- Email: [email protected]
Controllability of Sidestream Distillation Columns
Copyright e IFAC IDIegratioo of Process Design and Control. Baltimore, Maryland, USA, 1994
CONTROLLABILITY OF SIDE STREAM DISTILLATION COLUMNS
c. Remberg*, M. Flender**, G. Wozny**, G. Fieg*** and F.N. Fett* •
University of Siegen. Department ofMechanical Engineering. Institute of Energy Technology. 57068. Siegen. Germany
••
University of Berlin. Department of Chemical Engineering. Institute of Process and Plant Technology. 10623 Berlin. Germany
•••
Henkel KGaA. 40191 Dilsseldorf, Germany
Abstract. A control application for a distillation column with one sidestream is developed using an industrial tool for column and control system design. This tool is subject of an industry-university cooperation project under financial support of the government of Nordrhein-Westfalen and the companies Henkel KGaA, Dtisseldorf, and Scbmidding GmbH&Co., Koln. The supporting system for column and control system design is the result of this cooperation project (Remberg, 1994). Different control systems have been designed and realized in different production plants (Liider, 1992) showing satisfactory performance. Within this paper the structure of the supporting system and the recent developments and extensions will be presented. The experiences within the cooperation project will be pointed out. Key words. Distillation columns; control system design; control system analysis; controllability; decentralized control; decoupling; discrete systems; identification; PID control; model based control
applications have been designed using the supporting system and realized in different production plants of the industrial partners. The control systems applied have for the most part controllers designed according to the Internal Model Control-(IMC-) concept (Morari, 1989).
1. INTRODUCTION Distillation is regarded as the most important thermal separation process in chemical industry. Increasing requirements on economy, environmental acceptability and quality assurance lead to distillation columns more complex in structure and put special emphasis on the control system of those plants. Because of the great variety of distillation columns and operating conditions in combination with the problem of nonlinearity and multivariability the control system design represents a complex problem. To help process and control engineers to get insight into the process and to help screening out alternative control systems at an early stage of the design process a supporting system has been developed as an industrial tool. In the meantime different control system
The good results achieved for two product columns with this supporting system encouraged to extend it to distillation columns with sidestreams. Although distillation is a process covered extensively in literature, only some publications deal with the control of sidestream distillation columns. Mostly systems with two components are treated. Doukas and Luyben (1978) discuss SISO control of a ternary non-azeotropic sidestream column manipulating sidestream position and flowrate. Lang and Gilles (1991) present a nonlinear observer for a distillation column with 165
sidestream drawoffs. Koggersbol and Jorgensen (1992) investigate the dynamics and control of a specific type of three component homogeneous azeotropic distillation.
USE
Recently a tendency towards direct composition measurement with gaschromatographs is discernible. These measurement systems differ by long analysis times of about 30 minutes. For control systems this is equivalent to long sampling and deadtimes. Deviations from setpoints are realized late and changes of the manipulated variables can only be carried out at discrete times. In order to compensate the setpoint deviations large controller gains are necessary who may lead to instable control systems.
R
Fig. 1 Supporting system's architecture entire control system is investigated in case of disturbances and for setpoint changes using full order, nonlinear simulation programs.
The purpose of this paper is to illustrate under the given restrictions the design of a control system for a distillation column with one sidestream using the mentioned supporting system.
3. PLANT DESCIPTION 2. SUPPORTING SYSTEMS ARCIDTECTURE
The distillation column considered is a packed column with 42 theoretical trays. Its thermodynamic design follows data of plants used in industry. The column is equipped with a total condenser and an equilibrium reboiler. The average feed flowrate is 3500 kg/h. It is concerned the distillation of a ternary mixture of fatty acides. An accumulator and a distributor are assigned after every 4 meter packing, because of the maldistribution of the internalliquids. The sidestream is withdrawn on tray 30. The column pressure is adjusted to 15 mbar.
The design of control systems can be devided into five steps: formulation of control objectives, selection of control configuration, control system analysis, controller design, control system simulation. According to this classification the supporting systems is structured as shown in Fig. 1. Having formulated the control objectives for a specified distillation column an appropriate control structure is selected using heuristic criteria. The heuristic knowledge within the supporting system is represented as an expert system. After determining the control structure the intrinsic control characteristics of the system are examined. Procedures evaluating the process stability as well as the stability, interaction, decoupling and performance of the control loops are included in the module called "mathematical tools" . The design of appropriate controllers is purpose of the subsequent module. In a last step the behaviour of the
Provided perfect level and pressure control it is possible to restrict the control problem to composition control. Such a simplification is justified, since the level and pressure control loops react much faster than the composition loops. The distillation column is equipped with 3 gaschromatographs with an analysis time of 30 minutes. The primary control objec166
component for different feed flowrates.
tive for this process is to keep all product purities (top, side and bottom product) as close as possible to their setpoints under any disturbance that may occur. The control concept of the column, characterized as DSV-configuration, results from heuristic considerations. Distillate rate is used to control the top product, the sideproduct is adjusted by the sidestream rate and the boil-up rate controls the bottom product.
