heat exchanger process

1. WP4 -4:30
GAIN-ADAPTIVE COtPPROL APPLIED TO A HEATEXCEANGB PROCESS
USING A FIRST ORDER PLUS DEADTIHE COWENSATOR
bY
E. S. Chiangand L. D. Durbin
ChemicalEngineeringDepartment
Texas A M University
CollegeStation, TX 77843
SIIlnarY
The Smithdeadtimecompensatorwith and without
model gain-adaptation is applied via a d i g i t a l
computer t o a heat exchangeprocess. A f i r s t o r d e r
model v i t h deadtime foras the basis of the well-lmovn
compensation scheme A i c h is used in combinationwith
a main process controller of the proportional plus
integral(PI) form. Eere,adaptation of t h es t a t i c
model gain is added in an attempt to stabilize the
controlsystem in the face of certain types of
processchanges.Thisgain-adaptoralsousesPI
control of the static model gain to force the unde-
layed d e l response into agreementwiththeprocess
response.Further, as t h es t a t i c model gainchanges,
the main process controller gain is changed in an
attemptto maintain stability. Test runs were made
on w actualdouble-pipeheatexchanger of an
industrialsizeusing steam toheatvater.Control
of theoutletwatertemperature(processresponse)
was triedusingthedeadtime compensationschemes
and regular P I control by i t s e l f . The responsesfor
stepchangesinset-point vater temperature show
thesuperiortrackingbehavior of thedeadtime
compensationschemes.Fordecreases in the vater
flow rate, it is shornthatregularPIcontrol and
Smith's method cangiveoscillatoryresponses. With
maintain stability for this type of process change.
propertuningthe gain-adaptive procedure is shorn t o
Introduction
A dynamic step response obtained for many types
of fluid flow process with heat and mass transfer
resemblesanextended "S" shapedcurve.This
responsecurvecan be f i t t e d . almost by inspection,
to the stepresponsefor a first order process in
series with a deadtimeelement.Feedback controller
p a r a t e r s based upon this model canthenbereadily
calculated. Thus, the model has -use practical
u t i l i t y and appeal in that it is easytoapply and
mationsfor the controllerparameters. No formulations
generallyprovides,at least, good f i r s t approxi-
and solutions of complex sets of differential
equationsarerequiredsincetheactualprocess
response can oftentimesbeobtained and used.
Smith1*2.3 incorporated a lumped parameter
model withdeadtimeintothecontrolstructure(loop)
in such a manner that the model deadtimecancels
that of theprocess in the characteristic equation
knm as the Smith predictor since the model is used
for the controlsystem. The technique is conmonly
to predict the'response based upon the known valve
input. A regular proportionalplusintegral(PI)
controller may beused viththepredictor. Here,
thistechnique is termed Smith's DeadtimeCompensation
(SDC) Method. The method works vel1 when the model
and process agree to a certain extent with respect to
the model parametersused. As processoperating
conditionschange,thecompensation scheme can become
oscillatory (unstable) due t o model and process
parametermismatches.
For the same heatexchangerused in this study,
previous reports4~5 have dealt vith the problem of
providing good control in the face of processchanges.
This is forcontrol of theoutletcoolant(water)
Thesechangescanbe of the "signal" typesuch as
temperature via adjustment of the steam flov rate.
set-pointorload changes or of the"parametric"type
whichcan occurforchanges in the operating conditions
caused,for example, by a change in thecoolant(water)
flowrate. The application4 of anode1reference
adaptive control scheme yielded satisfactory results
formildchanges such as a change in steam supply
pressure. Also, severaldifferent"optimal" and
sub-optimal methodswere tried and reported5.
