Selection of the Best Control Configuration for an Industrial Distillation Column

Copyright © IFAC Dynamics and Control of Chemical Reactors (DYCORD+'92), Maryland, USA, 1992

SELECTION OF THE BEST CONTROL CONFIGURA TION FOR AN INDUSTRIAL DISTILLATION COLUMN D. Ariburnu, C. Ozgen and T. Gurkan Department a/Chemical Engineering, Middle East Technical University, Ankara, Turkey

Abstt'act. The best I'egulatory contl'ol stt'uctul'e is detel'mined fOI' an industrial, multicomponent, high purity ethylbenzene distillation column with 50 trays. Steady-state plant data and the design information is utilized with a steady-state model of the column. The column-model match is obtained by adjusting the column efficiency. Dynamic column behaviour is experimentally obtained by pulse and step testing. Steady-state rating programs are used to obtain the steady-state process and disturbance gain matt'ices of the (L, V), (0, V), (L, S) and (LID, V/B) contl'ol configurations. Steady-state control configut'ation selection methods RI, RGA, NI, MRI, JEC, SVD and RDG and the Eigenstl'uctul'e concept al'e made use of. Single-end and dual composition control of the column is e,
control;

distillation

column;

INTRODUCTION Vat'ious studies have been done on the selection of the best control configuration of distillation columns. Early ones started with the work of Rijnsdot'p (1965) and continued with those of Bt'istol (1966) and Niederlinski (1971). Deeper insight related to impot'tan t closed loop pt'opet't ies is obtained in the 1980's.

the control systems during the last decade. Wallet' and Finnet'man (1987) have suggested that among the various control schemes the structure giving the smallest interaction between the contt'ol loops is pt'eferable. The impot'tance of disturbance sensitivity of control structures has been theot'etically shown by Haggblom and co-workers (1988).

Singulal' Value Decomposition (SVD), developed by Bruns and Smith (1982), is a successful tool in the structut'al analysiS of multi-variable systems. Since pt'imat'y intet'est has been focused on control structut'es t'ather than the actual controller design, the analysis has been done with the open-loop tt'ansfer function. Relative Disturbance Gain (RDG) has been interpt'eted by Stanley, Gallaraga and McAvoy (1985) as a useful measure of the existence of favourable interaction in a control system. Some of the questions that have been raised about the RGA analysis could be removed since disturbance effects were taken into account. It has been proposed that RGA and RDG can be used togethet' in order to assess control-loop operability. The Jacobi Eigenvalue Ct'itet'ion (JEC) by Mijares and co-workers (1986) has been developed fat' the selection of best pait'ing of the contt'olled and manipulated variables for a multi-loop control system.

Dual composition contt'ol is highly t'ecommended by Skogestad and Morar i (1987). However it is difficult to design and tune them. In cel'tain cases, single-end control can have certain advantages ovel' dual composi t ion control with a small economic penalty. Luyben (1988) suggested that each process unit has an intrinsically self-regulating control structul'e which makes the system I'elatively sensi tive to load distut'bances and is self-optimizing and interaction can sometimes be preferable. Thus, Eigenstl'uctut'e concept suggests whethet' single-end control is appt'opriate at' not. Finco, Luyben and Polleck (1989) have carried out the steady-state modeling and analysis, dynamic modeling, control stl'uctut'e selection and Eigenstl'ucture concept of an industrial column. Recently, Papastathopolou and Luyben (1991) studied the control of a binary distillation column with a sides t I'eam conSidering different control conf igul'at ions.

Research on distillation column control has been concentt'ated on the stt'uctut'e of

219

SYSTEM STUDIED

Table 1

The distillation column e xamined in this work (Fig. 1) is an industrial, multicomponent, high purity ethylbenzene distillation column of a Monomer plant.

Plant Data and Specifications

Column

flow rates, Ibmol/hr feed distillate bottoms

58.744 55.994 2.7500

p."essure, psia ."eflux , Ibmol/hr ."eflu x ."atio

18.439 53.500 0.9554

compositions, mol fraction of EB disti llate 0.99986 0.00010 bottoms 0.95305 feed (back-calculated) condenser duty, reboiler duty,

HE fRC

50 21 42.36 42.04 2.992

3.48

+-0

L1

fR STEADY-STATE ANALYSIS

LC

Steady-state ."ating program was used in conjunction with the column design data for the evaluation of the column efficiency by trial and error procedure in order to assess the column-model match. The steady-state model was used to calculate steady-state gains and develop steady-state process and disturbance gain matrices for the four control configu."ations considet"ed: (L,V), (D,V), (L,B) and (L/D,V/B).

