process control of polymer extrusion

8/12/2019 Process Control of Polymer Extrusion

1/8

Process Control

of

Polymer Extrusion.

Part I: Feedback Control

BING YANG and L. JAMES LEE*

Department of Chemical Engineering

The Ohio State Uniuersity

Columbus Ohio

On-line computer control of extrudate thickness was

carried out using a

2 92

inch single screw plasticating

extruder. Predried poly methy1 methacrylate) PMMA) was

extruded through a

slit

die. Two feedback control methods,

a

conventional

PI

controller and

a

Smith predictor dead

time compensation, were tried for both se t point changes

i.e., extrudate thickness changes) and load changes i.e.,

screw speed changes]. Results showed

that

both the

PI

feedback control and the Smith predictor were satisfactory

for long term set point changes but not for load changes.

Since

the

Smith predictor may compensate the process

dead time,

it

would be useful for regulating short term set

point changes such a s barrel temperature settings.

INTRODUCTION

olymer extrusion

is

a complicated process.

P typical extrusion line generally includes

a n extruder,

a

die,

a

cooling line, and

a

take-up

device. The feedstock en ters the extruder in the

solid form. The extruder continuously conveys,

melts, an d pumps the polymer to the die. The

success of polymer extrusion relies upon the

production

of a

high quality product

at a

high

output rate, Recently the increasing cost of raw

materials, which ar e based upon crude oil and

natural gas, provides another stimulus for de-

veloping better technology in the extrusion

process. In addition to modifying the equip-

ment, applying modern control methods to the

extrusion line

is

a useful way of improving the

production. This approach

is

becoming more

attractive in recent years because the rapid

growth of digital computers, especially the

stand-alone type of mini- or micro-computers,

has enabled industry to apply more sophisti-

cated control methods to extrusion lines with a

reasonable cost.

The primary goal of extrusion control

is

to

maintain a quality production

at a

high output

rate. The term quality s determined by several

measurable quantities which are required to

match th e specifications of the product. These

measurable quantitie s generally fall into three

categories. One of these , which

is

aesthetic in

nature,

is

the visual appearance such

as

rough-

ness, gloss, haze, waviness , and s treaking of

To

whom

this correspondence should be addressed.

the product. The second one

is

functional in

that the products must meet certain physical,

chemical, or performance specifications. The

third one, which

is

th e goal of control in this

work, can be classified as dimension accuracy,

referring to

a

close dimensional tolerance.

In addition to an inappropriate die design, the

main cause of poor dimension accuracy of th e

extruded product is fluctuations in the extru-

sion line, which may be the start-up transient

disturbance or steady state disturbances. For

many extrusion applications, start-up

is

not

a

major problem since the extrusion line is mostly

under the steady state operation. However, for

some processes such as wire coating, rubber

extrusion, and tub e extrusion, they ar e subject

to frequent start-ups and shut-downs. The tran-

sient disturbances occurred in these periods

may produce

a

substantial amount

of

out-of-

spec products.

Even under steady stat e operations there are

still disturbances in the extrusion line. Accord-

ing to Tadmor and Klein ( 1 ) . disturbances at

steady

state

operation can be divided into four

categories: i.e., disturbances at the same fre-

quency

as

th at of screw rotation; disturbances

at intermediate frequencies 0.5 to 10 cycles/

min) caused by periodic breaking up of the solid

bed in the melting region or occasional starve

feeding in the solid conveying region; disturb-

ances at low frequencies caused by conditions

external to the extruder such

as

cycling in the

heater power controllers or variations in feed

polymer quality; and random disturbances.

There are

a

few studies on extrusion control.

POLYMER ENGINEERING AND SCIENCE, MID-FEBRUARY,

1986, VOI. 26, NO.

3

197


2/8

B.

Yang and L . Jame s Lee

Most of them are designated to regulate rela-

tively long-term drifts using PID type of feed-

back control. Wright 2) used a microprocessor

interfaced with an extruder to regulate the

screw speed and the barrel temperature pro-

files.

Dormeier

( 3 )

used a digital PID controller to

regulate the barrel temperature for

a

three heat-

ing zone extruder. The controller was tuned off-

line. The result was claimed better than the

conventional analog controller. However,

it

could not handle the temperature variations

caused by the surging problem.