Decreasingthecoolant(water)flov rate invariably
yielded a more oscillatory res onsebehaviorforeach
of the methods and p r o c e d u r e s . ~ ~ 5
For a decrease in c w l a n t flow rate to the heat
exchanger,the main parametriceffect is to increase
the steady state process gain, Kp, with small changes
in themajor time constant, TP, and effectivedeadtime,
Td?. I f a model is tobe used as part of thecontrol
structure such as with Smith's method, then a useful
controlprocedure would include adapting the model
gaintofollov that of theprocess. Reports697 of
simulationstudiesconcernedwithgain-adaptivepro-
ceduresindicatethat good results canbeobtainedfor
relativelylargechanges in processgain(doubled)
accompanied by small (to 30%) changes in thetime
constants.
The work reportedhere is concernedwith the
application of thegain-adaptiveproceduretothe
actualheatexchanger(process)and,thus,toprovide
method makes use of a f i r s t o r d e r plus deadtime d e l
some verification of t h e u t i l i t y of the method. The
as a Smith predictor.Inaddition,regularPIcontrol
and the SDC method (withoutthegain-adaptor) are
usedforcomparisons. The responsebehaviorforstep
changes in set-pointtemperature and stepdecreasesin
coolant(vater) f l w r a t e a r e shown.
THe Cantrol System
A schematicequipmentdiagram for the control
system is shown by Figure 1; whereas,thecontrol
methods are indicated by the block diagram of Figure 2.
The symbolicrepresentationsarefurtherdefined in
thedescriptionsthatfollow.
Control Equipment and Procedure
As indicated by Figure 1, a e t a 4/1800 d i g i t a l
computer(manufactured by Digital Scientific
0191-2216/80/0000-0292$00.750 1980 IEEE
292

2. Corporation) is used to control the coolant water
temperature, Cp, at the outlet of the heat exchanger
by means of an output,M, to the steam control valve.
This valve is a1% inch pneumatic double port control
valve vith linear trimas vrnufactured by Fisher
Controls Co. It is actuatedby means of a digital
output word to a D/A converter and I/P transducer.
The heat exchangeris a Type 40-1018 finned-tube
exchanger as manufactured by the Brown Fin Tube Co.
The inner pipe is23 feet long inside the U-form
of the outer pipe (shell). Steam flovs into the shell
with continuous dischargeof condensate. The f l w of
side which is terminated at the bottom bya condenser
cooling water in the inner pipe is countercurrent to
the steam flov. A surge typetank with another steam
control valveand pneumatic controller is used to
maintain the steam pressure to the heat exchanger.
This was nominally25 psig for the tests reported here.
The water flov rate,Fw, is adjusted manually with an
indication given by the differential across an
orifice plate.
The inlet and outlet water temperature(band
Two) can be monitored by means of platinum resistance
probes with the associated electronics by Stow Labs,
Inc. These provide a signal of10 millivolts,
nominally per1 degree Farenheit as set by the
manufacturer. This can change some, however. Here,
millivolts (MV) are used to indicate the vater
temperatures since a calibration vas not made right
before making the testruns. The process response,
Cp, or the millivolt signal for the outlet water
temperature is converted to a& digit BCD digital
word for the computer. This is achieved bymeans of a
dual slope AID module with conversion times in the
noisy to the extent ofabout 10 MV even with this
10 millisecond range. The water temperaturesignal is
integrating type converter.An external clock circuit
provides an interrupt to the Meta 411800 computer
after the A/D conversion has taken place at0.5
also amplified forrecording on an industrial type
second intervals. The analogtemperature signal is
strip chart recorder manufactured by Fischer6 Porter
Co. The pen lagis about one-half secondso that s ~ m e
smoothing of the recorded water temperature responses
occurs.
The control program usedon the e t a 4/1800
computer is written in Fortran withsome assembly
language subroutines for servicing the A/D and D/A
functions. Initiation and operational features are
selected by means of data entry svitches on the front
panel. Parameter specifications are nominally made by
means of card reader input. The on-line program
applies the selected control method at0.5 second
intervals after the timer interrupt indicating com-
pletion of the AID conversionis sensed by the computer.