The characteristic course with the varying concentration maximum is obvious. At the nominal operating point the concentration maximum will be located at the sidestream tray. Disturbances like varying feed flowrates shift the maximum towards the top or the bottom of the column, so that the concentration of the side product is determined by the profil flanks. Beside the deterioration of the side product concentration such a shift affects the performance of the control system. Under the given restrictions the design of appropriate controllers is rather difficult, because the shift of concentration maximum can be equivalent to a change of signs in the process model, which represents the high nonlinearity of the process. Usually the controller are designed via linearization around the nominal operating point. The shift of the concentration maximum is directly related to a change of the parameters in the linear process model. In principle three cases can be distinguished:
4. CONTROLLABILITY ANALYSIS Beside the problem of long sampling and deadtimes caused by the measurement system the main difficulty concerned with distillation columns with sidestreams is to adjust the controller parameters of the sidestream loop. Fig. 2a shows the concentration profil of the intermediate boiling .J g
~
2 , ......
4, :. 6
a) :
1 I
........... 1 ;--.;::, ' , ~ 1'\"
::.
_:)UD-..
:
,
'.r '
I
-7=
-- : --..~ _ :- - . . y
10 12
14 16
"
18';/o aauimum
' )
20
22 ~"';"""";'-'----f--',24"---;---~t--
26.;.... 1 ~----,~!:' :-~,f---;28 I i;
)0 1
1. Reduced gradients compared to the nominal operating point:
./ :
)2 ; , /
1
I
I
,
- Loss of performance due to small controller gains
1/1
)4
16 , , : V: I ' J 38 ' , , V ./ ' ,
~ '/~ " o
20
2. Larger gradients compared to the nominal operating point:
40 60 10 100 CIIIICICDlnIiaIllS tpa
- Large changes of manipulated variable due to the large controller gain may lead to instability 3. Change of sign: - The controller regulates into the wrong direction
10 :"-"~---;'--+---;"'-H----; 78----'---I.~. -', --\'--;
7 6 - - - - ' - - - - ;"-'... ' ---'--
.
74- ~-
72: _
_:_op
... : ~ ....
70 ' ,
I !\
,
! 1\
i
)
68 f{ 0 oponIiq poim)
1200
Fig. 2b shows the concentration of the intermediate boiling component versus the sidestream flowrate. Relating Fig. 2b to Fig. 2a the following statements can be derived:
)
_ : J1~OP :,-'_ \--+--
1600
2000
'\'
: \
i
2400
~-=~
Fig. 2 Concentration profil and concentration of intermediate boiling component as a function of sidestream flowrate
1. A concentration maximum below the sidestream tray is related to a nominal operating point situated on the left side of the maximum of the operating line. 167
derlinski, 1972), Relative Gain Array (RGA) as a measure of control loop interaction (Shinskey, 1984), Singular Value Analysis (SVA) as a measure of interaction and sensitivity (McAvoy, 1983) and the Condition Number CN as a measure of decoupling feasibility (McAvoy, 1983).
2. A concentration maximum above the sidestream tray is related to a nominal operating point situated on the right side of the maximum of the operating line. For ecomonic reasons the concentration maximum should be located above the sidestream tray. Thus for operation two cases are to distinguish:
Table 2 shows the steady-state results for the distillation column considered. Fig. 3 shows the RGA as a function of frequency. As can be seen from this data, the DSVconfiguration proposed by heuristic considerations is not recommended. The DVSconfiguration seems to promise better performance.
1. Due to disturbances the operating point has been shifted to the left side of the maximum of the operating line. The actual concentration is lower than that of the setpoint. Because of the wrong sign of the controller gain the controller regulates into the wrong direction. In this case the sign of the controller gain has to be changed until the operating point has shifted to the right side or the actual concentration is higher than that of the setpoint.
process gain k 104 hJkg
2. Due to disturbances the operating point has been shifted to the left side of the maximum of the operating line. The actual concentration is higher than that of the setpoint. Although at first an increase in error will be found out, the controller regulates into the right direction.
5l.23 52.93 40.44] 17.24 3l.38 3l. 94
time contant T 1
[
mm
time constant T 2
~e
Whereas a fullorder, nonlinear simulation model is used to verify the performance of the control system, the analysis of the intrinsic control characteristics of the system and the controller design are based on a linear process model. It is assumed that the process model is at most of third order and may include deadtimes. The parameters in the process model are identified by using a time domain procedure and adjusted by a least-square fit to the step responses of the fullorder, nonlinear simulation program. Table 1 shows the parameters of the transfer functions.
