Dynamics and Control of a Process with Recycle Streams

Copyright \\,· IFAC Advanced Control of Chemical Processes . Banff. Canada. 1997

DYNAMICS AND CONTROL OF A PROCESS WITH RECYCLE STREAMS

J. o. Trierweiler*, B. Schulte, and S. Engell Process Control Group, Department of Chemical Engineering, University of Dortmund, D-44221 Dortmund, German)', E-MAIL: {jorge.engell}@ast.chemietechnik.wli-dortmlllld.de Abstract: The dynamic behavior and the control of a heating system with recycle streams are analyzed using a nonlinear grey-box model. The analysis led to the conclusion that the system can become unstable at low frequencies . The instability was verified in experiments and possible solutions for this problem are discussed. A control strategy thm works for a wide range of distilling mixtures and operating conditions is derived. Finally, a startup procedure is presented. Keywords: processes with recycle streams, heating system control. control structure selection, grey-box identification, startup Fig. I has two functions: it prevents that the pump P3 runs dry and it increases the energy holdup in the HS thus reducing the coupling between the heat inflow and the outflow to the column. The energy is provided by adjustable electrical heating elements (EU) in the electrically heated tank (EHT). The water leaves the EHT following two parallel paths: one via the tube side of the vertical thermosiphon reboiler, thereby giving part of its heat to the column, and the other via the manual bypass valve V6. Both streams come back to the tank via the plate heat exchanger which is not utilized in normal operation. The control strmegy proposed in this work uses the measured temperatures TI_30 I. TI_302, TI_I 14, and TI_162 , and the volumetric flow FI_305 . The manipulated variables are RV3 (position of the control valve RV3) and EU (adjustable electric al heating elements).

1 INTRODUCTION Recycle streams occur when two systems are connected by at least onc forward and onc backward stream. Although often the subsystems of a system with recycle streams are rather simple (e.g., the trays of a column), their overall behavior can be complex and very different from the behavior of the individual elements . Complex dynamics may in particular result from positive feedback between the systcms. This paper deals with the heating system (HS) of a multi-purpose packed distillation column (MPPDC) at the University of Dortmund (Trierweiler, e[ al., 1996; Trierweiler 1996). The HS itself is interesting, since it is a prototype process with recycle streams. The HS provides the heat flux into the column, which is an important manipulated variable for composition control. The control goals to be achieved for the HS are fast closed loop respollse [0 se[poin[ changes and keeping [he heal dll[Y [ 0 [he colullln as constall[ as possihle. Achievement of the first goal provides decoupling between composition control and heat duty control. The second objective reduces the temperature variations in the column produced by the nonequilibrium temperature dynamic s as discussed in Trierweiler, e[ al. (1906). In this paper. a control strategy that achieves the mentioned control goal s for a wide range of distilling mixtures and operating condition s (e .g., v
(Q

T%J = surrounding temperature

C/I~li :eb

PHE

Tank

t. txr...

r-,

!v I ~ ~

i:\ : I I! : . I

~

i ~

{;;~ )

T.

" '---'"

.

A; " ', [ t/s[ ;

"' \I:sl! i

!:~ . ,

i

P3

Vb

s.H~

L-.: T"

2 DESCRIPTIO!'; OF THE HEATING SYSTEM

i ·.-~

I

0

I

.II

: 11 ' . 302 .

'

I.

i (~6~'J i

'-'

,

i _

~'fT~I ....

/n~-\ T_30 1• •

,v b, TC l-

:-,~l j

u_

T

!

Q~H

I X i_

~~

. f'-'~

_ _L---iM_ _ _ _&_C 5_ .-J1 ,

T;ri~

Fig . I shows the heating system in detail. The centrifugal pump P3 causes warm water to circulate in closed loop. To avoid that the water evaporates, the pressure in the heating system can be adju sted manually up to 10 har. The tank in

I

I

T,

RV3

F, [l is).

'El3

Fig. I : Healing sysleJll of the MPPDC

In the next section , wc show how a relatively simple moLlel C:.ln be uscd to sulve the control problem .

