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Distillation Absorption 2010
A.B. de Haan, H. Kooijman and A. Górak (Editors)
All rights reserved by authors as per DA2010 copyright notice
545
IMPROVED CONTROL STRATEGIES FOR DIVIDING-WALL COLUMNS
Anton A. Kiss1, Ruben C. van Diggelen2
1 AkzoNobel – Research, Development and Innovation, 6824 BM Arnhem, The Netherlands
Email: tony.kiss@akzonobel.com
2 Royal Haskoning,6522 DK Nijmegen, The Netherlands
Abstract
This study investigates the controllability of dividing-wall columns (DWC) and
makes an ample comparison of various control strategies based on PID loops,
within a multi-loop framework (DB, DV, LB, LV) versus more advanced controllers
such as LQG/LQR and high order controllers obtained by H∞-controller synthesis
and µ-synthesis. All these controllers are applied to a DWC used in an industrial
case study – the ternary separation of benzene-toluene-xylene. The performance
of these control strategies and the dynamic response of the DWC is investigated in
terms of products composition and flow rates, for various persistent disturbances in
the feed flow rate and feed composition. Significantly shorter settling times can be
achieved using the advanced controllers based on LQG/LQR, H∞ and µ-synthesis.
Keywords: DWC control, multi-loop PID controller, LQG/LQR, H∞ and µ-synthesis
1. Introduction
Distillation remains among the most important separation technologies in the chemical industry.
However, in spite of the flexibility and the widespread use, one important drawback is the considerable
energy requirements, as distillation can generate more than 50% of plant operating costs. An
innovative way out is using advanced process integration techniques. Conventionally, a ternary
mixture can be separated via a direct sequence (most volatile component is separated first), indirect
sequence (heaviest component is separated first) or distributed sequence (mid-split) consisting of 2-3
distillation columns. In the last decades, ternary separations progressed via thermally coupled
columns such as Petlyuk configuration to a novel design that integrates two columns into one shell – a
setup known today as dividing-wall column.1 DWC offers the following key benefits: high purity for all
three or more product streams reached in only one column, high thermodynamic efficiency due to
reduced remixing effects, lower capital investment due to the integrated design, lower energy
requirements compared to conventional separation sequences, and small footprint due to the reduced
number of equipment units. The DWC concept is a major breakthrough in distillation technology, as it
brings significant reduction in the capital invested as well as major savings in the operating costs, up
to 25–40%.2-3 Figure 1 illustrates the ternary separation alternatives using Petlyuk and DWC.
This study explores various DWC control strategies based on PID loops, within a multi-loop framework
versus more advanced controllers. The controllers are applied to an industrial DWC used for the
ternary separation of benzene-toluene-xylene. The performance of these control strategies is
investigated in terms of products composition and flow rates, for various persistent disturbances.
BC
AB
C
A
B
VAP
LIQ
ABC
DC
PF
C
A
B
ABC
DWC
Figure 1. Petlyuk configuration (left). Dividing-wall column (right).
A. A. Kiss et al.
546
2. Problem statement
The integration of two columns into one shell leads also to changes in the operating mode and
ultimately in the controllability of the system. Although much of the literature focuses on the control of
binary distillation columns, there are just a few studies on the controllability of DWC.4-6 The problem is
that different DWC separation systems were used hence no fair comparison of controllers is possible.
To solve this problem, we explore the issues of DWC control on a single separation system and
compare various multi-loop PID control strategies versus more advanced controllers – such as
LQG/LQR, GMC, and high order controllers based on the H∞ norm µ-synthesis7 – ultimately finding an
improved DWC control strategy.
3. Dynamic model
Several reasonable simplifying assumptions were made: 1. constant pressure, 2. no vapor flow
dynamics, 3. linearized liquid dynamics and 4. neglected energy balances and enthalpy changes. The
dynamic model of the DWC is implemented in Mathworks Matlab combined with Simulink and it is
based on the Petlyuk model previously reported in literature by Halvorsen and Skogestad.8 A rigorous
steady-state simulation was also developed in AspenPlus to validate the assumptions of the model.