After a testrun is ccmpleted, operational data and
the response values can be printed if they are desired.
Control Hethods
study are indicatedby the block diagram of Figure2.
The signal,M, to the steam control valve isa l s o
applied to the first order model operator,k,to
give 4.the undelayed model response. In the digital
computer thisis achieved by a standard fourth order
Runge-Kutta integration at0.5 second intervals of
time, t, for
The model-based controlschemes used for this
with
Here, % is the static model gain(MVlX valve opening)
and lMis the first order model time constant in
seconds. The model bias value Ci should be the inlet
water temperature forWO in the ideal case. This
factor is considered further in the discussion of the
experimental results. The computed value of is
stored for an integer number of time increments to
implement the time delay operation,Gm, vith model
deadtime, la,in seconds. The Smith predictor
structure is obtained by forming the effective feed-
back signal, B*, in Figure2 according to
B*=<+(Cp-<).
A PI controller is used for the main process
controller, Gcp, as part ofwhat is termed here
the Smith Deadtime Compensation(SDC) method. The
PI algorithm used is atwo point difference form for
= Mo + KmE * + -KcP I'E* dt;
lIP 0
where EhR-B* and R is termed the set-point (reference
or desired) outlet vater temperature.Tbe signal M is
held constantby the D/A over the next time interval
PI control (PIC) withoutSmith's predictor E* becomes
and is constrained to the0-100% range.For regular
the true error, E=R-Cp. Here,Kcp is the proportional
control gain( X valve opening/MV) andlIP is the
integral (reset) time in seconds.
The Gain-Adaptive Deadtime Compensation(GADC)
method is Implemented by usingEm=$- in another
two-point difference approximation forPI adjustment
of % according to
Here, Kc* is the proportional adaptor gain (11% valve
opening) and 'cIA is the adaptor integral tire
constant in seconds. The model gain% is not allowed
to become negative. Further, asI$, changes, the
proportional gainKcP of the main process controller
is changed suchthat vcp=K&remains constant.
This is an attempt to keep a prescribed effective
loop gain and, thus,maintain stability as the
static process gain,5,changes.
293

3. Experimental Results
The main experimental results of this study are
indicated by the outlet water temperatureresponses
shownby Figures 3-11. Otherdata are given in
Tables I and 11. The steadystateoperating
conditionsforthe test nms are listed in Table I
and some steady state results are given i n Table 11.
For a l l of the strip chart recordings of the tempera-
tureresponses shown in Figures 3-11, four
divisionscorrespondto 22.86 seconds.
For the base water flov rate Fwl, an open loop
valve between 30 and 50% open. The recordedresponses
test vas f i r s t made by stepchangingthe steam control
are reproduced in Figure 3. Based upon these
responses, a model deadthe of ~ ~ = 4seconds and f i r s t
ordertimeconstantof T =15seconds vere selected
M
for use withthe model-based control schemes. The
step-downresponse vas a l i t t l e slower than the
step-upresponse. The staticprocessgainvas com-
puted t o b e v 9 . 3 based upon the steady state
temperature variation for the outlet water from1355
t o 1541 MV. A startingvalue of %=lo vas f i r s t
selected for use vith the model-basedmethods and
appliesforFigures 4-7. ForFigures 8-11, a starting
valueof v 1 0 . 8 vasused as discussed later.
The control methods that vere tested are noted
again by the following list with the designations
that are used to identify the response curves in
Figures 4-11. These are as follovs:
"PIC"Method forregular P I control;
"SDC" Method forSmith's Deadtime
Compensationmethod;
Method for the Gain-Adaptive
DeadtimeCompensation procedure.
IIGADCII
For the PIC method, values of Kcp=0.3 and rIp-15
Nichols8settings)toobtainthe "A" responses shown
seconds vere used (in good agreementwiththeZiegler-
in Figures 4-7. For the SDC and GADC methods, the
value ofrIp=15secondsvasusedthroughoutthe tests.