Frigerle

4)

egulated the back pressure in the

extruder to control the melt temperature.

A

var-

iation on Dahlins dead-time compensation al-

gorithm was used. The system was able to pro-

vide

a

reasonable melt temperature control for

both set point changes and a disturbance con-

sisting of a change in the barrel temperature.

Rastogi 5)and Frederickson (6 )described a

general industrial system used to control the

extrudate thickness and the throughput for ex-

truders with flat dies. The control program writ-

ten in

a

microcomputer could control and retune

control parameters based on a process model

and the operating level. The control algorithm

Rastogi used was the Dahlins algorithm.

Ras-

togi also presented experimental data which

showed a 60 to

70

percent reduction in the

thickness variation under

a

closed-loop control.

Rudd

7)

presented ano ther industrial control

system on sheet extrusion. The method he pro-

posed was called automatic profile control APC)

which used

a

thermally controlled die bolt to

adjust the flexible die lip. The start-up transi-

tion was significantly reduced by using this

controller; however, details of t he control sys-

tem were not shown in the article.

Lee, et

al. 8),

eveloped

a

two-dimensional

control method of producing

a

profile extrudate

having controlled shape and size. On-line ad-

justments were made to size and shape devia-

tions by varying the line speed of extrusion an d

the temperature conditions in the extruder. The

control algorithm used in this method was

a

proportional type feedback controller with mul-

tiple gains , which was sufficient for regulating

long-term dimension drifts but was not able to

control any high frequency disturbances.

Costin, et

al. 9),

carried out

a

control study

on a

38

mm extruder. They tried a PI controller

and a PI controller with a n on-line filter.

A

self-

tuning on line controller with a time series

model was also used. The performance of the

self-tuning regulator was found not satisfac-

tory.

Most of these studies are aimed

at

regulating

relatively long-term drifts in t he extrusion line,

while the control of high-frequency disturb-

ances is much underdeveloped. Furthermore,

among the control studies, one can seldom find

a

detailed explanation

of the

control algorithm

and the experimental design usually varies

from one work to another work, which often

leads to

a

confusing conclusion when compar-

ing different studies. This work

is a)

o propose

several feedback and feedfonvard control meth-

ods for the control

of

long term

and

short term

disturbances in the extrusion line, and b) to

evaluate these methods using various load

changes on

a

single screw plasticating extruder.

Part presents the resul ts of feedback control-

lers, while Part

I

presents the resul ts of feed-

forward controllers.

CONTROLTHEORY

System Analysis

Before any control action can be taken, one

needs to define the control objective and the

variables to be used. There ar e many variables

in the extrusion process, some of which are

used

as

manipulated variables, i.e., variables

which can be changed by external manipula-

tion. Some others are controlled variables

which are controlled through the manipulated

variables. The rest of them are load variables,

i.e., variables which are difficult or impossible

to control. The relationship among those vari-

ables and the control algorithm are shown in

Fig.

1.

Table

1

lists most variables in an extru-

sion line and the possible usage of them. From

the process point of view, an extrusion line can

be broken down to three sections

as

shown in

F i g . 2.

Each section has

its

own dynamic char-

acteristic which can be determined through

MANIPULATED

VARIABLES VARIABLES

LOAD

VARIAELES

Fig. 1 .

Relationship among load variables, manipulated

variab les, and controlled variables in extrusion control.

Table

1.

Variables used in an extrusion line

Load Manipulated Controlled

Variables Variable Variable Variable

Resin pro perties

X

Resin shapes X

Feed rate

X X

Screw speed X

X

Screw torque X

Barrel temperature

X

X

Barrel heater pow er

X

Back pressure valve

X

Melt temperature X

X

Die temperature X

Die pressure X X X

Die flow restricto r X

Die lip or die size

X

Output rate X

Extru date quality

X

Extru date dimension

X

Take-up speed

X

supply

198

POLYMER ENGINEERING AND SCIENCE, MID-FEBRUARY, 1986, VOI. 26, NO. 3


3/8

Process

Control o Polymer Extrusion. Part

I : Feedback

Control

DYNAMIC

EXTRUDER

CHARACTERISTICS

DYNAMIC DYNAMIC

O I E

TAKE-UP

CHARACTERISTICS

-

HARACTERISTICS

open-loop tests. Control actions can be done

either on each individual section or on the whole

line. For example,

if

extrudate dimension

is

the

controlled variable, the take-up speed, the

screw speed, or the die flow restrictor may be

chosen

as

the manipulated variable.