3 NONLINEAR GREy-Box MODEL 3, J The llIathelllaticallllodel

* Present address : Laboratory of Process Control and Integration (LACIP) - http:// www .enq .ufrgs.br/-Jorge Rua Man::chal Floriano, 50 I ; 9()()~()-061 Porto Alcgre BRAZIL

As the system oper:.ltes ill closeLl-loop, i.e., there is no loss of mass in the HS , the system dynamic s are described by

221

the energy balances of the components. The model is given by (see Trierweiler (19lJ6) and Schulte (1995) for details):

elTT -K . F{(I(/t

-

I

f;)7 + f; F If F

7 -7 R

T

where r is the time necessary to achieve the end position for a given LlRV3. The valve RV" needs 60s from fully closed to fully open (100'7e). Small variatIOns of RV" thus are favorable for the control performance.

}-~(T -T) F".j T ( la)

3.3 Parameter estimation Two sets of data were used to validate the model. The first set was obtained by open loop experiments for the CEmixture. The second set was obtained in closed loop operation for the MAW-mixture. All experimental data was ohtained for the situation where the bypass valve V6 is set such that the maximal flow rate F, IS 1.3 l!s.

(Ib)

r

tlT =-K (T -7

tit

•

le

H

)"' ''(~+~+K' F' F'~"

F

II h7 .

)(IF,n)"·"

a) Parameter optimizatioll IIsillg open-loop data. Experimental results showed that matching the experimental data obtained by variations in RV3 is a lot more difficult than for variations of EL3. The parameters K,. K., K 15 • and Klh in (I b-c) were optimized. A simulation with optimal parameters is presented in Fig. 2. Observe that the simulation and the experimental results agree very well. Fig. 3a shows the simulation for the same experimental data as in Fig. 2 for the thermosyphon reboiler alone. The experimental results are exceptionally well reproduced indicating that the model can only be improved using a better model of the other components. With the model obtained for CE. we designed a controller which was also applied to the distillation of MA W. These experimental results are discussed in the next sections.

7

+ K, · EU (I c)

K7 /(4,3-KI7 · T,).(TR - ~) I

K"

I

(Id)

+~----~----,-

([ K,,' t;".• -IOO]K1,)

Only the parameters related to heat transfer coefficient in the EHT were optimized. The other parameters were determined from first principles and standard correlations.

3.2 Some aspects of the model a) Heat trallsfer ill the vertical thermosypholl reboiler. The modeling of thermosyphon reboilers is complicated due to the fact that the fluid circulation rate cannot be determined explicitly. Circulation rate. heat-transfer rate. and pressure drop are related, and an iterative calculation procedure has to be used to determine the heat flux. The typical procedure found in the literature for the calculation of the heat flux requires the knowledge of many physical and thermodynamical properties of the mixture. In Sinnott (1993) it is shown. however. that the iterative solution can be represented well as a function of the reduced temperature. Thus. we used the following expression for K7 in (Id):

(3) TI_301 and

T'~302

142

E1411':~TI _301

..... 140.5

140

TI_302

139. 50:---:C500~--C::'00:::D'----'I~500=--:2=OOO=---::2::':500:::--::3000::::::---:::35-:::00::---::4000=:---4-::500=-

1.4 , - -- - - - - - -- - - - - - - - - - 13.5 13 12~

12

(2) 04

where T, is the reduced temperature for organic mixtures or equal to I for aqueous solutions. For the determination of the parameters a and b, we used two different mixtures: the aqueous mixture Methanol! Acetonitril/Water (MA W) and the organic mixture Chlorobenzene/ Ethylbenzene (CE) (T,= 0.64). This model of the heat flux is the basis of the control strategy presented later. Note that T, automatically takes the effect of changing mixtures and/or operating conditions into account.

[I_(' - n. ]( -'(-.I'-

Mi ) LlRV3 ,, '

60s r = - - LlRV3. 100%

11

SOO

1000

1500

2000 2500 Time I s I

3000

3500

4000

4SOO

(a) CE mixture

(h) MAW Illixture

..'1-- - - - - - .

