WP4 - 4:30

GAIN-ADAPTIVE COtPPROL APPLIED TO A HEAT EXCEANGB PROCESS USING A FIRST ORDER PLUS DEADTIHE COWENSATOR

bY

E. S. Chiang and L. D. Durbin Chemical Engineering Department

Texas A M University College Station, TX 77843

SIIlnarY The Smith deadtime compensator with and without

model gain-adaptation is appl ied v ia a d i g i t a l computer t o a hea t exchange process. A f i r s t o r d e r model v i t h deadtime foras the basis of t he well-lmovn compensation scheme A i c h i s used in combination with a main process control ler of the proport ional plus in tegra l (PI ) form. Eere, adaptation of t h e s t a t i c model gain is added in an a t t empt t o s t ab i l i ze t he control system in the f ace of certain types of process changes. This gain-adaptor also uses PI cont ro l of the static model ga in t o fo rce t he unde- layed d e l response into agreement with the process response. Further, as t h e s t a t i c model gain changes, the main process control ler gain is changed in an at tempt to maintain s t a b i l i t y . Test runs were made on w actual double-pipe heat exchanger of an indus t r i a l s i ze u s ing steam to hea t va te r . Cont ro l of the outlet water temperature (process response) was tried using the deadtime compensation schemes and regular P I cont ro l by i t s e l f . The responses for step changes in set-point vater temperature show the superior tracking behavior of the deadtime compensation schemes. For decreases in the vater flow rate, i t is shorn that regular PI control and Smith's method can give oscillatory responses. With

ma in ta in s t ab i l i t y f o r t h i s t y p e of process change. proper tuning the gain-adaptive procedure is shorn t o

Introduction

A dynamic step response obtained for many types of fluid f low process with heat and mass t r ans fe r resembles an extended "S" shaped curve. This response curve can be f i t t e d . almost by inspection, t o the step response for a f i r s t o rde r p rocess i n series with a deadtime element. Feedback con t ro l l e r p a r a t e r s based upon this model can then be readily calculated. Thus, the model has -use p rac t i ca l u t i l i t y and appea l in that i t is easy to apply and

mations for the controller parameters. No formulations general ly provides , a t least, good f i r s t approxi-

and so lu t ions of complex sets of d i f f e r e n t i a l equations are required since the actual process response can oftentimes be obtained and used.

Smith1*2.3 incorporated a lumped parameter model with deadtime into the control structure ( loop) in such a manner tha t t he model deadtime cancels t ha t of the process in the charac te r i s t ic equa t ion

knm as the Smith predictor s ince the model is used f o r t h e control system. The technique is conmonly

to predict the ' response based upon the known valve input. A regular proport ional plus integral (PI) cont ro l le r may be used v i th t he p red ic to r . Here, this technique is termed Smith's Deadtime Compensation (SDC) Method. The method works vel1 when the model and process agree to a cer ta in ex ten t wi th respec t to the model parameters used. As process operating

conditions change, the compensation scheme can become osc i l la tory (uns tab le) due t o model and process parameter mismatches.

For the same heat exchanger used in th i s s tudy , p rev ious r epor t s4~5 have dea l t v i th t he problem of providing good cont ro l in the face of process changes. This is fo r con t ro l of the out le t coolant (water)

These changes can be of the "signal" type such as temperature via adjustment of t he steam f l o v r a t e .

set-point or load changes o r of the "parametric" type which can occur for changes in the operat ing condi t ions caused, for example, by a change in the coolant (water) f low rate. The application4 of a node1 reference adapt ive control scheme y ie lded s a t i s f ac to ry r e su l t s for mild changes such as a change in steam supply pressure. Also, several different "optimal" and sub-optimal methods were t r i e d and reported5. Decreasing the coolant (water) flov rate invar iab ly yielded a more osc i l l a to ry res onse behavior for each 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 t he hea t exchanger, the main parametr ic effect is to i nc rease the s teady s ta te p rocess ga in , Kp, with small changes

in the major time constant, TP, and effective deadtime,

Td?. I f a model is t o b e used as pa r t of the control

structure such as with Smith's method, then a useful control procedure would include adapting the model g a i n t o f o l l o v that of the process. Reports697 of simulation studies concerned with gain-adaptive pro- cedures indicate that good r e s u l t s can be obtained for re la t ively large changes in process gain (doubled) accompanied by small ( to 30%) changes in the time constants.