D

PUMPS

Fig.

-2.3741 1.9197

no. of t."ays feed tt"ay locat ion height, ft. rectifying section stripping section wei." height, in. diameter, ft.

fEED

fRC

6

10 Btu/hr 6 10 Btu/hr

1.

Industrial column.

PUMPS

ethylbenzene

(EB)

The feed to the ethylbenzene distillation column consists of liquid ethylbenzeneCEB), methylethylbenzenes (MEB) , and polyethylben z enes(PEB) such as diethylbenzene (DEB) , triethylbenzene and tetraethylbenzene with small amounts of benzene and toluene. The concentrations of triethylbenzene, tetraethylbenzene, benzene and toluene a."e ve."y small, therefore these are lumped into EB, DEB and MEB in the simulation studies. EB column plant data and specifications are given in Table 1. The EB composition in the feed is 95.351., in the distillate 99.8561., and in the bottoms 0.017.. The column has 50 t."ays and ope."ates at a reflux ratio of 0.9554. The column efficiency in the steady-state model was adjusted until the steady-state model matched the plant ope."ating data. The efficiency was found to be essentially 1001..

Development of Gain Matrices Gain calculations were done in two consecutive stages. In the fi."st stage, the effects of the manipulated inputs (reflu x , reflux ratio, boil-up, boil-up ratio, distillate and bottom flow rates on y o (EB top product composition) and x B were (EB bottom product composition) found. In these runs feed flow rate and feed composition we."e kept constant. In the second stage, the effect of each disturbance on YD and NB was found while manipulated va."iables were kept constant at the initial steady-state values. Small perturbations were given to the inputs from initial steady-state values in order to find the gains in the linear range (Luyben, 1987). The effect of such small changes on the outputs could only be detected with a model only possible in a simulation study and would not be meaningful in the case of an e xperimental study of an industrial column. The calculated gains are given in Table 2 (A."ibu."nu, 1990).

EXPERIMENTAL PROCEDURE the E xperiments were car r ied out on industrial EB distillation column to collect stead y -state and d y namic plant data. Stead y-s tate plant data was obtained at the column ' s normal operating conditions (Table 1 ). The dynamic plant data were obtained by giving step changes to inputs of the column. The selected inputs were the feed flow rate, reflu x and boil-up rates. Only one input was changed during each e xperiment. Feed flow r ate, distillate and bottom flow rates, steam rate, le v el s in sump and drums , temperatures at se v eral tray s and boil-up stream were recorded. Samples were taken from all inputs and outputs were taken for composition anal y sis.

Table 2 Steady-State P."ocess Gains III

~

m

2

it

le

I( 2~

12

L-V

0.018

-0.0028

O-V

-BE-05

-0.0027

L-B

5E-05

0

0.003

0

L / O-V / B

220

K

V

22

-0.46

-11

-0.24

-0.057

- 0.0013 0.54

0.34 -1.39

A Summary of the Indices Used for the Selection of Steady State Configut'ations

conjunction with RGA is a worthwhile effort to assess control loop operability since RDG overcomes a major limitation of the RGA in that the effects of disturbances are accounted fa.,. Fo.' a system the best al te.'native ;is the one with the smallest RDG and RGA. choice for RGA and RDG fat, a system is the small RDG and small RGA combination.

The control configuration selection indices which are indicative of interaction of the loops, integral stability and controllability are summat'i zed below Ri jnsdot'p Index (RI) is calculated using the four process gains RI=K ~2 K21 IK i t K22 . The static value of

by as RI

Evaluation of Altet'native St.'uctures wi th P.'oposed Ind ices

should be prefet't'ably smallet' than 1, and its value must be zet'o for a non-interacting control structure.

In Table 3 and 4 the indi~es of the different selection methods at'e given fa., the column under investigation. Each st.'uctu.'e conside.'ed has two control schemes as given in tables.

Relative Gain At't'ay (RGA) is easy to calculate and re9uires only steady-state gain infot'mation. Fat' a 2,,2 system, t'elative gain, ~£.is I/(I-RI). If ~ •• =I, there is no In this case, decoupled.

Contt'ol

Table 3a Steady-State Con t.'o 1 Indices Scheme

interaction in the system. the loops are completely

Niedet'linski Index (NI) is a useful tool for stability analysis. Niedet'linski"s theorem is only a sufficiency condition for structured unstability. It is defined as the t'a t i 0 of the detet'm i nan t of the steady-state gain matt'ix and the product of its diagonal elements of the matt'ix. If the index is negative, the system is structurally unstable. If it is positive, the system mayor may not be stable and fu.'the.' analysis is necessa.'y.