- - - -- - --=" /1

i~k~~~~·

c) The dYllamics of thl! control I'alve RV3. As one of the manipulated variables of the HS is the valve position RV3. it is important to know its dynamic characteristics and its relation to the volumetric flow F,. The valve RV3 is a motor valve which operates at constant speed. This is responsible for a special dynamic characteristic of RV3: the time required to change the volumetric flow depends on the amount of change. This is approximated hy the following irrational tr:lIlsfer function:

M2(S)

o

Fig. 2: Comparison of the experimental data for the CE mixture in open loop operation (dotted line) and the model (solid line)

b) Total flow rate alld thl! illfluence of thl! bypass. In (la-d) . the main nonlinearity results from the flow rates F. F ,. and F, (sec Fig. I). Only F, is measured (FI_305J. The other two flows arc ('.llilllut"" using the pump characteristic.

LlRV3(s) =

2

115

Fig. 3 : Simulation of the \'ertical Iherlllosyphon rcboikr (cq . ld) wilhoul the other cOlllponenls (resp . equations): (a) CE mixture (experimental dala of Fig . 2) and (h) MAW mixture (dala of FigA)

b) Parameter optimizatioll with closed-loop data. Parameter optimization for the MA W mixture was

(3)

222

performed using closed loop experimental data in the interval 0-3500 s. The rest of the experimental data of Fig. 4 was used to validate the model. Here the parameters K , . K~. KI~ ' and K~ II in (I b-c) were optimized. Fig. 3b shows that the model of the vertical thermosyphon reboiler is accurate for the MA W mi xture but th e quality of the overall model is not as good. in particular. the model predicts fast reactions of the system while the real system shows very smooth responses.

4.1 Lillearized models To analyze the system. we use a set of linearized model s. As the main nonlinearity of the system (I a-d) is the volumetric !low. we linearized the model for the CE mixture for different values of F~ . We chose 7 linearized model s corresponding to the following values of F~ : Cl : 1.2. C2 : 1.1. C3: 1.0. C4 : 0.9. C5 : 0.8. C6: 0.7. and C7: 0.6 lis. Q I-Q7 and IIT l-llD represent the corresponding linearized models of the structures with Q resp . .1T as outputs . For all transfer functions . channel I I represents the tran sfer function from RV3 to Q or .1T. channel 21 from RV 3 to TI_30 I. channel 12 from EU to Q or .1T. and channel 22 from EL3 to TI_301 .

"~ T.I_ 3.01 _

-~ u

, 88 ~ ~

.

.

. ~

82

.

..

.

There is a large difference between the response time s related to the manipulation of RV3 (or F1 ) and of EU. This difference is caused by the positive feedback introduced by the recycle stream. Fig. 6 illustrates the positive feedback mechanism that governs the response to EU. Each block in Fig. 6 can be represented by a low order transfer function. To keep the discussion simple. we assume that the effect of the bypass. the vertical thermosyphon reboiler. and the heat losses can be captured by a proportional ekment k. i.e .. the transfer function C, in Fig. 6 is given by

TI _ 302

84

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

(b) FI _3 05 and El 3

14.-------------~~--------------------, 50

40

-12

30~

u::

0

e

0 6

o

1000

2000

3000

4 000

5 000 6 000 Time I s)

7000

8 000

9000

0 10000

Fig. 4 : Comparision of the experimental data for the MAW mixture in closed loop operation (dotted line) and simulation with the non linear model (solid line) Only the experimental data until 3500 s was used for parameter estimation.

4

EL3 - Q - Qhm/to.Ho (5) - - - - - - - , OSkSI. EU This is equivalent to the assumption th at the tank inlet temperature TT;" is smaller than TI_301 by a factor k. i.e .. TT,"= k TI_301. The factor k depends on how much energy remains in the system ( EL3 -Q-Qnml'o.uo ) in comparison to the energy introduced (EU).

CONTROL STRUCTURE SELECTION

To control the heat duty. we can use the temperatures TI_30 I and TI_302 and the volumetric flow FI_305 as measured variables. and RV3 and EL3 as manipulated variables. One obvious candidate structure is the direct control of the heat duty Q. which can be calculated as

Q=pc t ,FI_305(TUOI.TU02) .

