THE TRANSIENT

PERIODIC"; POLYTECHSIC"; SER. TRA:\SP. EXG. VOL. 25, SO. 1-2, PP. 27-44 (1997)

ON THE TRANSIENT BEHAVIOUR OF CONTROLLED PROPULSION PLANTS

Gibor PAP

Department of Aircraft and Ships Technical "Cniversity of Budapest

H-1.521 Budapest, Hungary Received: 15 Apr. 1996

Abstract

This paper makes known the results of the investigations carried out into the transient behaviour of closed control loops of a ship propulsion plant. Transient characteristics of various speed governors as well as their applicability are compared. Comparison is made on the basis of transient characteristics gained by computer simulation, and represented in figures.

J{ eywords: transient characteristics. speed gm'ernors, propulsion plant.

1. Introduction

A series of computer simulations has been carried out at our department, in order to gain information on the transient behaviour of a ship's propulsion plant in waves.

Closed control loops, containing the following speed governors, have been com pared:

- a direct acting mechanical one,

- a PI-type hydraulic one, equipped with a compensating vanishing feed- back.

- two versions of a two-pulse electronic speed governor, co-operating with a constant-pressure fuel injection system.

The following characteristics as well as decisive phenomena of the closed control loops have been calculated and compared: momentary speed variation, time constants, frequency response, stability, optimum setting of com pensation, infl uence of the fuel injection system, the effect on the system dynamics of the deteriorating condi1;ions of the fuel pumps.

2. Models of the System Components 2.1. Basic A itributes

The applied mathematical models of the engine and of the speed governors are linearized and quasi-stationary. The matching point. i. e. the basis of linearization is defined by 67% fuelling and 90% engine speed. with reference to the nomina! values. In order to gain better-conditioned models. relative variables are applied, instead of physical characteristics. Having been di- vided by the matching point value, the change, referring to the matching point. of a variable yields its relative value.

The investigations have been carried out by means of state-space mod- e!s written in MATLAB supported by its own 'Control Tooibox'.

The excitation function has been considered sinusoidal. deterministic function of two variables. The wave pattern has been presumed to be regu- lar. The ship's advancing has been considered perpendicular to the crests.

In most cases the angular frequency and the relative amplitude of the exci- tation have been :..vg = 1.08 [rad/s] and Qe 0.325, respectively.

In the course of our investigations friction forces on the moving parts of the speed governors as \vell as that of the fuel injection system have been 2.ssumed to be proportional to the relative velocity of the moving parts, applying a \vide range of {j coefficient of proportionality. This approximation is based upon the vibrations of the lubricated moving parts.

The model accuracy in steady state condition. on the base of the test bench diagrams of the engine, proved to be sufficient for system dynamics application, while its correct transient properties have been justified hy sea trials.

2.2. ,vlodels of a Supercharged Jiarine Diesel Engine

A four-stroke, medium-speed, supercharged marine diesel engine 6:\VD48A- 2U type of SKL has been chosen, as the physical basis of the mathematical model.

Two different state-space models of the engine. for different applica- tions, have been set up. applying two different methods [1]. The applied setting-up methods of the state-space models are founded on the transfer function form of the mathematical model of a supercharged diesel engine developed by KRUTOV

[2].

According to these figures, ^Ii relative displacement of the fuel rack and Qe

relative load are the input signals, while :y relative speed of the engine is the output signal of the model. Most of the system components are of first-order proportional type.

A

a

s mbient

ir ^tps;

Compressor / / Turbine

w ~

j

L

I

Intake Exhaust

manifold manifold

if

,.

'=== e

~

J:

r=== iTIOV\:,! ^{/ /}

F=

1" ^{l( '\} lp

,---,

I Speed-

I 1=

aovernor I

I ~

L _ _ _ _ _ _ ..J

!