RI

NI

L-Yo;V-x B

6.3E-04

L-!{

1590

0.99570

0.026

-0.00159

39.98

D-Yo;V-x B -142.02

143.02

3.32

D-x B;V-YD

0.9930

0.30

B;V-yO

7.04E-04

-(X)

Singulat' Value Decomposition (SVD) is used to assess sensitivity. In the application of the SVD concept, singular values of the disturbance gain matrix must be found. Condition number is defined as the ratio of maximum singular value to the minimum singular value of the diagonal matt'ix, €. The CN should not be large (i.e. smaller than lOO). Lat'ge CN implies that the configut'ation is not robust and is sensitive to modeling

JEC

(X)

(X)

o

o

L/D-y 0; V/B-:
o

o

L/D-:
(X)

(X)

(X)

Table 3b Steady-State Cont.'ol Indices m£

et"rors ..

m

A

2

..

A

MRI

L-V

1.00063

0.9931

26

0.0255

D-V

0.00690

0.9931

59

0.0567

L-B

0

672

0.0013

202

0.9294

L/D-V/B

Morari Resilience Index (MRI) (Morari, 1983) gives an indication of the inherent controllability of a process. It is a useful tool for choosing alternative of manipulated va"iables. The MRI is the minimum singular value of the steady-state process gain matrix. The lat'get' is the value of MRI, the mo.'e controllable or t'esilient is the process.

CN

2i

0

Table 3c Steady-State Control Indices Disturbances

z

F

z ILB

F

z

DILB

WILB

F

111 .1+ 11121

Schemes

Jacobi Eigenvalue Criterion (JEC) is based on an analysis of the difficulty of finding the inverse of the steady-state gain matrix. It is the largest eigenvalue of the Jacobi itet'ation matrix A, [K=D (I-A) J. F.'om the eigenvalues of the Jacobi iteration matri:<, the designer may will be integral controllable and stable ot' not. The values of JEC should be between -1 and 1 and the alternative with the smallest JEC gives the best pairing.

F

L-Yo;V-X B

1. 94

1. 49

1. 88

29.3

D-:< B;V-Y

3.01

2.07

1. 55

(X)

D

L-:
(X)

L/D-yo;V/B-x s 1.32

(X)

4.14

(X)

3.36

00

00

The non-inter'acting scheme of a configuration can be .'uled out by the RGA analysis. Fat' differ'ent configut'ations one must select the positive values of A. c lose to 1. Ther'efot'e, cons ider ins i.j

Table

Relative Disturbance Gain (RDG) considers the disturbances affecting the system. It is used to decide if interaction resulting from a distut'bance is favorable at' unfavorable. The use of RDG in

~

.-~

,

221

RGA

suggests (L-:
and

schemes. The (L/D-YD;V/B-x ) B stability as measured by NI

integ.'al

m-xB; V-YD) ,

indicates

Table 4 Steady-State Oisturbance Gains L-V

O-V

L-B

0.982

0.088

L/O-V/B

11

2E-05

1( 12

-0.004

-0.35

-0.01

-0.009

K

--0.006

-0.01

-0.03

-0.01

-8E-04

-6E-05

f(

13

1.0

1(14

-2E-04

1(21

lE-05

I(~~

-0. 0 86

-0. 0 09

- 0 .099

-0.099

K..,..,..

- 0.00 13

-0.01 3

-0.00 45

-0.034

0.242

-0.0163

";;'.1'..

"':" -.J

1(24

0.162

0 20.7

21.16

applied to CL,V) structure v ia steady-state simulation of the column, it was obset'ved ft'om Fig. ' 5 2 and 3 that, for feed flow t'ate changes the manipulated variables L and V, and for EB feed compOSition changes, L varies almost 1 inea,'ly to keep product composi tions constant. The boil-up t'ate, V, remains constant as EB feed composition drops below its steady-state value(Fig. 3). Thus, there is a chance of single-end cont.'ol when V can be related to feed ,-ate in a feed-fot'ward control mannet' using the slope of the line given in Fig. 2 while the top pt'oduct composition can be controlled by manipulating reflux. This case, other single-end control case and dual composition controls are studied by dynamic analysis.