constant
29.31
9.73
5.97
16.59 8.00 [
mm
19.26
12.08
14.65 0.15] 4.57
6.15 10.15
TO [1~: ~~ ~. ~:
18.48] 9.82
10.99 10.36 10.69
mm
Table 1 Parameters of the transfer functions at nominal operating point
NI RGA, A
In order to analyse the intrinsic control characteristics the following steady-state and dynamic analysis methods are included: Niederlinski-Index NI as a measure of the systems closed loop stability (Nie-
8.39 [
1.029 -0.044
-0.068 0.198
0.038] 0.867
0.015
0.870
0.115
eN
63 .03
DIR
1.798
Table 2 Steady-state interaction measures 168
tion of closed loop stability if any of the loops is taken out of service or detuned arbitrarly is important. In this context Morari and Zafiriou (1989) defined the concept of Decentralized Integral Controllability (DIC). According to this definition in a DIC system every loop can be detuned arbitrarly without introducing instabilities into the system. By the time a general, necessary and sufficient condition for DIC is not known, but Yu and Fan (1990) derived such a condition for 3x3systems. If the following conditions are fulfilled, a 3x3-system is DIC:
The interaction problem related to the DSV-configuration can be reduced using decoupling strategies. Though nonlinear decouplers are preferable, often linear decouplers are applied, due to the comparatively simple realization. But if linear decouplers and constant decoupler gains are used imperfect decoupling has to be expected. In some cases decoupler errors can introduce instabilities into the system. Fig. 4 shows for the considered column the d~oupled relative gains as a function of the decoupler error. As can be seen, negative decoupler errors lead to imperfect decoupling, whereas positive decoupler errors do not have a significient influence. Although it is possible to design multivariable control systems (MIMO) using the supporting system, mostly decentralized systems have been designed, due to their greater acceptance. In this case the ques-
- eliminate pairings with NI s; 0 - eliminate pairings with Aii
- eliminate pairings (.p:;; +JAn
Relative Gain Array 10 1
10!
10 1
10'
frequency
(0
101
l/min
5. PID CONTROL VERSUS IMC CONTROL
Fig. 3 RGA as a function of frequency 1.5
1
.-----.....,---"T---~I---,
~
'..c'_ :::
In control systems using measurement systems without or with small measurement deadtimes « 10 minutes) simple PID controller show good performance. The performance of those controllers has been tested for systems with large measurement deadtimes like the considered. The supporting system offers different rules for the choice of the controller settings. By now there are included rules given by Ziegler and Nichols (1942), Chien et al. (1952), Takahashi (1971) and Latzel (1988). Another possibility is to adjust the controller settings by optimization. The rules given by Ziegler and Nichols, Chien et al.
.. ,-
, ' / /
'
/ /
,
Al_l (I)
/ / I
o.s - /
I
A2_1 (I)
-
I
I I
A3_1(1)
I I I
o '----.....' - - -....'---"'---,--..... -1
-D .5
0
~(I)
0 .5
+JA33) SI
Result: The DSV-configuration, selected according to heuristic criteria is in principle suitable but the DVS-configuration seems to show better performance. Another advantage of the DVS-configuration is, that decoupling is not as necessary, and that therefore instabilities caused by decoupling errors are not introduced into the system.
: ..... (1 . 1) : ..... (2 . 3) : ..... (3 . 2)
10 1
0
Table 2 shows, that this conditions are fulfilled for the DSV-configuration as well as for the DVS-configuration.
~,
-- , -
S;
1
Fig. 4 Decoupled relative gains as a function of the decoupler error 169
and Takahashi are not applicable in the considered case. They are only valid, if the sampling time is less than 1110 of the dominating time constant. But the rules given by Latzel and optimization turned out as applicable methods. The supporting system offers the possibility to adjust the controller parameters by optimization for the linear and for the nonlinear, full order process model.
..... 100 1 .....30.0 :
'" ><
!
IV 731 3.0 70
85- ; 15.0 ..!... f 82-;;1112.0 I 79" ~ 9.0 I
,
\ '. ! "
i
;
I
.
!!
.
0.0 +1 ---+~+__+__+_--+........-j--~--+----< o 2 4 6 8 10 12 14 16 18 20 time h
8
10
12
14
16
18 20 time h
DecxJupIer 1.0000 0.9263 0.0200 0.0299 1.0000 -0.0515 0.5039 1.8120 1.0000
..... ... .... ~ BBf~18.0 ~
85
\
11
15 0 .
821t;.12.0 79 i :i 9.0
73j
3.0
70
0.0
1-....
.... .... .... ..... .... ....
\
V
761~ 6.0 \
\ /
o
2
4
6
8
10
12
14
16
18 20 lime h
Fig. 7 Dynamic simulation of a + 10 % change in feedflow rate; PID control; GC error at the bottom after 5 hours
6. PROJECT The presented supporting system is part of an industry-university cooperation project. Despite of a great many of publications dealing with the control of distillation columns, only less about practical realizations is known. One reason for this disprorportion is the process diversity and complexity making standardized solutions impossible. Another is the lack of tools supporting process and control engineers. In order to help process and control engineers getting insight into the process, screening alternative control configurations at an early stage of the design process and
76 ~ ~ 6.0~'t---+~c-.....-~-+--t---~-j 3.0 -tJ""f--+--+-!--+--t--------~
6
::E 9H::E 21.0
...,.,~.,.,_i.
73 ~
4
t;. 9ot~~ 24.0 !1\, r.i 1::1 : i
! -'1--..,~~~,.,~.,.,-
70 ~
2
T 1001.....30.0 1 971_27.0
'
• ;"
o
f
1..