I

~r

(4 )

As Q is calculated from three measured variables (i.e .. FI_305. TI_30 I. and TI_302). the sensor noise may be amplilied considerably. If wc choose.1T< TI_301-TI_302) as the controlled variable instead of Q. the effect of sensor noise is reduced . since then the errors of FI_305 and .1T enter at different points of the control loop. Fig. 5 shows how the llT - structure must be implemented to control the heat !lux Q. In this figure C represents the plant dynamics (in the .1T-structure ) and K is a stabilizing controller for C. The sign reversal is necessary because of the coupling from the actuated variable to the reference signa\. r. T =---0-","'

pc FI 305

P

.o---+u

.

~K FI _305 G I

~-

EL3

Q_-

+ Reb

Fig. 6 : Schematic representation of the positiVI: feedback hetween ELl and T,-.101 According to the theoret ical model (I a-b) . C , and Cc re sult I I as C\(.I ) = - - , C~(s)= --. (6)

-r-'.1::::T~_

___

r\s+1

-LT

r2s+1

With these transfer functions . the closed-loop tran sfer function from EL3 to TI_301 is given by

Fig. 5: Implementation of the control of Q using the LiT-structure

TI_301(s)

As the HS has two process degrees of freedom . we can choose one other controlled variable . A natural chOICe is the control of TI_30 I. since thi s variable for maximal volumetric flow gi ves the maximal poss ible heat duty into th e column. Moreover. the temperature difference between TI_30 I and the bottom temperatu re of th e column is very important for the operation of th e vertical thermos yphon reboiler. Thus. the fo llowing two altern:lti ve structures are investigated : the Q-structure (RV3-tQ. EU-tTI_3(1) and

EU(s)

r I r ~s ~ + ( r I + r ~ )5 + I

'

(

r,r ~ s-+ r,+r~

)

)s+l-k C,. (s .

For k close to I . (7) represents a system with slow response and large steady-state gain. For k = I. the system has a pole at the origin . The high frequency response is independent of k indicJt ing that fast closed lo op control will reduce the vari:ltions of the dynamics . This is confirmed by the frequency responses of channel 22 in Fig. 7<1. The curves in Fig . 7 represent th e linearized model for different !low rates. equivalent to different values of k. In Fig. 7a. the transfe r function from RV3 to TI_301 (ch annel 21) at low

the ,H- structure (RV3-tllT. EL3-tTI_301).

223

stable under integral control if the condition

frequencies changes its sign twice when the now increases from 0.6 lis to 1.2 lIs . The steady-state gain is positive for G7(O.6 lIs): almost zero for G6 (0.7 lis): negative for G2. G3 . G4. and G5: and again positive for G I (1.2 lis). Two counteracting effects are responsible for this. The first effect is related to the tank inlet temperature TT," ' The second is related to thl! effect of the factor k in (7). The intluence of RV 3 can be analyzed as follows: 6 RV3 > 0 ~

f2 i,

Fj L

Qi , d

Igl'n - g~'l W2 = [(in"n)I "

I

r R~I

Fi ~

6T.1. , TI_302 i ~ TTill i ~ 6TI_301 > 0 (effect A) {

fl~.r('(//("'ICNI(O)W~)
~ 6TUOl<0 (effect

(8)

B).

(a) CE mixture

Uc:?J ,,'

:

,

\

,

"

_0 5

"

'"

~

- I ~

_ ,

,

", . .~:

- .,

II

-'

11

I

3

~

RE AL

(b ) MA W mixture C hilOlMJ'

C llilnnel 12

1 1

_0

'" ~

0 5~

-0 I

.

-0 IS! -u-1,I':;-,- - ; : ---;;-:;-----o: R E .... l C ha n nel 22

~ ~::; RE Al

',,'.,,' ....