29

Exhaust gas

- - - -^{- - ,} I

Rropeller i

I

- - - -^_...J

Fig. 1. Layout of the model of a supercharged diesel engine

2.3. Model of a Direct-acting PTE-type J1echanical Speed Governor The model is represented by its partial transfer functions connected in par- ailel

_ . ' f , 1 1

} n~ \p)

= - - = ----::---:::-

~ dg(p) Tjp2

+

+

1"0

9

(1)

(2) of the 0:g relative tensioning of the fty\';eight springs considered the second input signal. The output signal of the model is r; relative displacement of

4.

~'1

Lj!-

0=_'_

5 1;;jP+k_S ^{f, -} k;

5.

~~ ffi

~~

V.t' -

I

5 -r.p+k t k.

5J 5

I

I

6. 10.

§J.

.~ p _ Gp ~= yP = ^dIl.

[ Vs - T.prk ^.:'; k .. i

5] S

@~

1==1 YL - kL ~ Ye - leP+ke

8. 0:: 3.

t

ex El e 13. <P

r=\

v=--

⁼

⁼

~ 12. 2.

yk _ _ , _

- : ' j ! - 1 e - TeP-rk e

"" ^~

Fig. 2. Block diagram of the model of a supercharged diesel engine

the flyweight sleeve.

Both transfer functions (1) and (2) are of second-order proportional type. The state-space model of the governor has been set up on the ba- sis of the above transfer function representation, by means of converting commands in ?vlATLAB.

2.4- .'vJodel of a PI-type Hydraulic Speed Governor

This model is based upon the vYOOD\YARD CG proportional plus integral type hydraulic universal speed governor equipped \vith a vanishing type compensating feedback.

OX THE TRAXSIE,,·T BEHAVIOt:R

IPROPOR-TIONAL' 'I

, FEED-BACK

, i

rcr;~ ^_____ ~ ^{, : I}

^{I 1}

. SENSING UNlT .

L-________ .J 1

! I

31

-

a:g~: ¹⁰⁹

(P~ rfT!~O: ~I

x~!s~~~~~~gLrlF;~~

*~ I

! . '

I .

i !

I

_I

I

, ~ i~Y I t ^~Il !----·----i t

-. : I y,~)p) ^{i i I}

. I

L __ ._._. ___ .J I

i

L!.EE~-8~~ __

j

Fig. 3. Block diagram of a PI-type hydraulic uni\'ersal speed governor

~ 0.14

.§

0.02

o

:2

-0.02 Omega ;.~, -0.04 1.08 "

-0.25 -0.20 Re 1Wz.

l-theta

=

= ³⁰

-0.05

Fig. 4. :-\yquist diagram of the controlled variable

o

lA

U _Cl) 0.20

Alfa=-1 a. Cl) _f\

Ul

I \

0'1 0.18

c _B ^\

OJ \

OJ \

...

...

LL \

0.14 1 \ :2

\

0.12

0.10

0.08

0.06

0.04 1-theta = 20

2-theta= 30 0.02

0

0

8

Time1s Fig. 5. Step response of the controlled variable

According to its layout in transfer function representation (Fig. 3), Y and a~ partial relative tensioning of the flyweight springs are the input signals, \\·hile ,\ relative displacement of the servo-piston is the output signal of the model.

The transfer functions and the input-output signals of the subsystems in Fig. 3 are as follows:

- The integral type transfer function related to X relative displacement of the pilot valve. as the input signal of the hydraulic servo-amplifier unit. is

yx (.

;ervo p) = T .~ servo P

1 (3)

(\) 0.8

>

(\) (\)

"iii .c (!;

...

~ 0.6

"0 QJ

;:!

0 . .4

0.3

0.2

0.1

OS THE TRAi\SIE:''T BEHAVIOUR

Alfa=-1

1-theta =20 2 -theta

=

F · _Ig. 6 S _. tep response ^{Ol c} 1] Time,s

The output signal of the subsystem is A, the very output of the model.

The second-order proportional type partial transfer functions, nected in parallel. of the sensing unit subsystem are

ya ( )

gov P T2. _{g P} 2 -l.. _I 'T: _d p

+

of G g as one of the input signals, and y'P ( ) = 1

gov P Tjp2

+

+

33

con-

(4)

(5) of y considered the second input signal. The output signal of the subsystem is

r/

a.