I
I
0.0
"-
Fig. 6 Dynamic simulation of a + 10 % change in feedflow rate; IMC
'
f :t" '
"\
lID
I ....'····~····~·········t····i·········~··········
18.0
\
76 ~ )( 6.0 ~
97- _27.0T"" ~ ~_-,i Decoupler i 1.0000 0.9263 O.02OC ~ 94 - ~240 0.029910000-005151----~ ::l 0.5039 18120 10000 ::E 91 -::E21 .0 :: " . .
.~
!
79~~ 9.0
T l°O-~1.O; i :---r-~;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;---~
88 -
..-\ .... .... .... .... .... .... ..... .... ....
82 1~ 12.0
l. ><
BB ~T 18.0 85-1 15.0
Interesting questions to be asked in this context are how the control system and its performance will be affected if the gaschromatographs fail or detennine wrong compositions. Fig. 7 shows for the control system of Fig. 5 a dynamic simulation result under the assumption that the gaschromatograph of the bottom product detennines the wrong composition.
Cl)
!
;0
Cl)
DecxJupIer 1.0000 0.9263 0.0200 0.0299 1.0000 -0.05 15 0.5039 1.8120 1.0000
I; ,
'" 21.0 ::E 91 -::E
Fig. 5 shows for the output decoupled DVS-configuration the result of a dynamic simulation of a + 10 % change of the feed flowrate. The controller parameters are tuned using the rules given by Latzel. Beside the PID-Controller an IMC-controller has been designed for the considered column. Fig. 6 shows for the DVS-configuration the performance of this controller for a + 1()o1o change of the feed flowrate. A comparision of both results leads to the conclusion, that PID controller can achieve as good results as IMC controller, if the controller settings are well tuned.
t ,r·, :
I
1 1.. 97 ~ _27.0 It "!ui 9ot j ~24.0 i. t ."
Fig. 5 Dynamic simulation of a + 10 % change in feedflow rate; PID 170
7. REFERENCES
supporting that way a practical realization the described supporting system has been developed. Its scope, main problems and the results are listed:
Chien, K.L., Hrones, J.A., and Reswick, J.B. (1952). On the Automatic Control of Generalized Passive Systems. Trans. ASME 74, pp. 175-185 Doukas N., and W . Luybeo (1978). Control of Sidestream Colunms Separating Ternary
scope cooperation partner
: 2 universities 2 companies
co-worker
:6
project period
: 1990-1994
hMdware
: DEC-Workstations PCs
software
: FORTRAN, C DataViews·
~Dttu~,ISA,pp . 51-58
Koggersbol, A., and S.B. Jorgensen (1992). Dynamics and Control of a Distillation Colunm with a Sidestream. Reprints from Distillation and Absorption 92, pp. A429-A449 Laog, L. (1991). Proze.f3fohrung gekoppelter MehrstojJkolonnen am BeispieJ einer Destillationsan/age mit Seitenabzug, PhD-Thesis, Universitat Stuttgart Latzel, W. (1988). Einstellregeln fur kontinuierliche und Abtast-Regler nach der ~ethode der Betragsanpassung, Automatisierungstechnik 36,5, pp. 170-178 and 36,6, pp. 222227 Ltider, T. (1991). Ein Automatisierungskonzept for Rektifikationskolonnen auf der Basis der dynamischen Model/bi/dung .. PhD-Thesis, Universitat GH Siegen ~cAvoy, TJ.(1983). Interaction Analysis., Instrument Society of America ~orari, ~ . , and E. Zafiriou (1989). Robust Process Control., Prentice-Hall, Englewood Cliffs Niederlinski, A. (1971). A Heuristic Approach to the Design of Linear ~ultivariable Control Systems., Automatica 7, p. 691 Remberg, C., K. Intemann, F.N. Fett, and G. Womy (1994). Decision Supporting System for the Design of Control Systems for Distillation Colunms. Computers chem. Engng, Vol 18, Suppl., pp. S409-S413 Shinskey, F.G. (1984). Distil/ation Control for Productivity and Energy Conservation., ~c Graw Hill Book Company Takahashi, Y., Chan, C.S ., and Auslander, D.~ . (1971). Parametereinstellungen bei linearen DDC-Algoritbmen. Regelungstechnik 19,6, pp. 237-284 Vu, C.C., and ~.K.H. Fan (1990). Decentralized Integral Controllability and D-Stability. Chemical Engineering &ience, Vol 45, No. 11, pp. 3299-3309 Ziegler, J.G., and N .B. Nichols (1942). Optimum Settings for Automatic Controllers. Trans ASME 64, 1942, pp. 759-768
HEPROX·· problems - coordination of 4 cooperation partners in 4 different cities - autonomous networks - different programming standards - different intentions and objects - question of interfaces - question of program care - implementation of new design methods - update of knowledge bases - documentation, manual, handbook - service, support - high costs
results - high performance of the applied control systems
- design of new control concepts within 2 to 4 days and not weeks or months - improved know-how management and transfer - extensive documentation of results - easy to use, easy access DataViews Software: V.I. Corporation, 47 Pleasant Street, Northampton, MA 01060, USA •• Henkel KGaA, 40191 Diisseldorf, Germany •
171
CONTROLLABILITY OF SIDE STREAM DISTILLATION COLUMNS
c. Remberg*, M. Flender**, G. Wozny**, G. Fieg*** and F.N. Fett* •
University of Siegen. Department ofMechanical Engineering. Institute of Energy Technology. 57068. Siegen. Germany
••
University of Berlin. Department of Chemical Engineering. Institute of Process and Plant Technology. 10623 Berlin. Germany
•••
Henkel KGaA. 40191 Dilsseldorf, Germany
Abstract. A control application for a distillation column with one sidestream is developed using an industrial tool for column and control system design. This tool is subject of an industry-university cooperation project under financial support of the government of Nordrhein-Westfalen and the companies Henkel KGaA, Dtisseldorf, and Scbmidding GmbH&Co., Koln. The supporting system for column and control system design is the result of this cooperation project (Remberg, 1994). Different control systems have been designed and realized in different production plants (Liider, 1992) showing satisfactory performance. Within this paper the structure of the supporting system and the recent developments and extensions will be presented. The experiences within the cooperation project will be pointed out. Key words. Distillation columns; control system design; control system analysis; controllability; decentralized control; decoupling; discrete systems; identification; PID control; model based control
applications have been designed using the supporting system and realized in different production plants of the industrial partners. The control systems applied have for the most part controllers designed according to the Internal Model Control-(IMC-) concept (Morari, 1989).