The work reported here is concerned with the appl ica t ion of the gain-adaptive procedure to the actual heat exchanger (process) and, thus, to provide

method makes use of a f i r s t o r d e r plus deadtime d e l some ver i f i ca t ion of t h e u t i l i t y of the method. The

a s a Smith predictor . In addi t ion, regular PI control and the SDC method (without the gain-adaptor) are used for comparisons. The response behavior for step changes in set-point temperature and s tep decreases in coolant (vater) f l w r a t e a r e shown.

THe Cantrol System

A schematic equipment diagram fo r t he con t ro l system is shown by Figure 1; whereas, the control methods are indicated by the block diagram of Figure 2. The symbolic representations are further defined in the descr ipt ions that fol low.

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 Dig i t a l Sc i en t i f i c

0191-2216/80/0000-0292$00.75 0 1980 IEEE 292

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 a 1% inch pneumatic double port control valve vith linear trim as vrnufactured by Fisher Controls Co. It is actuated by means of a digital output word to a D/A converter and I/P transducer.

The heat exchanger is a Type 40-1018 finned-tube exchanger as manufactured by the Brown Fin Tube Co. The inner pipe is 23 feet long inside the U-form of the outer pipe (shell). Steam flovs into the shell

with continuous discharge of condensate. The f l w of side which is terminated at the bottom by a condenser

cooling water in the inner pipe is countercurrent to the steam flov. A surge type tank with another steam control valve and pneumatic controller is used to maintain the steam pressure to the heat exchanger. This was nominally 25 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 (b and Two) can be monitored by means of platinum resistance probes with the associated electronics by Stow Labs, Inc. These provide a signal of 10 millivolts, nominally per 1 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 test runs. 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 by m e a n s of a dual slope AID module with conversion times in the

noisy to the extent of about 10 MV even with this 10 millisecond range. The water temperature signal is

integrating type converter. An external clock circuit provides an interrupt to the Meta 411800 computer after the A/D conversion has taken place at 0 .5

also amplified for recording on an industrial type second intervals. The analog temperature signal is

strip chart recorder manufactured by Fischer 6 Porter Co. The pen lag is about one-half second so that s ~ m e smoothing of the recorded water temperature responses occurs.

The control program used on the e t a 4/1800 computer is written in Fortran with some 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 at 0 . 5 second intervals after the timer interrupt indicating com- pletion of the AID conversion is sensed by the computer. After a test run is ccmpleted, operational data and the response values can be printed if they are desired.

Control Hethods

study are indicated by the block diagram of Figure 2. The signal, M, to the steam control valve is a l s o applied to the first order model operator, k, to give 4. the undelayed model response. In the digital computer this is achieved by a standard fourth order Runge-Kutta integration at 0 . 5 second intervals of time, t, for

The model-based control schemes used for this

with

Here, % is the static model gain (MVlX valve opening) and lM is the first order model time constant in seconds. The model bias value Ci should be the inlet water temperature for WO 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 Figure 2 according to

B*=<+(Cp-<).

A PI controller is used for the main process controller, Gcp, as part of what is termed here the Smith Deadtime Compensation (SDC) method. The PI algorithm used is a two point difference form for

= Mo + KmE * + - K c P 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 constant by the D/A over the next time interval

PI control (PIC) without Smith's predictor E* becomes and is constrained to the 0-100% range. For regular

the true error, E=R-Cp. Here, Kcp is the proportional control gain ( X valve opening/MV) and lIP is the integral (reset) time in seconds.

The Gain-Adaptive Deadtime Compensation (GADC) method is Implemented by using Em=$- in another two-point difference approximation for PI 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, as I$, changes, the proportional gain KcP of the main process controller is changed such that 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.

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Experimental Results

The main experimental resul ts of t h i s s tudy are indicated by t h e o u t l e t water temperature responses shown by Figures 3-11. Other data are given in Tables I and 11. The s teady s ta te opera t ing condi t ions for the test nms a r e l i s t e d in Table I and some steady state r e s u l t s are given i n Table 11. For a l l of t he s t r i p cha r t r eco rd ings of t he tempera- ture responses shown in F igures 3-11, four divisions correspond to 22.86 seconds.

