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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,
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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
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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:
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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
POLYMER ENGINEERING AND SCIENCE, MID-FEBRUARY,
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.
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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.,
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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-
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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
203
-
8/12/2019 Process Control of Polymer Extrusion
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.
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