Figure 2 illustrates the simulated dividing-wall column. The column is divided into six sections, each
containing 8 trays, with a total of 32 trays in the main column and 16 in the prefractionator side. When
disturbances are not present, the feed flowrate is assumed to be F=1, feed condition q=1 (saturated
liquid) and equimolar compositions of A, B and C in the feed.
B
A
C
A,B,C
17
:
:
24
1
:
:
8
9
:
:
16
25
:
:
32
33
:
:
40
41
:
48
B
A
C
A,B,C
17
:
:
24
1
:
:
8
9
:
:
16
25
:
:
32
33
:
:
40
41
:
48
0
0.2
0.4
0.6
0.8
1
0 0.2 0.4 0.6 0.8 1
Side product
Bottom product Top product
Feed
X
B
X
A
Main column
Prefractionator
Figure 2. Schematics of the simulated DWC (left). Composition profiles inside the DWC (right).
4. Control strategies
PID loops within a multi-loop framework. The most used controllers in industry are the PID controllers.
In case of a DWC, two multi loops are needed to stabilize the column and another three to maintain
the setpoints specifying the product purities. As there are six actuators (D S B L0 V
0 R
L) using PID
loops within a multi-loop framework, many combinations are possible. However, there are only a few
configurations that make sense from a practical viewpoint. The level of the reflux tank and the reboiler
can be controlled by the variables L0, D, V0 and B respectively. Hence, there are four inventory control
options to stabilize the column, the combinations: D/B, L/V, L/B and V/D to control the level in the
reflux tank and the level in the reboiler. Figure 3 illustrates the control structures based on multi-loop
framework of PIDs.
Linear Quadratic Gaussian control (LQG) is a combination of an optimal controller LQR and optimal
state estimator (Kalman filter) based on a linear state-space model with measurement and process
noise. LQG is an extension of the optimal state feedback that is a solution of the Linear Quadratic
Regulation (LQR) which assumes no process noise and availability of the full state for control. An
additional feed-forward controller can be added or LQG can be extended with an integral action.
Improved Control Strategies for Dividing-Wall Columns
547
A
C
DB/LSV
CC
LC
CC
LC
B
CC
A
B
C
DV/LSB
CC
LC
CC
CC
LC
A
B
C
LB/DSV
LC
CC
CC
LC
CC
A
B
C
LV/DSB
LC
LC
CC
CC
CC
Figure 3. Control structures based on PID loops within a multi-loop framework.
Multivariable controller synthesis. Two advanced controller synthesis methods were used in order to
obtain a robust controller: loop shaping design procedure (LSDP) and the μ-synthesis procedure. In
contrast to previous studies, the inventory control and regulatory control problems are solved
simultaneously in this work.
5. Results and discussion
In this work, we use the ternary mixture benzene-toluene-xylene (equivalent to A, B, C) and the purity
setpoints [0.97 0.97 0.97] for the product specifications. For the dynamic simulations performed in this
study, disturbances of +10% in the feed flow rate (F) and +10% in the feed composition (xA) were
used, as these are among the most significant ones at industrial scale. Note that persistent
disturbances give a better insight of the quality of the controller than zero mean disturbances, as
typically after a temporary disturbance the product compositions return to their given setpoints.
Moreover, the effect of measurement noise on the control performance was also investigated.
As shown next by the results of the dynamic simulations, all PI control structures cope well with
persistent disturbances. The PI control structure LB/DSV controls the DWC in a similar timescale to
DB/LSV. The disturbances resulting from the changes in the nominal feed are controlled away;
showing only a small overshoot in the product purities; less than 0.02 for both cases. However, the
control structure DV/LSB and LV/DSB make the DWC return to steady state only after a long settling
time (>1000 min).
Note that the RGA analysis clearly distinguishes between the LV/DSB and DB/LSV control structures,
where the DB/LSV option is preferable to LV/DSB. The pairing xA-V and xB-V is predicted and also
proved to be more effective than xB-L and xC-L.
The LQG controller with feed forward control has only good results for disturbances in the feed
flowrate. For other disturbances the tuning of the feed forward terms is less straightforward. The
controller has no feedback on the error term that is the difference of the setpoints and the measured
values. As a result offset in the product purities appears. This problem is solved by combining the
LQG controller with an integral term (Figure 4).