U"I 1- FI rel. spe~d 3-ETA rel. displace-

:0 0.20 theta

=

=

~

o ^e-

;:: theta

=

=

w 0.10 \

"Cl

c 0.05

o o

'0 <l.!

<l.!

~-0.05

~-0.10

....

<l.!

....; -0.15

<l.!

'-

G:

\

\

3 \4

\

\

- 0.25 0~---+---~---:~----'!l~--~10

Fig. 7. Time history of '-P iind T) Time,s

The proportional type transfer func~ion of the inner proportional feed- back is

Yfb(p) = .

e

A is the input signaL and (}~ partial relati;;;e tensioning of the fl~'\\'eight springs is the inner feedback signaL as the output one of the subsystem.

The first-order derivative lype transfer function of the compensating vanishing feedback

; .. TPJ'

}vj(p) = lL;3PI--.-'---

l+TPJ'p ⁽

"7)

I }

has A input signal and Ti" partial relative displacement of the flyweight sleeve.

where Tp! andu are the time constant and the rate of the compensation, respectively.

The state-space model of the governor has been developed by simple conversion in YL\TLAB. Detailed information on the models of the speed governors is available in [3J, [4J.

2.5 .. Uodels of a Two-pulse Bing-bang Type Electronic Speed GOl'ernor The operating method of this governor is supposed to be similar to that of the mechanical speed governors, operating on two-stroke, low-speed marine

ON THE TRA!\SIE!';T BEHAVIOL·R

"0 0.02 , . . . - - - ,

<l!

<l!

0..

V1

.ci L-

.,... :J

~ Lr..

"0 C o

o

ui -0.02

<l! V1

L-e.

Vi o

.c:

~

o

0:::

-0.06

-0.08

\

\

\

\

\

\

\ '\

~

Alfo =-1 Theta

=

1 - FlS 2- RO

-0.1 00'---1

2- - - - 1 .

4- - - . . l . .

6

---is

Time,s Fig. 8. Step response of 'Ps and p

35

diesel engines. Thus, value of the controlled propeller speed is maintained by the governor between upper and lower limits, applying successive cut-out of injection or successive reduction in amount of the injected fuel.

Two models of this kind were developed, both of them have been writ- ten in form of :VI-files in MATLAB, by using logical variables. The only difference between these models refers to the rate of fuelling during the cut-out periods, one of them cuts out injection in these periods completely.

Speed governors of this type have been supposed to be co-operating

0.015r---

I

_0.010

.ri '- ::::;

...

~

if)

r;: 0.005

"0

c

o

Ul Ul <I>

l -

Q.

...

lfl o

.0 o 7ii

:; -0.005 cc

I

Theta

=

- 0.01 0::-

o 20

Time,s Fig. 9. Time history of y sand p

with electronically controlled constant-pressure injection systems [5]. Time lag represented by the applied electro-hydraulic injector valves has been neglected.

3. Results of the Investigations

3.1. Closed Control Loop, Comprising a Direct-acting PD3-type }vlechanica{ Speed Governor

Figs

4-7

the effect of the changing condition of the fuel injection system. on

OS THE TR.:'.XSJE.\;Y BEH.:"i/lOC"R

~

0.3 ,---,

QJ 1 - TPI = 0.1 S Alfa=-1

Q.

U1 2-TPI=0.2s u=0.5

01 3 - T PI

=

C QJ

~

0.2

! L

0.1

1/

V

-0.1

-02 ~

I

-0.30~---~---2~---~~3 Tlme1s Fig. 10. Step responses at various pairs of u and TPJ

37

the .\'yquist gain-phase characteristics of the closed control loop (Fig. 4).

- the step response ofy controlled variable at ^0:= = 1 sudden load rejection (Fig. 5).

the step response of TJ relative displacement of the fly\\-eight sleeve at o.e

=

the time history of 'P and TJ at sinusoidal excitation ofu.:_g

=

angular frequency (Fig. 7).

a3

IJ'I 0\

C OJ Qj

l...

.-.