~.>',','

11 XII

:

Tahle I : Steady-state robust stahility analysis using ('}) Nominal Model Q3 Q4 0 .67 0.46 0 .22 0 . 15 O. I'} 0 0 0 .21 (U8 0 .65 0 .85 1.17 1.60 1.2~ 1.24 1.60

G.

-J.-

u~ i "' " : , ,

0 . c-----o-

_01 \

NI IRn..' - gnnNI ' Inx .. is the identity matrix of dimension

Rnl

is satisfied (Morari and Zafiriou. 1989). In (9) g/ and g./ are the elements ij of GN and of C, E P={CI ..... Cl}. respectively. Table 1 presents the evaluation of (9) for the Q models obtained for the CE-mixllIre. Based on these results. we can conclude that if we design an inverse-based controller using Cl . C2 . G3. or C4 as the nominal model. the closed loop system will not be stable for all flows F! . Table I also shows that using C5 as the nominal model yields the largest stability margin and the closed loop system stays stable for an inverse-based controller based upon models C5. C6. or Cl. These results are related to the change of the sign at low frequencies that occurs in channel 21 (cr. Fig. 7a) . but this sign change is not sufficient to explain the instability. since Q 1 has a good stability margin for the nominal model Q4. whereas Q7 has not, and in both cases. channel 21 has a di fferent sign at low frequencies. For the stability analysis it is necessary to consider the effects in all channels simulaneously. Nonetheless the sign change in channel 21 is a good indicator of the stability prohlem and its physical origin which is related to the bypass flow F,. Note that C6 and Cl are models where the nows F, (= 0.6 lIs) and F! are about the same. Similar conclusions hold for the LlT-structure.

Effect A has positive gain and the effect B has negative gain. Thus. for G7 effect A > B; for G6 A = B: for G2. G3. G4. and G5. A < B: and forGI A> B.

(!I

-

(i" xn)n1

QI Q2 Q3 Q4 Q5 Q6 Q7

H EAL

Fig.7: Nyqui st·plot s for the ~T - struclUrc for (a) CE and (b) MAW mixtures : ~TI (points ). ~T2 (solid line). ~T4 (dashdot line ). ~T6 (dashed line). and ~T7 (dotled line). All responses turn clockwi se with increasing frequen cy.

Max

QI 0 0 .69 0 .89 0.71 0.69 0 .76 1.21 1.21

Q2 0 .60 0 0 . 17 02K 059 I IK 1.66 1.66

(G",)

Q5 0.41 0.41 0 .51 0 .34 0 0.42 0 .76 0 .76

Q6 0 .43 0.75 082 0 .67 0 .37 0 OJI OK2

Q7 0.63 0 .94 0.99 OK5 059 0 .27 ()

O.'}'}

The same analysis was performed for the MA W model I not shown here) and showed that the Q and LlT models obtained for the MA W mixture do not exhibit thi s effect. Thus we conclude that if instability is observed at the real plant for the MA W mixture. the model for MA W is not correct at low frequencies .

In Fig . 7a. the responses were generated from the grey-box nonlinear model obtained from open loop identification with input signals concentrated at middle and low frequencies . Fig . 7b. on the other hand . corresponds to closed loop identification. i.e .. to input signals with more medium and high frequency content. A comparison of Figures 7;]. and 7b shows that at higher frequencies both models agree to some extent . but at low frequencie s there are significant differences . markedl y in channels 21 and 11 .

4.3 Experimental collfirmation of instability Figures g and 9 show experimental results obtained with the following decentralized controllers:

5.216s~ +O.254s+0.000111

. { -0.1219

K ..H4 = d/{/~

The disagreement at low frequencies between both model s in Fig. 7 can have two reasons: (i ) the MAW mixture modifies the response of the thermosyphon reboiler so that the effect A in (8) is always smaller than the effect B or (ii) the mathematical model for the MA W-mixture does not represent the system dynamics correctly. This was already indicated by Fig. 4 and is supported by the results in the next section .