3.54

0

60 .00 r - - - - - - - - - - - - - - - - - - ,

that all schemes e xcept

-.: .J::;

dt'e

5750

"-

"0

integrally stable. Therefore, schemes ( L-YOlV- xB', ( O- x B;V-YO" (L- x BlB-yO) and

E

~

(L / D- YDlV/B-x B) are the ones that deserve

~

further consideration. This result is also suppot-ted by RI and JEC since RI value must be zero or close to zero for obtaining a non-interacting scheme and 6(A) ( 1 for a controllable and stable system. Howevet- , MRI suggests (L/D,V/B) ratio configuration since this scheme has the largest value of the inde x .

;;::

.,'"

55.00 52.50

:::J

a::

50.00

® Steady-stale

130.00 122.00

~

~

114 .00

E f!

It is observed that only (L,VI configuration gives a condition number close to 10 (26). However, it is stated by Skogestad and Mot-ari (1986) that, fothigh purity columns, the singular values are always different in magnitude which results in high condition numbers. In the application of RDG, three composition and feed flow rate distut-bances at-e considet-ed. In ZF,E:B distut-bance, 3% dect-ease is given to EB while the composition ratio of others are taken as constant. In ZF,DE:B and ZF,MEB, 3% increases are considered in DEB and MEB respectively and the ratio of others are taken as constant. In the feed is flow rate disturbance a 3% inct. . ease gi v en. Since the sum of the t-elative gains of the two control loops must be smaller than 2, (L,V) control configuration with (L-YOlV- X ) gives B satisfactory result for the disturbances. The ROB is not less than 2 e v en for the CL,VI control configuration for the feed flow rate disturbance, however it is the only one which is not infinity. Thus, considering the eight schemes, all the indices e xcept MRI favours CL,V I configuration with (L-yO;V- x ) scheme. B

>

106.00

%

'5 CD

98.00 90.00'--_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _....... 52.00

54.60

57 .20

Feed Flow

59.80

62.40

65.00

Rote,F (lbmol/hr)

Fig. 2. Change of L and V with flow rate to keep product comp. constant. DYNAMIC ANALYSIS Mathematical Model The dynamic simUlation of the column is done by a softwat'e named DAL. The plant data could be matched with the simulation results by adjustment of the time constant of the bottom drum (Alkaya, 1990). Controller Design The results obtained by the application of the various control configuration selection methods showed that the dual composition contt-ol can be successful wi th (L-yO; V- x B) scheme. Howeve,',

EIGENSTRUCTURE STUDIES The Eigenstructure concept is applied to see whether a simple control strategy, that is single-end control, can be used for the column. The method is based on the determination of changes necessitated in the manipulated v ariables as feed compositions or feed rate changes when the products at-e hold at the specified purities. With the aid of the steady-state control configuration selection methods, the best feasible structw-e was found to be (L->' Dl V- x ). B Thus, when the Eigenstt-uctUt'e con c ept was

Eigenstructure analysis revealed that Single-end control can also be successful for the EB column under study. Therefore, during dynamic studies to check the steady-state analysis, the single-end controls were also tested.

For the single-end control, considering the (L,V) structure, either the boil-up rate,V or the reflux,L, is varied as the feed rate changes by using the slopes of the curves given in Fig. 2. The other

222

6300

® Sleady-slale

Table 5 Parameters of Transfer and PI Con tt-o 11 ers

60 .00

K

Loop

57.00

Top

...J ,(

54.00

T

P

0.02

Bottom -11

:::J

e

P

K

Functions T

c

I

T C

1.39

0.05

468

1.4

0.14

1.60

0.81

-0.14

2.0

0.65

;;:::

• 0::

51.00

RESULTS 48 .00 130.00

Steady-state and dynamic plant data have the steady-state and been used with dynamic models of the EB distillation column. The IL,VI, ID,VI, IL,BI and IL/D,V/BI control configurations at'e

116.40 102.80

>

1.00,.----------------,

89.20

ci :::J

'5

ID

75.60

L!J

6006 0.90

0 .80

,., 0.97

0.95

0.94

0.92

0 .99

0 .60

EB

o '"'ID
Feed EB Composition. l F. EB

0.40

8

Fig. 3. Change of L and V with feed EB comp. to keep p,-oduct comp. constant.

~

- - No Conlrol - - - Wilh Conlrol

0.20

o

0.

8E ends a'-e cont,-olled using PI controlle,-s. The tt-ansfe,- functions between the EB concentrations and the manipulated va,-iables are found by the Cohen and Coon techni9ue by dynamic simulations IAriburnu, 19901. The parameters of the tt'ansfe,- functions and the IMC based PI controllers for single-end and dual composition cont,-ols are given in Table 5.