LL

0.10

Alfa:: -1

U :: 1.5

0.08

1- TPI :: 0.2 s 2 - TPl :: 0.5 s 3 - T PI :: 1.0 s 0.06

0.04

0.02

o

-0.02

-0.04~---~---~---~

o

Time,s Fig. 11. Step responses at various pairs of u and TpI

Figs 8 and 9 comprise the step response and the time history, at

Wg = 1.08 [rad/s] sinusoidal excitation, of p relative boost pressure and 'Ps relative speed of the supercharger.

0."'-: THE TR,,!,.\"Sn::-':T BEHA VIOCR 39

~ 0.03 , - - - .

~ TPI=1.0s

Vl 1-u=0.5s

01 2-u=1.0s

~ 3-u

=

~ 0.02

0.01

o

- 0.01

-0 ·02

- 0 ,03

o

Time,s Fig. 12. Time hislOry of;; at various pairs of u and T PI

.3.2. Closed Control Loop, Comprising a PI-type Hydraulic Speed Gocernor Figs 10-12 represent the influence of the varying u, TPJ pairs on the step- response (Figs 10 and 11) as well as on the time history at :...Jg = 1.08 [rad/s]

sinusoidal excitation, of controlled variable c.p(Fig. 12).

Fig. 13 shows the time history of A relative displacement of the servo- piston, at :':':g = 1.08 [rad/s] sinusClidal excitation.

a. \Il

"0 C 0

...

. is.. \Il I 0 >

L..

(!)

\Il

0:;

L..

«

m

«

0.4

0.3

0.2

0.1

0

-0.1

-0.2

-0.3

I

t

f

=

I

=

=

-0.40~--~---~~---~10 Time,s Fig. 13. Time history of ,\ at various pairs of u and TPJ

In Fig. 10 curves 2 and 3 relate to stable settings, while curve 1 to an instable setting of the compensating system. Optimal compensation pro- vides quick response of the system. \\'ithout hunting or surging of the prime mover. In Fig. 11 curve 1 corresponds to an undercompensated, curve 3 to an overcompensated, \\'hile curve 2 to the optimally compensated settings of the system, whereas all these settings yield stable operation. In Fig. 12 on the curve 1. likewise on the curve 1 in Fig. 13. small wavelets have been su- perposed to the sine-shaped output signal. This phenomenon demonstrates hunting of the prime mover due to an undercompensated setting of TPJ and ^IL.

u en

>-

<lJ

<lJ '-01

<lJ

u

<lJ

Q, c

Ci

<lJ U1

..c: Ci 0...

OX THE: TR.-\.\;SJE.'\·T BEHAi/IOL:R 41

---

-50

-100 1- u = 1.0 and TPl = 0.4 ,stable -150 2-u=0.5andTPI=0.1in'stable

-2001~----~I,,----LI.---~I---LI ____ ~I __ ----~I , -__ ~ 10~3 ^{10-2 10-1 1 10 102 103 104}

0 -100 -200 -300 -400 -500 -600

10-³

Phase margin:

1-(+30) degree 2-(-30) degree

Omega I rad . 51 1- u= 1.0 and TPI=0.4 stable 2\- u = 0.5 and TPI = 0.1 instable

1

10

Omega I rad' 5- 1

Fig. J 4· Bode diagram of the open control loop

Fig. L{ contains the Bode logarithmic plots of the open control loop.

These plots have b~en calculated at a stable. as \\'ell as at an instable pair of u and TPJ variables of the compensating \'anishing feed back.

Figs 10-14 ha\'e been plotted assuming new condition of the fuel in- jection system, such as the fuel rack. linkage and the constant-stroke. edge- controlled fuel pumps.

3.3. Closed Control Loop. Comprising a TIL'o-pulse Bing-bang Type Electronic Speed Gm:er7lor

Figs 15 and 16 reprrosent the time history of:y controlled variable and that of t1 relative displacement of the fuel rack. at;"';g 1.08 [rad/s] sinusoidal excitation. Pre-set lower t1 limit has been t1

=

=

-0,:32.5 in Fig. 16,

Comparing the time history of the :y controlled variable in Fig. 15 to that in Fig. 16. the latter shows better control performance. By applying smaller gap between the upper and lower fuelling limits result fluctuation at lower frequenc~' of the :y relative engine speed.

a; - iJ _l...