Values of Kcp=0.3, 0.4, and 0.5 with YlO were f i r s t
t r i e df o rt h e SDC Method. InFigures 4-7, the "B"
and "C" responses are for the SDC Method with Km=0.3
and 0 . 5 , respectively. For the "E" response i n
Figure 6, a value of Km=0.4 vasused.Forthe SDC
responses in Figures 8-11, a value of Kcp=0.5 vas
used.
For the GADC Method, a value of rIA-20 seconds
was used for a l l nms. Values of KcA=0.05 and Km-0.5
vere used to obtain the results shown by the I'D"
respoasesinFigures 4-7. Inthesecases a model
biastemperatureof %=SO0 MV w a s used.Thisagrees
with the inlet watertemperatureof 902 MV for these
nms. When the model biastemperature vas raised to
1017 MV, it vas foundnecessary to use a KCA-0.01 t o
obtain the GADC responses shown in Figures 8-11.
A value ofK0cKcp5=5 vas considered appropriate
f o r t h i s systemwith SDC and GADC methods. The larger
Km=0.5 canbe justified since the deadtime is a
deadtimeequal to or greater than the time lag, a
fraction of thetimelag. For a processwiththe
more conservativevalueof KO; in the range of 2 t o 3
vould be appropriate as rec-nded by Palmorand
Shinnar .9
The responses for the outlet vater temperature
point from 1400 W t o 1300 HV; vbereas, thosefor
shovn in Figure 4 are for a step-dovnchange in set-
Figure 5 are for 1300 W t o 1400 W . These are for
theconstant water flow rate Fwl. The PIC method
shovs more oscillations for the step-downdue to the
increasingprocessgain in thatdirection. The
model-based responses for the SDC and GADC methods
showgood behavior in thesecases.
Responses at a constantset-point of 1400 MV and
Figures 6 aad 7. For Figure 6, a sizeablestep-
forstep-decreases in water flow rate are shown in
PIC method becomes continuouslyoscillatory. The
decrease in vater flow rate vas made. As shown, the
SDC method with Kcp=0.5 or K '-5 andCi=900 MV is on
theverge ofdoing so. Eovwer,forvalues of K0p4
and 3, the SDC responses are shovn t o become more
stable and convergent.InFigure7, responses are
shovn for a more moderatestep-decrease in water flov
r a t e from Fwl to Fm. The PIC method is beginning t o
show the sustained oscillatory conditions; vhereas,
the other methods giveaboutthe same behavior.
OL
The response Curve "D" for the GADC method shown
in Figure 6 would seem t o confirm that the method
maintainedstability as desired. Upon checkingthe
"print-out", it vas notedthat % was adjustedto
about14.5beforethetest run vas begun. The reason
thisoccurred is thatthegain-adaptorvasforcing a
matchbetween the steady state process and model
responses. It did mean, hovever,thatthevalue of
Km had already been adjusted to about 3.5 before
evenwithoutgain-adaptationtheresponsevouldbe
thestep-decrease in vaterflovrate w a s made. Thus,
convergent,similarto Curves "B" and "E" on Figure 6.
The problemnotedabovepertainingtothe initial
adjustment of the model gainstems from thenon-linear
nature of theprocess. The staticprocessgainvaries
withthe steam valveopening, M, at any givenvater
flovrate. In ordertohelpclarify and characterize
this, the steady state outletwatertemperaturevas
obtainedforeachofseveralvalvesettings, M, as
shown in Table 11. As expected,thedata show the
static process gain decreasing as thesteamvalve is
opened. Infactasthevalve is opened,slugging
of a steam-condensatemixtureoutofthecondenser
use a linear model, it vas decided to adjust the bias
can occur a t the lower vaterflow rates.In orderto
temperature(intercept) and v i s u a l l y f i t a straight
line tothedatafortemperatureversusvalveopening
up t o 50% forthevaterflovrate Fwl. Thisyielded
a b i a s v a h e of %=lo17 MV and a model gain value of
5=10.8. These values were used for the SDC and GADC
methods toobtaintheresponses shovn inFigures 8-11.