1. INTRODUCTION Distillation is regarded as the most important thermal separation process in chemical industry. Increasing requirements on economy, environmental acceptability and quality assurance lead to distillation columns more complex in structure and put special emphasis on the control system of those plants. Because of the great variety of distillation columns and operating conditions in combination with the problem of nonlinearity and multivariability the control system design represents a complex problem. To help process and control engineers to get insight into the process and to help screening out alternative control systems at an early stage of the design process a supporting system has been developed as an industrial tool. In the meantime different control system
The good results achieved for two product columns with this supporting system encouraged to extend it to distillation columns with sidestreams. Although distillation is a process covered extensively in literature, only some publications deal with the control of sidestream distillation columns. Mostly systems with two components are treated. Doukas and Luyben (1978) discuss SISO control of a ternary non-azeotropic sidestream column manipulating sidestream position and flowrate. Lang and Gilles (1991) present a nonlinear observer for a distillation column with 165
sidestream drawoffs. Koggersbol and Jorgensen (1992) investigate the dynamics and control of a specific type of three component homogeneous azeotropic distillation.
USE
Recently a tendency towards direct composition measurement with gaschromatographs is discernible. These measurement systems differ by long analysis times of about 30 minutes. For control systems this is equivalent to long sampling and deadtimes. Deviations from setpoints are realized late and changes of the manipulated variables can only be carried out at discrete times. In order to compensate the setpoint deviations large controller gains are necessary who may lead to instable control systems.
R
Fig. 1 Supporting system's architecture entire control system is investigated in case of disturbances and for setpoint changes using full order, nonlinear simulation programs.
The purpose of this paper is to illustrate under the given restrictions the design of a control system for a distillation column with one sidestream using the mentioned supporting system.
3. PLANT DESCIPTION 2. SUPPORTING SYSTEMS ARCIDTECTURE
The distillation column considered is a packed column with 42 theoretical trays. Its thermodynamic design follows data of plants used in industry. The column is equipped with a total condenser and an equilibrium reboiler. The average feed flowrate is 3500 kg/h. It is concerned the distillation of a ternary mixture of fatty acides. An accumulator and a distributor are assigned after every 4 meter packing, because of the maldistribution of the internalliquids. The sidestream is withdrawn on tray 30. The column pressure is adjusted to 15 mbar.
The design of control systems can be devided into five steps: formulation of control objectives, selection of control configuration, control system analysis, controller design, control system simulation. According to this classification the supporting systems is structured as shown in Fig. 1. Having formulated the control objectives for a specified distillation column an appropriate control structure is selected using heuristic criteria. The heuristic knowledge within the supporting system is represented as an expert system. After determining the control structure the intrinsic control characteristics of the system are examined. Procedures evaluating the process stability as well as the stability, interaction, decoupling and performance of the control loops are included in the module called "mathematical tools" . The design of appropriate controllers is purpose of the subsequent module. In a last step the behaviour of the
Provided perfect level and pressure control it is possible to restrict the control problem to composition control. Such a simplification is justified, since the level and pressure control loops react much faster than the composition loops. The distillation column is equipped with 3 gaschromatographs with an analysis time of 30 minutes. The primary control objec166
component for different feed flowrates.
tive for this process is to keep all product purities (top, side and bottom product) as close as possible to their setpoints under any disturbance that may occur. The control concept of the column, characterized as DSV-configuration, results from heuristic considerations. Distillate rate is used to control the top product, the sideproduct is adjusted by the sidestream rate and the boil-up rate controls the bottom product.