O.3r---~

0

-

-0 .5

-

n ^{i! i ! i}

0.5 1.0 1.5 2.0 3.5 4.5

15. Time history of ;: and ^1(. Clnr,ivlnG K

=

4. Concluding Remarks

On the basis of our im'estigations the following conclusions can be clra\,'n:

Applying a direct-acting rnechanical speed governor. amplitude ratio of cp controiled I'ariable. at regular sinusoidal v;aves as all excitation.

is basically determined by the fuel injection system. Assuming dete- riorated conditions of the fuel rack. lin and of the fuel pumps.

~'P damping factor of the second-order system. representing the speed gOl'ernoL is far from being optimum. even at robust dimensions of the governoL Application of constant-stroke, edge-controiled fuel pumps results considerable drawbacks, constant-pressure fuel illjection sys- tems are favourable in this regard. However, on the other hand, this governor is less influenced by the varying excitation frequency (Figs

.f··

7) .

Regarding direct-acting mechanical speed governors. at a sudden change in load, e.g. due to lost propeller, controlled variable probably cannot be maintained below 120o/c of its nominal value prescribed as ^Cl limit by the rules of registers, thus application of an independent overspeed protection is necessary. Applying a governor of this type, influence of the speed and torque fluctuations due to waves, concerning noise and vibration, cannot be disregarded (Figs 5 and 6).

~13

NO 1.0 ,-,.-,----",.---...---,rr.."-,-"-,.---,,---,,..-,.,,rT"l I !

~

I

! ⁱ

~ 0.5

<0

~

0

01

~-0.5

.

,

2 6

Time IS

!

~-02~ _r-

IUI~~~L

-O.40'~--....L---,L----~---!__---=---::1

2 3 4 5 6

Fig. 16. Time nistory of y and K. applying le = -0.:32.3 limit Time-Is Transient behaviour and stability of a closed control bop. containing a PI-type h~'draulic speed governor. is highly influenced by the excita- tion frequenc~·. Optimum setting of u and ^Tp! is basically frequenc~'

dependent. The momentary speed variation. the length of the tran- sient process. surging and stability are sharply influellced bv the pair of u and TpI (Figs 10-16).

- T\\'o-pulse speed governors are less sensiti',e to the excitation fre-

quenc~' and to the deteriorated conditions of ^t he fuelling system. Ho',\'- ever, the scope of application for the two-pulse speed governors is lim- ited b~' the torsional vibration of the shafting. Their application in propulsion plants. containing reverse-reduction gears or flexible cou- plings, is conditional (Figs 15 and 16).

Surging in the angular \'elocity of the turbo-supercharger impeller proved to be negligible in this engine category, applying e\'en the less favourable t:vpe of the investigated speed governors at a sudden load change (Figs 8 and 9).

References

[1] HARA::\GOZO, E. PAP, G. (1995): Linearized .\lode! in '\IATLAB of a Supercharged Diese! Engine. Jdrmuvek. Epltoipari es .vfezogazdasdgi Gepek, :\0. 10 pp. 349-354 (in Hungarian).

[2J KRLTOV. V. I. (1987): Automatic Control of Internal Combustion Engines . .\1ir Pub- lisher . .\loscow.

[3] PAP. G. (1995): Investigations into the Transient Process in Waves of a :,larine Propul- sion Plant Equipped with Different Kinds of Speed Governors. Dissertation at the Technical 17niversity of Budapest (in Hungarian).

[4J PAP. G.: Investigations into the Transient Process in Wan,s of a '\larine Propul- sion Plant Equipped with Different Einds of Speed Governors (Proc. of the 5th .\filii

Conference on Vehicle System Dynamics. Budapest. 1996).

[5J PARKER, S. (19S·±): Development Driven by Emissions L~gis!ation. The .Hotor Ship.

:\0.3, pp. 25-28.