A stop criterion is used for all test cases in order to have a fair comparison of the controllers – the
simulation is stopped if the condition ||(xA,xB,xC) – (0.97,0.97,0.97)||2 < 1e-10 holds at time t1 and also
holds at time t2=t1 + 40 min, where t1<t2. The dynamic responses of the DWC at persistent
disturbances – smaller settling times meaning better control – are shown in the next figures (5-12).
Figure 4. LQG controller with feed-forward (left), or extended with integral action (right).
A. A. Kiss et al.
548
0100 200 300 400 500 600 700 800 900
0.955
0.96
0.965
0.97
0.975
Time / [mi n]
Mola r fraction / [-]
xA
xB
xC
0100 200 300 400 500 600 700
0.966
0.968
0.97
0.972
0.974
0.976
0.978
Time / [mi n]
Mola r fraction / [-]
xA
xB
xC
Figure 5. Dynamic response of the DB/LSV control structure, at a persistent disturbance of +10% in
the feed flow rate (left) and +10% xA in the feed composition (right).
0500 1000 1500
0.96
0.965
0.97
0.975
0.98
0.985
0.99
Time / [mi n]
Mola r fraction / [-]
xA
xB
xC
0500 1000 1500 2000
0.9
0.92
0.94
0.96
0.98
Time / [mi n]
Mola r fraction / [-]
xA
xB
xC
Figure 6. Dynamic response of the DV/LSB control structure, at a persistent disturbance of +10% in
the feed flow rate (left) and +10% xA in the feed composition (right).
0100 200 300 400 500 600 700 800 900
0.955
0.96
0.965
0.97
0.975
0.98
Time / [mi n]
Mola r fraction / [- ]
xA
xB
xC
0100 200 300 400 500 600 700
0.968
0.97
0.972
0.974
0.976
0.978
0.98
Time / [mi n]
Molar frac tion / [-]
xA
xB
xC
Figure 7. Dynamic response of the LB/DSV control structure, at a persistent disturbance of +10% in
the feed flow rate (left) and +10% xA in the feed composition (right).
0200 400 600 800 1000 1200 1400 1600 1800 2000
0.93
0.94
0.95
0.96
0.97
0.98
0.99
Time / [mi n]
Mola r fraction / [-]
xA
xB
xC
0500 1000 1500
0.955
0.96
0.965
0.97
0.975
0.98
0.985
Time / [mi n]
Molar frac tion / [-]
xA
xB
xC
Figure 8. Dynamic response of the LV/DSB control structure, at a persistent disturbance of +10% in
the feed flow rate (left) and +10% xA in the feed composition (right).
Improved Control Strategies for Dividing-Wall Columns
549
0100 200 300 400 500
0.964
0.965
0.966
0.967
0.968
0.969
0.97
Time / [mi n]
Molar frac tion / [-]
568
xA
xB
xC
0100 200 300 400 500 600 700 800 900
0.97
0.971
0.972
0.973
0.974
0.975
Time / [mi n]
Molar frac tion / [-]
916
xA
xB
xC
Figure 9. Dynamic response of the LQG controller combined with integral action, at a persistent
disturbance of +10% in the feed flow rate (left) and +10% xA in the feed composition (right).
050 100 150 200 25 0 300 350 400
0.963
0.964
0.965
0.966
0.967
0.968
0.969
0.97
0.971
Time / [mi n]
Molar frac tion / [-]
xA
xB
xC
050 100 150 200 250 300 350 400
0.969
0.97
0.971
0.972
0.973
0.974
0.975
Time / [mi n]
Molar frac tion / [-]
xA
xB
xC
Figure 10. Dynamic response of the LSDP-controller, at a persistent disturbance of +10% in the feed
flow rate (left) and +10% xA in the feed composition (right).
0100 200 300 400 500 600 700 800 900
0.95
0.955
0.96
0.965
0.97
0.975
Time / [mi n]
Mola r fraction / [- ]
xA
xB
xC
0100 200 300 400 500 600 700 800 900
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
1.1
S
D
B
F
L
V
Time / [mi n]
Flow rates / [kmol/min ]
Figure 11. Dynamic response of the μ-controller, at a persistent disturbance of +10% at t=50min in
the feed flow rate while there is white measurement noise and a time delay.