The characteristic course with the varying concentration maximum is obvious. At the nominal operating point the concentration maximum will be located at the sidestream tray. Disturbances like varying feed flowrates shift the maximum towards the top or the bottom of the column, so that the concentration of the side product is determined by the profil flanks. Beside the deterioration of the side product concentration such a shift affects the performance of the control system. Under the given restrictions the design of appropriate controllers is rather difficult, because the shift of concentration maximum can be equivalent to a change of signs in the process model, which represents the high nonlinearity of the process. Usually the controller are designed via linearization around the nominal operating point. The shift of the concentration maximum is directly related to a change of the parameters in the linear process model. In principle three cases can be distinguished:
4. CONTROLLABILITY ANALYSIS Beside the problem of long sampling and deadtimes caused by the measurement system the main difficulty concerned with distillation columns with sidestreams is to adjust the controller parameters of the sidestream loop. Fig. 2a shows the concentration profil of the intermediate boiling .J g
~
2 , ......
4, :. 6
a) :
1 I
........... 1 ;--.;::, ' , ~ 1'\"
::.
_:)UD-..
:
,
'.r '
I
-7=
-- : --..~ _ :- - . . y
10 12
14 16
"
18';/o aauimum
' )
20
22 ~"';"""";'-'----f--',24"---;---~t--
26.;.... 1 ~----,~!:' :-~,f---;28 I i;
)0 1
1. Reduced gradients compared to the nominal operating point:
./ :
)2 ; , /
1
I
I
,
- Loss of performance due to small controller gains
1/1
)4
16 , , : V: I ' J 38 ' , , V ./ ' ,
~ '/~ " o
20
2. Larger gradients compared to the nominal operating point:
40 60 10 100 CIIIICICDlnIiaIllS tpa
- Large changes of manipulated variable due to the large controller gain may lead to instability 3. Change of sign: - The controller regulates into the wrong direction
10 :"-"~---;'--+---;"'-H----; 78----'---I.~. -', --\'--;
7 6 - - - - ' - - - - ;"-'... ' ---'--
.
74- ~-
72: _
_:_op
... : ~ ....
70 ' ,
I !\
,
! 1\
i
)
68 f{ 0 oponIiq poim)
1200
Fig. 2b shows the concentration of the intermediate boiling component versus the sidestream flowrate. Relating Fig. 2b to Fig. 2a the following statements can be derived:
)
_ : J1~OP :,-'_ \--+--
1600
2000
'\'
: \
i
2400
~-=~
Fig. 2 Concentration profil and concentration of intermediate boiling component as a function of sidestream flowrate
1. A concentration maximum below the sidestream tray is related to a nominal operating point situated on the left side of the maximum of the operating line. 167
derlinski, 1972), Relative Gain Array (RGA) as a measure of control loop interaction (Shinskey, 1984), Singular Value Analysis (SVA) as a measure of interaction and sensitivity (McAvoy, 1983) and the Condition Number CN as a measure of decoupling feasibility (McAvoy, 1983).
2. A concentration maximum above the sidestream tray is related to a nominal operating point situated on the right side of the maximum of the operating line. For ecomonic reasons the concentration maximum should be located above the sidestream tray. Thus for operation two cases are to distinguish:
Table 2 shows the steady-state results for the distillation column considered. Fig. 3 shows the RGA as a function of frequency. As can be seen from this data, the DSVconfiguration proposed by heuristic considerations is not recommended. The DVSconfiguration seems to promise better performance.
1. Due to disturbances the operating point has been shifted to the left side of the maximum of the operating line. The actual concentration is lower than that of the setpoint. Because of the wrong sign of the controller gain the controller regulates into the wrong direction. In this case the sign of the controller gain has to be changed until the operating point has shifted to the right side or the actual concentration is higher than that of the setpoint.
process gain k 104 hJkg
2. Due to disturbances the operating point has been shifted to the left side of the maximum of the operating line. The actual concentration is higher than that of the setpoint. Although at first an increase in error will be found out, the controller regulates into the right direction.
5l.23 52.93 40.44] 17.24 3l.38 3l. 94
time contant T 1
[
mm
time constant T 2
~e
Whereas a fullorder, nonlinear simulation model is used to verify the performance of the control system, the analysis of the intrinsic control characteristics of the system and the controller design are based on a linear process model. It is assumed that the process model is at most of third order and may include deadtimes. The parameters in the process model are identified by using a time domain procedure and adjusted by a least-square fit to the step responses of the fullorder, nonlinear simulation program. Table 1 shows the parameters of the transfer functions.