This way a f a i r e r comparisonbetween the methods
couldbeobtained. It vas necessary,hovever,to
avoid conditions for vhich the steady state valve
vas now about117 MV larger than that for the inlet
openingvouldapproachzerosincethebiasvalue
water temperature. Of course,negativevalues of
couldnotbeallowed.
%
In Figure 8 and 9,thetemperatureresponses are
shown for step-decreases in vater flov rate with the
differentset-points. For therevised model
SDC and GADC procedurescontrollingforthree
294

4. conditions (new bias value and gain) the SDC procedure
with Kcp=0.5 is shown by Figure 9 to converge fairly
well at the 1400 MV set-point. This was notthe case
for the bias value of 900 MV used to obtain the "C"
curve in Figure 6. This is an interestingsituation
thatrequiresfurtherinvestigation. As theset-point
is lovered to 1300 MV the SDC system oscillates for
theindicatedwaterflow rate change. A t thehigher
set-pointof 1400 MV, it tookagreaterchange in
the water flow rate to effect oscillatory behavior.
The gain-adaptiveprocedurewith KcA=0.05 did
not yield satisfactory results either for the water
flow rate changes made at the higher and lower
set-points. It didprovidesatisfactoryresultsfor
the 1400 MV set-point as indicated by Figure 9. This
time the model gain was close to the initial value of
10.8 when the test run was made. For theother
set-point cases noted for Figure 8, the KCA value of
0.05 would result in the model gainchangingtoo much
asthe steam controlvalveclosed. This aspectalso
requires further study to see i f some modification
of thealgorithm would help. The problem is similar
in some respectsto"reset-windup"forregularPI
control vith unconstrained integral action.
yield satisfactory results for the different cases
astheresponses in Figures 8 and 9demonstrate. One
very slow i n convergingtothatoftheprocessafter
problemnoted was that the model temperature was
theupset. With theadaptorgain of 0.02 and the
new bias value, the GADC method provides set-point
responsebehavior which is similar to that for the
SDC. This is shown by Figures 10 and 11.
An adaptorgain of 0.02 was t r i e d and found t o
Conclusions
A procedure which includes adaptation of the
model gaininSaith'slinear(deadtime)compensation
process.Adjustmentofthe steam flow(valve) is
scheme has been applied to an actual heat exchange
After some adjustmentofparametersforthepro-
requiredtocontroltheoutletwatertemperature.
cedure, it is shown tosuccessfullyadapttheprocess
controller gain to provide a stable control system in
rate.Smith's method withoutthegain-adaptor is
theface of significant decreases in the water flow
poorerperformance is obtained vlth regular PI control.
shown t o f a i l ( o s c i l l a t e ) i n some cases and much
This actual application has directed attention to
problems associated with properly biasing the linear
model response.These stem from thenon-linearvar-
iation of theprocessgainwithcontroleffort(valve
opening) and furtherconsideration is certainly
indicated.
References
1. Smith, 0. J. M., ChemicalEngineeringProgress,
2. Smith, 0. J. M., FeedbackControlSystems,
3.Smith, 0. J. H., ISA Journal, Vol. 6, No. 2,
Ch. 10, McGraw-Hill, New York (1958).
pp.28-33(1959).
4.Davidson; J. M. and L. D. Durbin,1979 Joint
AutomaticControlConferenceProceedings,
p. 468 (1979).
5. Huang, L. E. and L. D. Durbin,1978Joint
AutomaticControlConferenceProdeedings,
Vol.53, NO. 5, pp. 217-219 (1957)-
Vol. 2, pp.109-121(1978).
6.Chiang, H. S. and L. D. Durbin,1980 Joint
AutomaticControlConferenceProceedings,
Vol. 2, Paper PAS-E (1980).