If

melt

temperature

is

the controlled variable, barrel

heater power supply, back pressure valve, or

die temperature may be chosen

as

the manipu-

lated variable. Here the take-up characteristic

has little effect on the control action. In

all

cases, dynamic relationship among controlled

variables, manipulated variables, and load vari-

ables has to be determined before any closed-

loop control action. Detailed dynamic modelling

of th e polymer extrusion

is

given elsewhere 1

0).

In this study, the take-up speed was used

as

the

manipulated variable, the measured extrudate

thickness was used

as

the controlled variable,

while the screw speed was chosen

as

the load

variable. The schematic diagram of t he feed-

back control mechanism used in this study

is

shown in F i g .

3.

Digital Fil ters

Noises in the measurement may affect the

control action, therefore, on-line filtering

is

needed in the control algorithm. Owing to the

easy use of the digital filters, analog type of

filters are not considered. There are several

digital filters available ( 1

1 13).

( 1 )

Digital Version of Analog Filter:

This filter

is

the discrete-time formulation of

the conventional analog filter, sometimes called

first-order filter or exponential filter, and can

be expressed as:

Xk+ l = ffUk + ( 1

- Y)Xk

( 1 )

where

X is

the filtered output,

U is

the meas-

ured signal,

k is

the k-th data point, Y

=

1 exp

- t s / T f ) , t,

is

the sampling time, 7 is the filter

time co nstant, and

0

5

Y

5

1 .

2)

Double Filter:

Double filter

is a

cascade of two first-order

filters. This filter can further remove the drift

in th e raw signal. The discrete expression

is:

x k + , =

y x k +

( 1

y ) x k

2)

where 0

5 y 5 1 . Xk s

the output from

E q 1.

(3)Moving Average Filter:

filter

is:

The discrete expression of the moving average

l N

where N

is

the N-th data point and

P

is number

( 3 )

N=

1

Xk

p k = N - P

Fig. 3 Schematic diagram of control mech anism used in

this study.

of data points used for calculating the average

value. This filter is not as effective as the ex-

ponential filter for

a

dynamic response since it

only takes a n arithmetic mean of data points.

4) High Order Filters:

In a general sense, any transfer function

is a

filter since it transforms input s ignals to output

signals dynamically. The first order filter may

introduce

a

phase lag in t he closed-loop control

system.

A

high order filter developed in the

Laplace domain can solve this problem and it

can also be used

as

a band-pass or

a

band-stop

filter.

A

typical band-stop filter used by Costin,

et al. 9), as in the form

( s+

)2

H s )

=

s + a) s+ b )

4)

where a and b are the lower and upper cutoff

frequencies.

The digital version analog filter and the dou-

ble filter were tried in th is study because of

their simplicity. From the off-line analysis, dou-

ble filter was found only slightly better tha n the

digital version analog filter. Therefore the la tter

was used in this study where

a

was chosen

as

0.4.

The cutoff frequency of a filter was affected

by the sampling frequency. There

is

no good

theory about th e sampling and controlling fre-

quencies. In most literatures, authors did not

discuss the frequencies they used. In polymer

extrusion analysis, Menges,

et al.

14). used

a

sampling period of three seconds to control the

extruder throughput. Kochhar,

et al.

15),used

a

sampling period of 12.5 seconds to determine

the dynamic response of melt temperature.

Rudd 7) entioned a scanning rate of

30

sec-

onds in a sheet extrusion control. Hassen, et al.

16).used

a 10 H z

sampling frequency for the

control of melt temperature. Costin,

et al 9),

used

2 H z as

their sampling frequency for the

process control.

There seems to have no agreement in choos-

ing appropriate frequencies. Higher frequency

sampling and controlling may increase the bur-

den of computer. On the other hand , lower fre-

quency sampling and controlling may not be

able to catch the dynamic response of the proc-

ess. Fertick 17) proposed that the sampling

frequency of a PI controller should be:

POLYMER ENGINEERING AN D SCIENCE, MID-FEBRUARY,

1986,

Vol,

26,

NO. 3

199


4/8

5)

and th e controlling frequency of the PI control-

ler should be

where

t,

is

the controller integral time, ts is the

sampling period, t,

is

the controlling period, tps

is

the process time constant, and

rr is

the filter

time constant. However, he did not explain the

criteria of determining these frequencies.

