

00

1. 00 %. CI:I J

(XI

4 00 ,

a::

HZ

HZ

Fig.17

Ft, c Ir.

U N

U W

-'---------'

p

5'

...

000

u m

o o

o

~

I'

D

Power Spectrum of the Type II Governor

RP,.,

Tor

Q

u

r 0

t

.. u m p

Ft

I

C Ir.

,.

0 , I t Ion

0-,-_ _ _ _--,

6-,--------,

o

o

-

~ : 1·

Cl

o

oc

>-

0

UN

~;-'j------

0 . 00 1. 00 %. 00 3 .00 4 . OC ' .00

H2

Fig.IS

6

H2

hZ

Power Spectrum of the Conventional Governor

Proposition of a New Unified Ship's Governor SystelTI In this chapter, basing on the above results, we propose an entirely new governor system

considering ship's motions.

As described in the last paper, there were three causes for the

fluctuations ( K.Ohtsu (1989) ). The first one is due to disturbance induced in a main engine itself. This disturbance brings out generally high frequency fluctuations but it is unknown. The second one is due to vertical motions of propeller's position which is mainly ind uced by ship's heave and pitch motions . This disturbance brings out lower frequency fluctuations and is more dominate than the first one. These ship 's motions are measurable and predictable if there are some measurement instruments and the appropriate model is obtained. Especially in rough sea, strong ship's vertical motion induces the excess of propeller torque shaft (torque

rich) , propell er racing and turbo charger's surging. The conventional governor does not always provide the ability to cope with such a strong disturbance. The last one is due to rudder motion. This motion also changes in the same frequency domain with the one in the second one . The stream field around the rudder always changes , asso ciating with rudder motion. This motion may be fundamentally known and predictable, if we can design a unified system connecting a governor system with an autopilot system . The governor system which was developed in the last chapter , is rather designed so as to regulat e the fluctuations of propeller revolution and/or propeller shaft torque in high frequency domain .

35

However, our new governor system must also aim at regulating the fluctuations of them in low frequency domain induced by ship's motions and rudder motion. The possibility to realize such a system is shown in Fig. 19. This system is constructed by double feedback loops. The below loop sends the optimal control signal to an actuator of a governor in order to regulate fl uctuations of rate of propeller revolution and/or propeller shaft torque.

Dlsturoance:=' ~r

____~~Smp~--~~~

~Dl

Fig.19

Schematic Diagram of New Governor System

On the other hand , the above loop generates the optimal reference signal of the rate of propeller revolution and/or propeller torque to cope with the actual fluctuations of them in low frequency, induced by ship's motions and rudder motion. Thus, we reaches a unified control taking account of the related ship's motions which are observed by appropriate sensors and the rudder motion which are obtained through an autopilot system.

7

Conclusions

In the first half part of this paper, the authors tried to identify a statistical auto regressive model to the propeller - governor system, using full scale record by a small training ship. And an impulse response function and a frequency response function were obtained through the fitted model. Nextly, a 3rd order 's transfer function including l/s for representing the system was proposed by analogy from the shapes of their functions . In the latter half chapters,the authors discussed two governor systems for regulating fluctuations of rate of propeller revolution, propeller torque. The first one aimed at regulating fluctuations of the rate of propeller revolution. And the authors implemented the full scall experiments using the training ship and succeeded to reduce the variance of the rate of propeller revolution to about 1/4 at the maximum by about half of the governor's motion, comparing with those in the conventional one. The second one aimed at regulating fluctuations of not only rate of propeller revolution but also propeller shaft torque. This system achieved in the full scale experiments to reduce fluctuations of the propeller torque to about 1/2 at the maximum by smaller motions of governor than those in the conventional one. However, in this case , fluctuations of the rate of propeller revolution is larger than the one in the conventional one. Lastly, the authors proposed an entirely new governor system based on the results obtain ed in this paper.

ACKNOWLEDGEMENTS The authors express their sincere thanks to their colleagues , Dr .and Prof.M .Horigome, Chief Eng .T.Hotta and Mr.M.Hara in Tokyo University of Mercantile Marine. They also devote their thanks to Dr.and ProL G.Kitagawa in the Institute of Mathematical Statistics and Mr.I.Ueda in NYK Line Co. Ltd ..

36

REFERENCES 1. D.E.Browns (1971). The Dynamic Trnasfer Characteristics of Reciprocating Engines. Pro-

ceedings of Institute of Mechanical Engineer, Vol.185 pp.185-201. 2 . K.J.Astrom and B.Wittenmark (1984). Computer Controlled Systems: Theory and Design.

Pr en tice-H all, Englewo od Cliifs,N J. 3. H.Akaike (1968). On the use of a liner model for the identification of feedback systems.

Annal.Inst.Statis.Math., Vol. 20. 4 . H.Akaike (1974). A New look at the statistical model identification. IEEE, Trans., AC-19. 5. K.Ohtsu, M.lshizuka, G.Kitagawa, T.Hotta and M.Horigome (1989).

An optimal marine

engine control using multi-variated auto-regressive model. IFAC Workshop, CAMS '89,

Denmark. 6. M.lshizuka, K.Ohtsu, T.Hotta and M.Horigome (1991). Statistical Identification and Optimal Control of Marine Engine System ( Part 1). Journal of The Society of Navel Architects of Japan. Vol. 170. 7. M.lshizuka, K.Ohtsu, T.Hotta and M.Horigome (1992). Statistical Identification and Optimal Control of Marine Engine System ( Part 2). Journal of The Society of Navel Architects of Japan . Vol .171. 8. M. Horigome, M. Hara, T.Hotta and K.Ohtsu (1990). Computer control of main diesel engine speed for merchant ships. Proceed. of ISME Kobe 90', Vol. 2.

37