For the base water f lov ra te Fwl, an open loop

valve between 30 and 50% open. The recorded responses test vas f i r s t made by step changing the steam cont ro l

are reproduced in Figure 3. Based upon these responses, a model d e a d t h e of ~ ~ = 4 seconds and f i r s t

order time constant of T =15 seconds vere se lec ted M f o r use with the model-based cont ro l schemes. The step-down response vas a l i t t l e slower than the step-up response. The s ta t ic p rocess ga in vas com- puted t o b e v 9 . 3 based upon the s teady state

temperature var ia t ion for the out le t water from 1355 t o 1541 MV. A s t a r t i ng va lue of %=lo vas f i r s t

s e l ec t ed fo r use v i t h t h e model-based methods and appl ies for Figures 4-7. For Figures 8-11, a s t a r t i n g value of v 1 0 . 8 vas used as discussed later.

The cont ro l methods that vere t es ted a re no ted again by the following list with the designat ions t h a t are used to ident i fy the response curves in Figures 4-11. These are as fo l lovs :

"PIC" Method for regular P I cont ro l ; "SDC" Method for Smith's Deadtime

Compensation method; Method fo r t he Gain-Adaptive Deadtime Compensation procedure.

I I G A D C I I

For t he PIC method, values of Kcp=0.3 and rIp-15

Nichols8 set t ings) to obtain the "A" responses shown seconds vere used (in good agreement with the Ziegler-

in Figures 4-7. For t h e SDC and GADC methods, t h e value of rIp=15 seconds vas used throughout the tests.

Values of Kcp=0.3, 0.4, and 0.5 with YlO were f i r s t

t r i e d f o r t h e SDC Method. In Figures 4-7, the "B" and "C" responses are f o r t h e SDC Method with Km=0.3

and 0 . 5 , respectively. For t h e "E" response i n Figure 6, a value of Km=0.4 vas used. For the 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 f o r a l l nms. Values of KcA=0.05 and Km-0.5

vere used t o o b t a i n t h e r e s u l t s shown by the I'D"

respoases in Figures 4-7. In these cases a model bias temperature of %=SO0 MV w a s used. This agrees

with the inlet water temperature of 902 MV for these nms. When the model bias temperature vas r a i s e d t o 1017 MV, it vas found necessary t o u s e a KCA-0.01 t o

obtain the GADC responses shown in Figures 8-11.

A value of K0cKcp5=5 vas considered appropriate

f o r t h i s system with SDC and GADC methods. The l a rge r Km=0.5 can be jus t i f ied s ince the deadt ime is a

deadtime equal t o o r g rea t e r t han t he time lag , a f r ac t ion of the t ime lag. For a process with the

more conservative value of KO; in the range of 2 t o 3

vould be appropriate as rec-nded by Palmor and Shinnar .9

The responses for the outlet vater temperature

point from 1400 W t o 1300 HV; vbereas, those for shovn in Figure 4 are f o r a step-dovn change in set-

Figure 5 are for 1300 W t o 1400 W . These are f o r the constant water flow rate Fwl. The PIC method

shovs more osc i l la t ions for the step-down due t o t h e increasing process gain in tha t d i r ec t ion . The model-based responses for the SDC and GADC methods show good behavior in these cases.

Responses a t a constant set-point of 1400 MV and

Figures 6 aad 7 . For Figure 6 , a s izeable s tep- for step-decreases in water flow rate are shown in

PIC method becomes continuously oscil latory. The decrease in vater flow rate vas made. As shown, the

SDC method with Kcp=0.5 or K '-5 and Ci=900 MV is on

the verge of doing so. Eovwer, for values of K0p4

and 3 , the SDC responses are shovn t o become more s t ab le and convergent. In Figure 7, responses are shovn f o r a more moderate step-decrease in water f l o v r a t e from Fwl t o Fm. The PIC method is beginning t o

show the sustained osci l la tory condi t ions; vhereas , the other methods give about the same behavior.