The sampling frequency and the controlling

frequency used in this s tudy were

1 Hz.

PI Controller

Proportional and integral control is a common

feedback control method. The general expres-

sion in the time domain is ( 1 1 ,

12, 18):

where

V

is the controller output,

e is

the error

between the set point and the measurement,

K ,

is

the proportional constant gain),and T J

is

the

integration constant reset time). The function

of K , is to increase the process response rate

and the effect of

71 is

to decrease the offset

caused by K c . Because the PID controller

is

much more difficult to tune and the noise in th e

measured data may make the system unstable,

the derivative action

is

not considered in this

control algorithm.

In terms of the digital control, the discrete

expression of the

PI

controller can be written

as

where

n is

the nth controlling point and

t,

the

sampling period. In this study,

V

is

the take-up

speed and e is the error between the measured

thickness an d the set point.

Smith Predictor Dead Time Compensation

One difficulty faced by the conventional feed-

back control

is

the relatively long dead time

compared with the process response time. For

most industrial extrusion lines, the measuring

devices are located

far

away from the die. The

long dead time usually makes the feedback con-

trol difficult to tune 1 , 18).

Smith, in

1957,

proposed a mechanism which

may compensate thi s dead time by a postulated

process model. The block diagram

is

shown in

Fig.

4 ,

where block 1)

s

the process transfer

function, td

in

block

2) s

the dead time of the

process, block

4) is

the postulated process

transfer function,

t 2

in block

3)

s

the estimated

dead time of the process, and block

5)

is

the

controller. The combination of blocks

(3 ) , 4)

and 5) is called the Smith predictor, which is

coupled with the control function. If the postu-

lated process transfer function and dead time

are exactly the same

as

the process function

and dead time, for

a

set point change, the sys-

tem response ca n be written

as

B Yang and

L.

James

Lee

200


1986,

Vol. 26, No. 3

where

y,

y, and

y*

are intermediate variables

shown in F i g . 4 .

E q u a t i o n

1 1

shows that with th e Smith pre-

dictor, the process dead time can be compen-

sated and the system block diagram can be

simplified to the one shown in F i g . 5a.

The essences of th e Smith predictor are the

postulated process function and the dead time

chosen. Among the two, the accuracy of t he

estimated dead time

in

the model

is

more im-

portant t ha n the accuracy of t he postulated

process function owing to the exponential func-

tion accompanied with

it.

For

a

load coming into the control loop by-

passing the Smith predictor, the Smith predic-

tor cannot compensate th e dead time effect as

shown in F i g . 5b where

CL is

the combination

of blocks

(3 ) , 4)

and

5) n

F i g .

4 .

Meyer, et al. 19)used a simulation program

to evaluate the response of the Smith predictor.

Results showed that with

a

significant time

delay, the Smith predictor worked better than

the PID controller

for a

set point change.

Since the take-up speed was used

as

the ma-

nipulated variable, the line speed changed dur-

ing the controlling period. Therefore, the dead

time in this study was not

a

constant, which

must be calculated on-line by the following

equation

L

F i g . 4 .

Block diagram

of

the Smith predictor dead time

cornpensat ion.

i a i

Y ( S 1

Lbl

-

I S )

I I

Fi g .

5 (a)SimpltJiedblockdiagramof the Smith predictor

fo r set point changes,

[b)

implified block diagram

of

the

Smith predictorfo r load changes.


5/8

Process Control

o

Polymer Extrusion. Part I : Feedback

Control

POLYMER ENGINEERING AND SCIENCE, MID-FEBRUARY, 1986, VOI.

26,

No. 3

201

L

t d

=

U

where L

is

the distance between the measuring

device and the die, while

u is

the take-up speed.

For the on-line process control, a digital version

of the Smith predictor was used. The derivation

is

given in the Appendix.