'

.\

. r - 0.0962

K l> T6 =dwR i

l

0

.1'-+0.01775.1'

5.652 s~ + 0.2071s+ 0.00005} , >

.l"

f (IOa)

J

.1"-+0.01353.1'

.( IOb )

The controllers Km and K~T' were calculated based on the nominal model t.T4 and 6T6 . respectively. using a sequential design procedure . Figures 8 and 9 show that the CE-model predicts the instability correctly. Only for the controller designell for t.T4 . the HS becomes unstable for small now rates (less than 0.2 lIs). Moreover. this results conlirms our

4.2 Instability ullder illtegral cOlltrol A stable nominal 11 x 11 system C N subject to real. stable . independent. channel perturbations 8, will he rohu stly

224

hypothesis that the instability is related to the low frequency characteristics of the HS. since in Fig . 8 it takes almost 2 minutes until the instability hecomes visible. Fig. <) confirms the prediction that a controller design hased on G6 (or G5) will give better robu st stahility . Although the flow rate reaches a very small value W. I I/s) the closed-loop system does not become un stable . la ) 0

Loosely speaking, the controller in this G1Se will have a performance equi valent to Km for setpoint changes and act as K' Th for disturbzmce compensation . Reduction of the manipulating range of RV3 . The instability only occurs when the !low through the bypass valve V6 is larger than through RV3 . The experimental results indicate that it happens when the valve RV3 is less 30% open . Hence. if we reduce the operating range of the valve RV3 from 0-1000/,- to 30-100o/c . the instability problem is solved automatically. As we will see in section 5, this reduction of the operating range does not affect the controllability of the system.

I kW I ( Solid I ,n .) I 0,.1 Cdoll.ct line )

The third solution is the simplest alternative to be implemented in a process control system and, therefore . was our choice. In the choice of the operating conditions for the HS, the brpQss m/l'e V6 and the lelllperalllre differellce (TI_30 1-TI_I 14) are important. • The bypass valve V6 has a strong innuence on the dynamics of the HS . Experimental and simulation results show that if the bypass valve V6 is closed, the unstable hehavior produced by an inverse-based controller will not occur. The main purpose of the bypass is to guarantee a minimal flow :hrough the electrically heated tank (EHT) . This minimal !low can be guaranteed as well if we limit the operating range of the valve RV3 (e.g .. from 0-100% to 20-100%) . This however is not a good solution, since the main nonlinearity in the EHT is caused by the !low F =F 1+F2 (see Fig. I). Thus the variation in the now F increases with the reduction of the now FIo i.e., by closing the bypass valve V6. Therefore , for the EHT, opening of valve V6 is favorable . The opposite situation is encountered in the thermosyphon reboiler. since here the range of the now F~ is reduced by opening V6. This causes a reduction in the range in which we can change the heat duty Q by manipulation of RV3 . • The temperature difference TC301-TC1l4 determines the gain from RV3 to Q and is fundamental for the correct operation of the thermosyphon reboiler. Due to the special dynamics of the valve RV3 which depends on flRV3 (see (3))' small flRV3 variations are preferred impl ying that only a reduced range should be used in normal operation .

;~:~~~---~--7200~~300~~..~O~.~s~. O.~.~WO~~7~ . . . .O~/~.~o ~l, pi~~~~3~ 1 Time t · ]

Fig. 8: Experimental verilic:lIion of the instability for the CE mixture using a controller basell o n the inverse o f t-T4 . l a ) O ! kW I (SOhd lon e ) 1 0,e' (do n.-d Ion. )

~:;~~ o

SOO

1000

(b ) FI _ 30S { lis

I (s o lid

1 500

2 000

2500

hn e ) I T I _ 301 _ TI _ 3 02 (dashdo lllne )

'r '----------~-------------------------,·

_oar £ 06~

"

~, o . l

0:

I

o

p

2r 0'

o

5 00

1 SOO

. :'

~'

i 'n"

~: ~'

2000

51'!

2500

Fig. 9 : As Fig. II but with controller (lOb) .