constant
29.31
9.73
5.97
16.59 8.00 [
mm
19.26
12.08
14.65 0.15] 4.57
6.15 10.15
TO [1~: ~~ ~. ~:
18.48] 9.82
10.99 10.36 10.69
mm
Table 1 Parameters of the transfer functions at nominal operating point
NI RGA, A
In order to analyse the intrinsic control characteristics the following steady-state and dynamic analysis methods are included: Niederlinski-Index NI as a measure of the systems closed loop stability (Nie-
8.39 [
1.029 -0.044
-0.068 0.198
0.038] 0.867
0.015
0.870
0.115
eN
63 .03
DIR
1.798
Table 2 Steady-state interaction measures 168
tion of closed loop stability if any of the loops is taken out of service or detuned arbitrarly is important. In this context Morari and Zafiriou (1989) defined the concept of Decentralized Integral Controllability (DIC). According to this definition in a DIC system every loop can be detuned arbitrarly without introducing instabilities into the system. By the time a general, necessary and sufficient condition for DIC is not known, but Yu and Fan (1990) derived such a condition for 3x3systems. If the following conditions are fulfilled, a 3x3-system is DIC:
The interaction problem related to the DSV-configuration can be reduced using decoupling strategies. Though nonlinear decouplers are preferable, often linear decouplers are applied, due to the comparatively simple realization. But if linear decouplers and constant decoupler gains are used imperfect decoupling has to be expected. In some cases decoupler errors can introduce instabilities into the system. Fig. 4 shows for the considered column the d~oupled relative gains as a function of the decoupler error. As can be seen, negative decoupler errors lead to imperfect decoupling, whereas positive decoupler errors do not have a significient influence. Although it is possible to design multivariable control systems (MIMO) using the supporting system, mostly decentralized systems have been designed, due to their greater acceptance. In this case the ques-
- eliminate pairings with NI s; 0 - eliminate pairings with Aii
- eliminate pairings (.p:;; +JAn
Relative Gain Array 10 1
10!
10 1
10'
frequency
(0
101
l/min
5. PID CONTROL VERSUS IMC CONTROL
Fig. 3 RGA as a function of frequency 1.5
1
.-----.....,---"T---~I---,
~
'..c'_ :::
In control systems using measurement systems without or with small measurement deadtimes « 10 minutes) simple PID controller show good performance. The performance of those controllers has been tested for systems with large measurement deadtimes like the considered. The supporting system offers different rules for the choice of the controller settings. By now there are included rules given by Ziegler and Nichols (1942), Chien et al. (1952), Takahashi (1971) and Latzel (1988). Another possibility is to adjust the controller settings by optimization. The rules given by Ziegler and Nichols, Chien et al.
.. ,-
, ' / /
'
/ /
,
Al_l (I)
/ / I
o.s - /
I
A2_1 (I)
-
I
I I
A3_1(1)
I I I
o '----.....' - - -....'---"'---,--..... -1
-D .5
0
~(I)
0 .5
+JA33) SI
Result: The DSV-configuration, selected according to heuristic criteria is in principle suitable but the DVS-configuration seems to show better performance. Another advantage of the DVS-configuration is, that decoupling is not as necessary, and that therefore instabilities caused by decoupling errors are not introduced into the system.
: ..... (1 . 1) : ..... (2 . 3) : ..... (3 . 2)
10 1
0
Table 2 shows, that this conditions are fulfilled for the DSV-configuration as well as for the DVS-configuration.
~,
-- , -
S;
1
Fig. 4 Decoupled relative gains as a function of the decoupler error 169
and Takahashi are not applicable in the considered case. They are only valid, if the sampling time is less than 1110 of the dominating time constant. But the rules given by Latzel and optimization turned out as applicable methods. The supporting system offers the possibility to adjust the controller parameters by optimization for the linear and for the nonlinear, full order process model.
..... 100 1 .....30.0 :
'" ><
!
IV 731 3.0 70
85- ; 15.0 ..!... f 82-;;1112.0 I 79" ~ 9.0 I
,
\ '. ! "
i
;
I
.
!!
.
0.0 +1 ---+~+__+__+_--+........-j--~--+----< o 2 4 6 8 10 12 14 16 18 20 time h
8
10
12
14
16
18 20 time h
DecxJupIer 1.0000 0.9263 0.0200 0.0299 1.0000 -0.0515 0.5039 1.8120 1.0000
..... ... .... ~ BBf~18.0 ~
85
\
11
15 0 .
821t;.12.0 79 i :i 9.0
73j
3.0
70
0.0
1-....
.... .... .... ..... .... ....
\
V
761~ 6.0 \
\ /
o
2
4
6
8
10
12
14
16
18 20 lime h
Fig. 7 Dynamic simulation of a + 10 % change in feedflow rate; PID control; GC error at the bottom after 5 hours
6. PROJECT The presented supporting system is part of an industry-university cooperation project. Despite of a great many of publications dealing with the control of distillation columns, only less about practical realizations is known. One reason for this disprorportion is the process diversity and complexity making standardized solutions impossible. Another is the lack of tools supporting process and control engineers. In order to help process and control engineers getting insight into the process, screening alternative control configurations at an early stage of the design process and
76 ~ ~ 6.0~'t---+~c-.....-~-+--t---~-j 3.0 -tJ""f--+--+-!--+--t--------~
6
::E 9H::E 21.0
...,.,~.,.,_i.
73 ~
4
t;. 9ot~~ 24.0 !1\, r.i 1::1 : i
! -'1--..,~~~,.,~.,.,-
70 ~
2
T 1001.....30.0 1 971_27.0
'
• ;"
o
f
1..