OL

The response Curve "D" f o r t h e GADC method shown in F igure 6 would seem t o confirm that the method maintained s tabi l i ty as desired. Upon checking the "print-out", i t vas noted that % was adjusted to

about 14.5 before the test run vas begun. The reason this occurred is that the gain-adaptor vas forcing a match between the s teady s ta te p rocess and model responses. It d id mean, hovever, that the value of Km had already been adjusted to about 3.5 before

even without gain-adaptation the response vould be the step-decrease in v a t e r f l o v r a t e w a s made. Thus,

convergent, similar to Curves "B" and "E" on Figure 6.

The problem noted above pertaining to the init ial adjustment of t h e model gain stems from the non-linear nature of the process. The s ta t ic p rocess ga in var ies with the steam valve opening, M, at any given vater f l ov r a t e . In order to he lp c la r i fy and charac te r ize th i s , the s teady state outlet water temperature vas obtained for each of several valve settings, M, as shown in Table 11. As expected, the data show the s ta t ic process gain decreasing as the steam valve is opened. In f ac t a s t he va lve is opened, slugging of a steam-condensate mixture out of the condenser

use a linear model, it vas decided t o a d j u s t t he b i a s can occur a t t he lower vater f low ra t e s . In order to

temperature (intercept) and v i s u a l l y f i t a s t r a i g h t line to the data for temperature versus valve opening up t o 50% f o r t h e v a t e r f l o v r a t e Fwl. This yielded

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 f o r the SDC and GADC

methods to obtain the responses shovn in Figures 8-11. This way a f a i r e r comparison between the methods could be obtained. It vas necessary, hovever, to avoid condi t ions for vhich the s teady s ta te valve

vas now about 117 MV l a r g e r t h a n t h a t f o r t h e i n l e t opening vould approach zero since the bias value

water temperature. Of course, negative values of

could not be allowed. %

In Figure 8 and 9, the temperature responses are shown for s tep-decreases in v a t e r f l o v rate with the

different set -points . For the rev ised model SDC and GADC procedures control l ing for three

294

conditions (new bias va lue and gain) the SDC procedure with Kcp=0.5 is shown by Figure 9 to converge fa i r ly

well at the 1400 MV set-point. This was no t t he case fo r t he b i a s va lue of 900 MV used t o o b t a i n t h e "C" curve in Figure 6. This is an in t e re s t ing s i t ua t ion tha t requi res fur ther inves t iga t ion . As the set-point is lovered to 1300 MV t h e SDC sys tem osc i l la tes for the indicated water flow rate change. A t the higher set-point of 1400 MV, it took a greater change in the water f low ra te to effect osci l la tory behavior .

The gain-adaptive procedure with KcA=0.05 did

not y ie ld sa t i s fac tory resu l t s e i ther for the water flow rate changes made at the higher and lower set-points. It d id p rovide sa t i s fac tory resu l t s for t h e 1400 MV set-point as indica ted by Figure 9. This t ime the model gain was c l o s e t o t h e init ial value of 10.8 when the test run was made. For the o ther set-point cases noted for Figure 8, the KCA value of 0.05 would r e s u l t in the model gain changing too much a s t he steam control valve closed. This aspect a lso requi res fur ther s tudy to see i f some modification of the algorithm would help. The problem is s imi la r in some respects to "reset-windup" for regular PI control v i th unconstrained integral act ion.

y i e l d s a t i s f a c t o r y r e s u l t s f o r t h e d i f f e r e n t c a s e s as the responses in Figures 8 and 9 demonstrate. One

very slow i n converging to that of the process after problem noted was t h a t t h e model temperature was

the upse t . With the adaptor gain of 0.02 and t h e new bias value, the GADC method provides set-point response behavior which is s i m i l a r t o t h a t f o r t h e SDC. This is shown by Figures 10 and 11.

An adaptor gain of 0.02 was t r i e d and found t o

Conclusions

A procedure which includes adaptation of the model gain in Saith 's l inear (deadtime) compensation

process. Adjustment of the steam flow (valve) is scheme has been applied to an actual heat exchange

After some adjustment of parameters for the pro- required to control the outlet water temperature.

cedure, i t i s shown to successful ly adapt the process control ler gain to provide a s table control system in

rate. Smith's method without the gain-adaptor i s the face of s ign i f icant decreases in the water flow

poorer performance is obtained vl th 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 appl icat ion has directed a t tent ion to problems associated with properly biasing the l inear model response. These stem from the non-linear var- i a t i o n of the process gain with control effor t (valve opening) and fur ther considerat ion is ce r t a in ly indicated.