0 .00 ~-----------------_l

.., e U

:::J

-0.20

0.

-0.40

0.

o

-ID .~ LLI

.. ::!: -0.60

c

o

ii .s:

-0.80

o•

The ,-esponses of top and bottom compositions to 3% increase in both feed flow ,-ate and DEB composi tion a,-e shown in Fig. · s 4,5 and 6.

-------------ID

--1-------MEB

-004

~-008 0.35 0.30 oE ..

-x ..,0<1 0 .25

.,; 0.20 c:

.E 0 ~:E 0

..&.

~ E

0.15 0.10

"

0

c<..>

0 .05

I

I" I

, I

;"-,\

I

CD

\

__ No Conlrol - - - With Conlrol

x

-0 .12

,;

0 .016

~

0 .02


\

c

\ \... E8

' 0; 0

\

0.

\

'\

', .........

E 0

0 .20

..,U

0 .16

u

---

~ID EW 0 .08

-0 .10

.e

-0.15 -0.20

'0

0.04

.

0 .00

.~;

.,'

<> 8"~ -
o~

'\

ffi -0 .20

....2

c:'"

o

EB

0"

~g, '> E .. 0 c<..>

-------L ---

c o +=

- - No Conlrol - -- W~h Control

5.-

EB

on

.!:

'gw

NoConlrol - - - Wilh Control

0.12

0

-0 .05

'ii
--

:::J

-0.4 -0.6 -0.8

-0.40 -0.60

'\

'\ '\

'\ '\

"-

.... _----

-1.00 L _ _.l.-_ _...I...-_ _....L_ _.....I..._ _.....I...---I 500

0.00

100

200

300

400

500

Time. min.

Fig. 5. Response of product comp. to feed ,-ate and comp. changes. Single-end control [L=fIFIJ.

Fig. 4. Response of product camp. to feed rate and comp. changes. Single-end control [V=fIF)J.

223

N I

ILl

~

0.11,--------------------, /"'--- .... , 0.09 /" -~'~-,,-------


..

0.07

c:

~

/

0 .04

In o

0-

~

/

u

,

"

""

- - No control ---With control

EB

"' , ,,

,

I

0 .02

u

/

I

" ""

,

~

,,

,

with the (L- YD;V-x ) 8 control scheme is selected as the best cont,'ol st,'uctu,'e. The dynamic analysis of the cont,'olled column and the controllers designed with IMC showed that single-end control of the column is possible as suggested by Eigenstructure analysis.

0 .00 k - - - - - - - - - - - - - - - - - - - l

-6o

,. ,.

;;. -002 0-

~

-004

.~

-0 .07

.

/

MEB

/

,. "

-0 .09

o

./

REFERENCES

""

/

(;

":

/

-----

O.bU)---------::..:..-----------/ /./

0.48

".... -----........,

,

"

./

0.35 ID

X
I

/

0.23

Cl)

0.10

-

0.00 0.10

c:

I

0

I

I

/

"

- - No Control --- With Control

\

EB

'\

/

, ----,

/

"

0

'in

Cl.

E

u

0

-0.02 t:"....

u

-0.14

-

:::> "0 0

"

\

,..",\

.E <5

/

\

\

~ -0.26

E

\

/

,,

", ,

-0.38

DEB /

' ........

.0

-0.50 .S -0.04 Cl)

c: 0

·15

.s; Cl>

0

configuration

-0.0

------" "

/

/

/

"

"

"

/

"',. ....,

, , , .... -'~-.... ------_ .... '" ,,-

./

./

-0.07

MEB

-0.13 -0.19 -0.25 0.00

100

200

300

400

500

600

Time,min . Fig. 6. Response of product comp. to feed rate and comp. changes. Dual cont,'ol. analyzed using the steady-state control configu,'ation selection methods RGA, RI, NI, MRI, JEC, McAvoy' s Imp,'oved Pai"ing Rule, SVO and ROG. Among the selection methods, seven out of eight (except MRI) susgest (L-yO;V-x ) scheme. B SVO and ROG play a major ,'ole in the final decision. Single-end control of the column [L-YO;V=+(F)], siven in Fig. 4, as sugsested by the Eigenstructure analysis resulted with a better cont.'ol having sho,'te,' ,'esponse time and smalle,' maximum deviation even compared to dual composition control. This is believed to be the result of fast response of feed-forwa,'d cont,'ol scheme wh ich faces feed rate changes immediately by varying boil-up rate. CONCLUSION Several cont,'ol configu,'ation selection methods are applied to the industrial distillation column and (L,V) control

224

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