I
I
0.0
"-
Fig. 6 Dynamic simulation of a + 10 % change in feedflow rate; IMC
'
f :t" '
"\
lID
I ....'····~····~·········t····i·········~··········
18.0
\
76 ~ )( 6.0 ~
97- _27.0T"" ~ ~_-,i Decoupler i 1.0000 0.9263 O.02OC ~ 94 - ~240 0.029910000-005151----~ ::l 0.5039 18120 10000 ::E 91 -::E21 .0 :: " . .
.~
!
79~~ 9.0
T l°O-~1.O; i :---r-~;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;;---~
88 -
..-\ .... .... .... .... .... .... ..... .... ....
82 1~ 12.0
l. ><
BB ~T 18.0 85-1 15.0
Interesting questions to be asked in this context are how the control system and its performance will be affected if the gaschromatographs fail or detennine wrong compositions. Fig. 7 shows for the control system of Fig. 5 a dynamic simulation result under the assumption that the gaschromatograph of the bottom product detennines the wrong composition.
Cl)
!
;0
Cl)
DecxJupIer 1.0000 0.9263 0.0200 0.0299 1.0000 -0.05 15 0.5039 1.8120 1.0000
I; ,
'" 21.0 ::E 91 -::E
Fig. 5 shows for the output decoupled DVS-configuration the result of a dynamic simulation of a + 10 % change of the feed flowrate. The controller parameters are tuned using the rules given by Latzel. Beside the PID-Controller an IMC-controller has been designed for the considered column. Fig. 6 shows for the DVS-configuration the performance of this controller for a + 1()o1o change of the feed flowrate. A comparision of both results leads to the conclusion, that PID controller can achieve as good results as IMC controller, if the controller settings are well tuned.
t ,r·, :
I
1 1.. 97 ~ _27.0 It "!ui 9ot j ~24.0 i. t ."
Fig. 5 Dynamic simulation of a + 10 % change in feedflow rate; PID 170
7. REFERENCES
supporting that way a practical realization the described supporting system has been developed. Its scope, main problems and the results are listed:
Chien, K.L., Hrones, J.A., and Reswick, J.B. (1952). On the Automatic Control of Generalized Passive Systems. Trans. ASME 74, pp. 175-185 Doukas N., and W . Luybeo (1978). Control of Sidestream Colunms Separating Ternary
scope cooperation partner
: 2 universities 2 companies
co-worker
:6
project period
: 1990-1994
hMdware
: DEC-Workstations PCs
software
: FORTRAN, C DataViews·
~Dttu~,ISA,pp . 51-58
Koggersbol, A., and S.B. Jorgensen (1992). Dynamics and Control of a Distillation Colunm with a Sidestream. Reprints from Distillation and Absorption 92, pp. A429-A449 Laog, L. (1991). Proze.f3fohrung gekoppelter MehrstojJkolonnen am BeispieJ einer Destillationsan/age mit Seitenabzug, PhD-Thesis, Universitat Stuttgart Latzel, W. (1988). Einstellregeln fur kontinuierliche und Abtast-Regler nach der ~ethode der Betragsanpassung, Automatisierungstechnik 36,5, pp. 170-178 and 36,6, pp. 222227 Ltider, T. (1991). Ein Automatisierungskonzept for Rektifikationskolonnen auf der Basis der dynamischen Model/bi/dung .. PhD-Thesis, Universitat GH Siegen ~cAvoy, TJ.(1983). Interaction Analysis., Instrument Society of America ~orari, ~ . , and E. Zafiriou (1989). Robust Process Control., Prentice-Hall, Englewood Cliffs Niederlinski, A. (1971). A Heuristic Approach to the Design of Linear ~ultivariable Control Systems., Automatica 7, p. 691 Remberg, C., K. Intemann, F.N. Fett, and G. Womy (1994). Decision Supporting System for the Design of Control Systems for Distillation Colunms. Computers chem. Engng, Vol 18, Suppl., pp. S409-S413 Shinskey, F.G. (1984). Distil/ation Control for Productivity and Energy Conservation., ~c Graw Hill Book Company Takahashi, Y., Chan, C.S ., and Auslander, D.~ . (1971). Parametereinstellungen bei linearen DDC-Algoritbmen. Regelungstechnik 19,6, pp. 237-284 Vu, C.C., and ~.K.H. Fan (1990). Decentralized Integral Controllability and D-Stability. Chemical Engineering &ience, Vol 45, No. 11, pp. 3299-3309 Ziegler, J.G., and N .B. Nichols (1942). Optimum Settings for Automatic Controllers. Trans ASME 64, 1942, pp. 759-768
HEPROX·· problems - coordination of 4 cooperation partners in 4 different cities - autonomous networks - different programming standards - different intentions and objects - question of interfaces - question of program care - implementation of new design methods - update of knowledge bases - documentation, manual, handbook - service, support - high costs
results - high performance of the applied control systems
- design of new control concepts within 2 to 4 days and not weeks or months - improved know-how management and transfer - extensive documentation of results - easy to use, easy access DataViews Software: V.I. Corporation, 47 Pleasant Street, Northampton, MA 01060, USA •• Henkel KGaA, 40191 Diisseldorf, Germany •
171