EXPERIMENTAL

Equipment

The extruder used

is

a

2 4 2

inch diameter, 24

to 1

L/D

ratio single screw plasticating extruder

made by NRM Corporation. The barre l

is

heated

by four separate heater sections controlled by

time proportioning controllers and on-off relay

switches. Screw speed can be controlled man-

ually or remotely by sending different voltages

into

a

Reliance control motor. The correlation

between th e input voltage and th e screw speed

shows

a

linear relationship except

at

very low

screw speeds i.e.,


6/8

B

Yang and L.

ames

Lee

START

CHOOSE:

1.

P I CONTROL L ER

2. SMIT H PREOICTMI TAKE-UP

3. FEEOFODUARD CONTROLLER

4 ,

TAUE-UP SPEED CHANGE

5 . SCREW SPEEO CHANGE

SCREW

U/

ENTER CONTROLLER

PARAMETERS

TYPES OF CHANGE

_I

I

CONTROLLER

e l l - 1

MIT H PDEOICTOR FEEOFORWARO

4

PLOT THICKNESS

1 ko

F i g . 6 .

Flow chart of t he control progr am.

= 6

s),T is the process time constant = 3

s ) ,

and T~

s

the controller reset time.

Under the set point change, the IAE criterion

gives:

KK c = 0.758 = 0.417 15)

-0.861

T

=

1.02

+

0.323

=

0.374 16)

71

and K, = 0.42, 7

=

8.0

These calculated values were used as the initial

guess for the controller.

Figure 7 shows typical dynamic responses to

a

screw speed change from 6 to 14 rpm. All

pressure responses and extrudate thickness

change were modelled well by first-order trans-

fer functions.

PI

Controller

and

Smith Predictor

Figure

8

shows the response of th e

PI

con-

troller for

a

set point change from 18 to

15

mils

at the screw speed of 10 rpm. The filter time

constant used was

0.4

and Kc = -0.35, 71

=

12.0.

Figure 9

shows the control result for a

step change in screw speed from 14 to 10 rpm.

All parameters were the same as those in Fig.

8.

The Smith predictor was tested for a set point

change from 18 to 15 mils. The result

is

shown

in

Fig. 10.

The screw speed was 10 rpm. Kc was

-0.35,

while T~was 12.0. The process time con-

stant was set at 8.0 seconds. The initial guess

of kc was -0.49 and

T~

was

8.0.

For screw speed

changes, the results are similar to those of the

PI

control.

Judging from

Fig.

8, the PI controller worked

938.8

1781.8

820.

8

3053. 8

2050.4

3

p2

0.0 25.8 51.2 78.8 102.4

T I M E (SEC)

Fig.

7.

Dynamic responses to the screw speed change

from

6 to 14

rpm P.5: die pressure (psi). P l - P 4 : barrel

pressures psi),TB: barrel temperature PF , TD: melt t em-

perature

P F ) .

H : extrudate thickness (mil)).

m

~ t. . . . . . . , . . . . l . . . . l

0 50

100 150

200

CONTROL

CYCLES

1 HZ 1

F i g . 8 . Experimental result o the

PI

controller fo r a

set

point change rom 18 to

15

mils IAE

= 8.1).

m

m .

F i g . 9 Experimental results of the PI controller fo r a

screw speed changefr om

14

to

10

rpm

flAE= 9.2).

well for the st ep change of set point except that

there was a time delay due to the process dead

time. For load changes, the

PI

controller was

not very efficient owing to the process dead time

in the extrusion line. The reason that IAE val-

ues are not significantly different for load

changes and set point changes

is

because the

existence of measurement delay. The actual

thickness response was sensored several sec-

202


1986,

Vol.

26,

NO. 3


7/8

Process Control of Polymer Extrusion. Part

I :

Feedback Control

onds later by the LVDT.

If

one takes into ac-

count this measurement delay, the IAE for set

point changes will be much better than that of

load changes .

The performance of th e Smith predictor was

slightly better t ha n the PI controller for the step

change of s A point as judged from the integral

absolute error shown in

F i g s .

8 and

10.

Fluc-

tuations in the response curve were due to the

inaccuracy of the postulated process model, the

error in the estimated process dead time, and

the digital sampling problem. For large process

dead time or frequent changes of set point

which is unlikely in the case that extrudate

thickness is the controlled variable, but

is

very

common in the case that barrel temperature

settings ar e controlled variables), the Smith pre-

dictor would work much better tha n the PI con-

troller.