In Trierweiler (1996) it is shown that the instability of the HS is not specilic for the flT-structure and the CE mixture. but is caused by the bypass !low F 1• Moreover, it is not directly caused by the control of the temperature TI_30 I. i.e., the instability is due to the control of Q. As we can see by the comparison of the controllers K,,, and Km (lOa, b). channel II for the controller K' T/, is slower than for K,,, which en sures the stability of the HS for low !low rates. Theoretically Q can be increased by increasing F~ and/or flT (see (4» . Due to the recycle stream. increasing F~ will

5 THE CONTROL CONCEPT 5.1 Normal operation

always decrease flT (cl'. ligures 8 and 9). The instability occurs when the variations in F~ are fast in comparison to the flT-variations . Experimental results indicate that the maximal variation rate of F, to avoid the instability is a function of the bypass setting.

The main purpose of HS is to control the heat duty Q to the column. We have two manipulated variables. RV J and EL3 , at our disposa l. Until now , we have seen that RV3 causes a fast response of Q, whereas EL3 gives a very slow response. Loosely speaking, thc HS can be seen as a bnk' where the energy holdup depends on the recycle now rate. In this picture, the energy nux to the reboiler comes from EL3 , i.e .. EL3 is the inlet stream to the 'tank'. For short periods , more cnergy can be transfered to the reboi ler (Q>EU) using part of the energy stored in the HS . The valve RV 3 regulates the outlet stream. We implemented a sort of feedforward control. so that if more Q is required. EL3 is automatically increascd thus avoiding that the 'tank' becomes 'empty' . Another point to be considered is that the temperature ditlerence between the HS and the column bottom must be adjusted to maintain etlective operation of the vertical thermosyphon reboiler.

4.4 Solution of the instability problem One solution for the instability problem would be to use a slow controller as K' T" but this causes a slow res ponse (cl'. Fig . 9). There are several soluti o ns for this problem that preserve the performance but avoid the instahility: Increasing the controller order. Increasing the controller order means to use a PlO controller instead of the PI controller. The problem with this solution can be the measurement noise level. Therefore, increasing also the denominator order is recommended . - Addition of a degree of freedom in the control configuration. The addition of a prelilter can solve the prohlem with the noise level while preserving the performance for set point changes without in stahility.

We c;m write the heat duty as

Q=U R AR flT/"M

225

~ UR AR(TI_301-TU62).

(11)

For a given value of Q"., , we can express TI_301 as TI

-

301=~+TI U AR -

natural convection increases. the difference between TI_114 and TI_162 decreases. Fig. II shows that in the final phase (~30 rnin) the temperature TI_114 has an inflection. This pOint represents the ideal point to put the controllers into Operation . Although the determination of the intlection point for TI _ 114 is possible, we chose to implement a simpler criterion based on the temperature difference between TI_162 and TI_114. When TI_162-TI_114<4.5°C the controllers are put into operation . This startup procedure works for both mixtures and different operating conditions (Trierweiler, 1996).

(12)

162.

R

If we consider the expression for URA R given by (2), the last equation can be written as : TUOI =

(43-3.67;.)

Q"1 +TU62 .

(13)

KO?

This equation can be used to compute the setpoint of the control loop EU ~ TI_30 I. To change the steady state position of RV3 (i .e .. RV3 = 60o/c open) , we include an additional parameter 1Il/l' so that the final formula implemented in the process control system is T_30I rer =IIlA Q"1 +TI_162+IIlB' (14)

~'~~

The parameter III.~ is IIlA = 0.7 (4 .3-3 .6T,). Here T, takes the mixture and the operating conditions into account automatically. The 'theoretical' value of IIlA WJS slightly modified in the practical implementation of this strategy to allow to use the same 1Il/l value for all mixtures. The practicJI and theoretical vJlues are listed in Table 2 for the MA Wand CE mixtures.

o

MAW

CE

m" (practical)

0 .63 1. 34

O.B 1. 25

1 SOo

1000

(82

Tahle 2: Parameters used in ( 14)

m" (theorectical )

soo

o

1 1

soo

1000

1 500

2000

2500

J(X)()