References

1. Smith, 0. J. M., Chemical Engineering Progress,

2. Smith, 0. J. M., Feedback Control Systems,

3. Smith, 0. J. H., ISA Journal, Vol. 6, No. 2 , Ch. 10, McGraw-Hill, N e w York (1958).

pp. 28-33 (1959). 4. Davidson; J . M. and L. D. Durbin, 1979 Jo in t

Automatic Control Conference Proceedings, p. 468 (1979).

5. Huang, L. E. and L. D. Durbin, 1978 Joint Automatic Control Conference Prodeedings,

Vol. 53, NO. 5, pp. 217-219 (1957)-

Vol. 2 , pp. 109-121 (1978).

6. Chiang, H. S. and L. D. Durbin, 1980 Jo in t Automatic Control Conference Proceedings, Vol. 2 , Paper PAS-E (1980).

7. Chiang, H. S. and L. D. Durbin, 1980 Annual ISA Conference Proceedings, (Oct. 1980).

8. Zieg ler , J. G. and N. B. Nichols, Transactions of t he ASME, p. 759 (Nov. 1949).

9. Palmor, 2. J. and Shinnar, R., 1978 Jo in t Automatic Control Conference Proceedings, Vol. 2 , pp. 59-70 (1978).

TABLE I

Steady State Operating Conditions for the Test Runs

Steam Pressure to Heat Exchanger = 25 psig. I n l e t Water Temperatures, TWI:

902 MV fo r t he Responses in F igures 3-7; 894 MV fo r t he Responses in F igures 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 in F igures 4-7, the water f low ra tes a re those in ( ). These were higher due to an unexpected increase in water supply pressure a t the end of the extended period required to make the t es t runs .

MODEL SET-POINT

DSC KETA 411800 COWPUTER READER

PRINTER

t ELECT.

PT. SENSOR - - I * Two OUT 4 WATER

HEAT EXCHANGER

Fig. 1. Equipment Diagram f o r Heat Exchanger Control System.

B*

Fig. 2. Control System Block Diagram Showing the Gain-Adaptor = G

CA'

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TABU I1 Steady State Heat Exchanger Data

A. For Water Flow Rate FYI:

Valve + 10 20 30 40 50 60 ( X open) Two (W)+ 1105 1240 1360 1472 1542 1567

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 Responses for 30-50% Valve Opening at Water Flov Rate Fwl. . . . . . . +-g .. WATER m w RATE = FA. 4 1 -

. .

.... ... ._ . -.+ - +L..:-*...JA:L.-2-A

- - -. D. (GADC; Kcp=0.5; Ku=0.05) . .

A. (PIC; Kcp=0.3)

Fig. 4. Controlled Temperature Responses for a Step-Down in Set-Point from 1400 to 1300 HV.

Fig. 5. Controlled Temperature Responses for a Step-up in Set-Point from 1300 to 1400 MV at Fn.

"Z" marks zero time for all responses.

Fig. 6. Controlled Temperature Responses for a Step- Decrease in Water Flow Rate from Fwl at 1400 MV Set-Point. to Fw3

296

D. (GADC; Km=0.5; KcA=0.05)

Fig. 7. Controlled Temperature Responses for a Step- Decrease in Water Flow Rate from Fwl to Fm at 1400 MV Set-Point.

Fig. 8. Revised* SDC and GADC Responses for Step- Decreases in Water Flow Rate. (Curves "A" and "B" are for a 1300 MV set- point with a water flow rate change from Fwl to Pw3 . Curves "C" and "D" are for a 1450 MV set-point with a water flow rate change from Fwl to Fw4.)

*Figures 8-11 are for the SW: and GADC methods with KGp=0.5 and the revised values of 9 1 0 1 7 W and

%=10.8.

Fig. 9. Revised* SDC and GADC Responses at 1400 KV Set-Point and a 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