. ? t . . . . l . . . . I . . . . I . . . . I

0 50 100

150

200

CONTRM CYCLES 1 HZ 1

F i g . 10.

Experimental result

o

the Smith predictorfor

a

set point change r om

18

to 15 mils

IAE

=

7.4).

CONCLUSIONS

This study provided an on-line process con-

trol of a single screw plasticating extruder. Two

feedback control algorithms, a conventional PI

controller and the Smith predictor, were tested

by step changes of set point and load variable.

Results showed that both the PI controller and

the Smith predictor were satisfactory for step

changes of s et point, but not for load changes.

Because of the inconsistency of the extrusion

line and the inaccuracy of the process model,

the Smith predictor showed only a slight im-

provement over the

PI

controller in this study.

ACKNOWLEDGMENT

The authors would like to express their ap-

preciation to Professor W.

K.

Lee and Messrs.

R. W.

Nelson,

D.

Chan, and

M. B.

Kukla for their

help and useful discussions. This work was

supported by the

OSU

Polymer Engineering Re-

search Program, which

is

sponsored by Amoco

Foundation, General Motors, Huntsman Chem-

ical, and Plaskolite Companies. We than k Plas-

kolite Company for the material donation.

APPENDIX

Derivat ion of Sm i t h Pred i c tor in the Discrete

Form 12)

The Smith predictor algorithm shown in

Fig .

5 can be redrawn

as

in

F i g . A- 1 .

where

G ( s )= Gp(s)ePtdS

s the process transfer

function

Gc s)

=

K 1

+

s the controller transfer

function.

is

the estimated process trans-

b

G ~ ( s )

r s +

1

fer function.

[

1 exp -st,)

Gho

s the zero-order hold

S

y

is

the thickness output.

u k is the filtered thickness in the discrete

form.

Ysp

s

the set point in th e discrete form.

t ,

is

the sampling time.

M is

the value of manipulated variable output

from the controller.

C,(z) is

the

Z

transform

of

the model output.

E l ,

Ekr

B m . k .

nd

C m . k

are intermediate

vari-

ables.

From this plot, the model output C ,

is

related

to the input

M

as

If the estimated process model

Gb(s)e-tis

s

identical to the process model

G(s ) ,

hen

Substituting the trans fer function into

E q A-1

we get

For the process dead time, if we denote the

integer number of sampling period as N , then

the following equality holds:

t 2

=

(N

+

p ) t s

A-4)

where

p is a

value between

0

and 1. With this

expression of

t d E q A - 3

can be rewritten

as:

L S1

S)

I

t.

F i g . A-1. Detailed block diagram of the Smith predictor.

POLYMER ENGINEERING AN D SCIENCE, MID-FEBRUARY, 1986, Vol. 26 No.

3

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8/8

B.

Yang and

L.

James

Lee

Taking transform

of

E q A-5,

it

gives

where

A2 =

e-

and A3

=

e Ofs/T

To compensate th e process dead time, we define

Cross multiplying and inverting gives

B m , k

= K p 1 Az)

uk 1

+ A2Brn.k-1

A-9)

so

Ek

=

Y s p k

-

u k f n.k

c m . k )

A-10 )

Note that if the proposed model is correct, then

uk

=

C m . k

and the input to the controller

G,

will be

Ek

=

Y s p k B m . k

A-1 1)

For the PI controller

so

A-

13)

or

M k =

Mk-1 tK , 1 Ek -

KcEk-1 A-15 )

For the process control, E q s

A-7 ,

A-9, A - 1 0 ,

and

A-15

are used. To sta rt th e control action,

the most recent output voltage of take-up device

is

stored into the

M

array

as

the initial value of

Mk .

If

the process dead time varies during the

control action, th e values of A2, AS,and N will

vary

at

every controlling interval. A t

a

given

moment, the dead time is calculated from the

most recent take-up speed. The drawback of

this calculation

is

that, unless the take-up

speed

is

constant, the calculated dead time will

always deviate slightly from the actual dead

time.

REFERENCES

1.

2.

3.

4.

5.

6.

7.

8.

9.

10.

11.

12.

13.

14.

15.

16.

17.

18.

19.

20.

21.

22.

23.

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NO.

3

process control of polymer extrusion

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