3500

4000

~~; 2000 2500 Tlme { s I

3000

3500

4000

Fig. 10 : Performance of the final control configuration for the MAW

Fig. I shows the linal control configuration for the HS using the f.T-structure , but it can also be implemented using the Q-structure . Note that only one setpoint must be given (i .e., Q"l)' The setpoint for the temperature TI_301 is automatically calculated from (14). Fig. 10 illustrates how this control conliguration works in the practice. During the experiment shown in Fig . 10, the component with the higher boiling temperature (water) was fed into the column, what increases the bottom boiling temperature. Note that the RV3 is almost always in the optimal position of 60% allowing fast variations in Q of ± 2 kW. To avoid the possibility of instability we used a lower bound of 30% for RV3. The reduction of the range of RV3 makes no difference in practice. Other experiments with the column at low pressures also confirmed the sucess of the proposed control configuration .

~,

mixture and 6.T-structure

____________~__I~ . '_ T_ _ ~p_ , ,_ ,,_U'_ " ______~________

1S0-

U l00 ~ ~

_ ...... :

:. :. -_ - - - - - -- :

50F-_ _ _ __

-

: -- -- - -

-

0' 10

20

(b)_0 _( _ solid ). Ore' ( doned ____ _ _ _ _Itne ______ _ hne J , EL3 ( cUsh ed hne )

15

60

I '

-,o'f: ~

~

,

Q

~

________________~4 0

~

20

w

I:

o 5~

me •• me' Powe, ot!

cont~'.rs

ELl

Fig. 11: Experimental verification of the startup procedure for the CE mixture. On the left side of the vertical dotted line (at 32 minI. the valve RV3 is 100 % open and EU is maximal. On the right side the controllers for Q and TI_30 I are operating.

5,2 Startup procedure The startup phase of the column should be as short as possible. Thus, the maximal power in the HS must be used. The critical issue here is the determination of the point when the heating power is retluced to the normal operating conditions. A late power reduction mJY c;)use !looding of the column and bad operJtion of the vertical thermosyphon reboiler. When the maxinul power is used in the startup phase, the resistance to the heat !low into the column is mainly in the thermos yphon reboiler. since in thi s phase the natural convection antl the phJse chJnge. which are resp onsible for the he:ll transfer rate in the thermosyphon reboiler, Jre reduced .

6 CONCLUSION The heating system analyzed here has interesting dynamics due to the recycle stream. We showed how a mathematical model can be used to analyse the process dynamics. This allowed us to implement a suitable control strategy . The tinal control configuration works with very ditlerent di stilling mixtures and shows excellent performance . We also showed how the startup procedure of the HS can be automated for a variety of mixtures and column pressures .

7 REFERENCES Morari, M. and E. Zatiriou (1989 ). Rob/Ht Process COIl/rol. Prentice-Hall International. Schulte. B., ( 1995). Regl'/tmgsstmktllrallalysl' Imd Elltll'lII/ eill£'s rohllstell Reglers fiir die BeheiZlIllgs(llllagl'. Studienarbeit. Univ . of Dortmund. Sinnott. R.K .( 1993). COlllsOIl & Richard.wn ·s-Chem.Eng. Volllllle 6, page 667, Pergamon Press Ltd .. Engbnd . Trierweiler. 1.0 . (1996) . A S~'J{elllatic Approach l~ COlltrol Slmclllre Design . Ph.D . Thesis. Univ . of Dortmuntl . Trierweiler, 1.0 .. V. Rol.\mJnn, S. Engell (1996). Modeling and Control of an Experimental PJcked Distillation Culumn . CESA '96 IMACS. Lille. Fran ce. pp. 456-461 .

Thu s, the mJin problem during startup is to determine the switching point, i.e .. the point where the nJturJI convection in the rcboiler is sufliciently large. The solution of this problem is very simple. We use two temperature measurements. one at thc input and the other one at the output of the thcrmosyphon reboiler. c.g .. TI _ 162 and TI _ I 14 in Fig . I. In normJI operation. TI_114 is slightly higher ( ~ 1°C) thJn TI_162 , but at the beginning. when natural convection is Wo low the opposite situation occurs. i.t! .. TI _ 162 IS higher thJn TI_114 (cl' Fig. Ill. When the

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