The dynamic simulations show no control or stability problems of the closed loop system.
Furthermore, there is a trade off between a short settling time in the case of no measurement delay
and noise, and a very smooth control action in case of measurement noise. A short settling time
results in a more chaotic control if noise is present.
Settling time for +10% persistent disturbance in feed flowrate
714
1000
790
1000
432.5
510
645
642
0 200 400 600 800 1000
DB/LSV
DV/LSB
LB/DSV
LV/DSB
LQR-FF
LQR-IA
LSDP
μ-contr oller
minutes
Settling time for +10% persist ent disturba nce in x
A
feed
525
1000
561
1000
0
839
569
569
0 200 400 600 800 1000
DB/LSV
DV/LSB
LB/DSV
LV/DSB
LQR-FF
LQR-IA
LSDP
μ-controller
minutes
Figure 12. Settling time for +10% disturbance in the feed flow rate and XA in the feed.
A. A. Kiss et al.
550
6. Conclusions
The advanced control strategies presented in this work were applied to a DWC separating the ternary
mixture benzene-toluene-xylene. The results provide significant insight into the controllability of DWC,
and gives important guidelines for selecting the appropriate control structure. The dynamic model of
the DWC used in this study is not a reduced one, but a full-size non-linear model that is representative
for industrial separations. Due to practical considerations based on the physical flows, there are
basically four control strategies possible based on PID loops within a multi-loop framework: DB/LSV,
LB/DSV, DV/LBS, LV/DSB. The results of the dynamic simulations show that the first two are the best
among the decentralized multivariable PI structured controllers, being able to handle persistent
disturbances in short times.
The DWC model is not only non-linear but also a true multi-input multi-output (MIMO) system, hence
the applicability of a MIMO control structure starting with a LQG controller was also investigated. Two
options were explored: feed forward control and addition of an integral action. The LQG-FF controller
has good results for a persistent disturbance in the feed flowrate. However, for changes in the feed
composition and condition it is difficult to find a good tuning. Moreover, persistent disturbances other
than the ones used for tunning cannot be controlled with LQG. Nevertheless, combining LQG with an
integral action and reference input solves the problem. Moreover, robustness against measurement
noise results in a more conservative tuning.
The loop-shaping design procedure (LSDP) used in this work leads to a feasible μ-controller that has
some additional benefits, while specific model uncertainties can be incorporated in the control
structure. However, reduction of the LSDP controller is not possible since the reduced controller is
unable to control the column. In contrast, the μ-controller can be reduced while still having a good
control performance. In the DWC case described here, the obtained μ-controller is able to minimize
the settling time when handling persistent disturbances. While PI control structures are also able to
control the DWC, significantly shorter settling times can be achieved using MIMO controllers.
Moreover, persistent disturbance are efficiently controlled using a MIMO controller.
Acknowledgements
We thank Karel Keesman (Wageningen University and Research Centre, NL) for the helpful
discussions, and Da-Wei Gu (Leicester University, UK) for the technical support. The financial support
given by AkzoNobel to Ruben van Diggelen (Delft University of Technology, NL) during his internship
and final M.Sc. project is also gratefully acknowledged.
References
1. A. C. Christiansen, S. Skogestad, L. Liena, Comput. Chem. Eng., 21 (1997) 237-242
2. R. Isopescu, A. Woinaroschy, L. Draghiciu, Rev. Chim., 59 (2008) 812-815
3. A. A. Kiss, J. J. Pragt, C. J. G. van Strien, Chem. Eng. Comm., 196 (2009) 1366-1374
4. M. Serra, A. Espuña, L. Puigjaner, Comput. Chem. Eng., 24 (2000) 901-907
5. R. Adrian, H. Schoenmakers, M. Boll, Chem. Eng. Proc., 43 (2004) 347-355
6. H. Ling, W. L. Luyben, Ind. Eng. Chem. Res., 48 (2009) 6034-6049
7. R. C. van Diggelen, A. A. Kiss, A. W. Heemink, Ind. Eng. Chem. Res., 49 (2010) 288-307
8. I. J. Halvorsen, S. Skogestad, Comput. Chem. Eng., 21 (1997) 249-254