7. Chiang, H. S. and L. D. Durbin,1980 Annual
ISA ConferenceProceedings,(Oct.1980).
8. Ziegler, J. G. and N. B. Nichols,Transactions
of the ASME, p. 759(Nov. 1949).
9.Palmor, 2. J. and Shinnar, R., 1978 Joint
AutomaticControlConferenceProceedings,
Vol. 2, pp. 59-70 (1978).
TABLE I
SteadyStateOperatingConditionsfortheTest Runs
Steam Pressureto HeatExchanger = 25 psig.
Inlet Water Temperatures, TWI:
902 MV for the Responses in Figures 3-7;
894 MV for the Responses in Figures 8-11.
Coolant(Water) Flow Rates(lbm/mln):
FW1 = 164 (172); Fw2 = 131.7(141.2);
FW3 = 103.4(113.3): FW4 = 83.1.
For the GADC responses shown inFigures 4-7, the
waterflowratesarethosein ( ). These were higher
due to an unexpected increase in water supply pressure
at the end of theextendedperiodrequiredto make
the test runs.
MODEL
SET-POINT
DSC KETA 411800 COWPUTER
READER
PRINTER
tELECT.
PT.SENSOR
-- I *Two OUT
4WATER
HEAT EXCHANGER
Fig. 1. Equipment Diagram for Heat Exchanger
Control System.
B*
Fig. 2. Control SystemBlock Diagram Showing the
Gain-Adaptor = G
CA'
295

5. TABU I1
Steady State Heat Exchanger Data
A. For Water Flow Rate FYI:
Valve + 10 2030 40 50 60
( X open)
Two (W)+1105 1240 1360 147215421567
B. For Water Flow Rate Fw3:
Valve + 10 20 30 40
( X own)
Two (XV)+ 1213 1421 1591 1711
C. For Water Flow Rate FwL:
Valve + 10 14.2 20
( X open)
Two (W)+1287 1400 1502
Inlet Water Temperature, 893 MV for the above.
%I=
Fig. 3. Open Loop Step Responsesfor 30-50% Valve
Opening at Water Flov Rate Fwl.
......+-g. . WATER m w RATE = FA. 41 -
. .
.......
._.-.+
- +L..:-*...JA:L.-2-A
- - -. D. (GADC; Kcp=0.5; Ku=0.05)
. .
A. (PIC;Kcp=0.3)
Fig. 4. Controlled Temperature Responsesfor a
Step-Down in Set-Pointfrom 1400 to 1300 HV.
Fig. 5. Controlled Temperature Responsesfor a
Step-up in Set-Point from 1300 to 1400 MV
at Fn.
"Z" marks zero timefor all responses.
Fig. 6. Controlled Temperature Responsesfor a Step-
Decrease in Water Flow Rate from Fwl
at 1400 MV Set-Point. to Fw3
296

6. D. (GADC; Km=0.5; KcA=0.05)
Fig. 7. Controlled Temperature Responses fora Step-
Decrease in WaterFlow Rate from Fwl toFm
at 1400 MV Set-Point.
Fig. 8. Revised* SDC and GADC Responses for Step-
Decreases in Water Flow Rate.
(Curves "A" and "B" are fora 1300 MV set-
point witha water flow rate change from
Fwl to Pw3 . Curves "C" and "D" are for a
1450 MV set-point witha water flow rate
change from Fwl toFw4.)
*Figures 8-11 are for theSW: and GADC methods with
KGp=0.5 and the revised valuesof 9 1 0 1 7 W and
%=10.8.
Fig. 9. Revised* SDC and GADC Responses at 1400 KV
Set-Point anda Step-Decrease in Water
Flow Rate from Fwl to Fw3:
I
-. _.4 -. . - $t.. _.__! ,-__ .- -.+
. . . ,-. .. . i.. . . - 1 . .- -'I
-D b
I
(GADC; R- 130 to 140) i
Chl.. - ..
297