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Decentralized control and identified-model predictive control of divided wall columns
Journal of Process Control 22 (2012) 1582–1592
Contents lists available at SciVerse ScienceDirect
Journal of Process Control journal homepage: www.elsevier.com/locate/jprocont
Decentralized control and identified-model predictive control of divided wall columns Manuel Rodríguez Hernández ∗ , José A. Chinea-Herranz Autonomous System Laboratory, Universidad Politécnica de Madrid, José Gutierrez Abascal, 2, Madrid 28006, Spain
a r t i c l e
i n f o
Article history: Received 2 February 2012 Received in revised form 22 June 2012 Accepted 22 June 2012 Available online 22 July 2012 Keywords: Integrated process control Divided wall column Model predictive control System identification
a b s t r a c t As a thermal separation method, distillation is one of the most important separation technologies in the chemical industry. Given its importance, it is no surprise that increasing efforts have been made in reducing its energy inefficiencies. A great deal of research is focused in the design and optimization of the divided-wall column (DWC). Its applications are still reduced due to distrust of its controllability and robustness. Previous references have studied the decentralized control of DWC but still few papers deal about model predictive control (MPC) applied to DWC. In this work we present a decentralized control of both a divided-wall column along with its equivalent MPC schema, both approaches are compared. Instead of building a rigorous model or performing the step test to an existing plant, the MPC model is obtained by identification of a rigorous simulation. An ARX model is demonstrated to represent adequately the DWC column behavior. This approach might be very convenient if plant testing is not available. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Basically, in every production process some of the chemicals go through at least one distillation column on their way from raw species to final product. Distillation is and will remain the separation method of choice in the chemical industry (by the year 2002 there were more than 40,000 columns in operation around the world [1]). Despite its flexibility and widespread use, this unit operation is very energy demanding, which constitutes one important drawback. Distillation can generate more than 50% of plant operating costs and it is responsible of 3% of the energy usage in the U.S. [1] (notice that thermodynamic efficiency of a typical distillation column is around 10% [2]). In order to reduce this drawback new approaches and configurations have appeared. The divided-wall column (the name is given because the middle part of the column is split into two sections by a wall) is an important example of process intensification and integration. Both energy consumption and capital cost can be reduced in some systems compared to a conventional two-column direct separation sequence when using these types of columns. DWC is very appealing to the chemical industry, with Montz and BASF as the leading companies. Kenig et al. state that there are more than 125 industrial applications nowadays and if the exponential trend continues there will be more than 350 by 2015 [3].
∗ Corresponding author. E-mail address: [email protected] (M. Rodríguez Hernández). 0959-1524/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jprocont.2012.06.015
DWC can separate three or more components in one vessel using a single condenser and reboiler, hence reducing capital and operating costs. In fact, using dividing-wall columns can save up to 30% in the capital invested and up to 40% in the energy costs [3], particularly for close boiling species. DWC is considered to be on the path for energy conservation and green house gases emissions decrease. The control of a divided-wall column is more difficult than the control of a conventional schema with two columns for the separation of ternary mixtures because there is more interaction among control loops. Besides, the absence of controllability could mean the absence of energy savings if the optimal operation is not accomplished. The paper is organized as follows. Section 1 introduces the importance of the separation operation and its relation with energy consumption, the problem of control in integrated solutions as well as the state of the art in the field. Section 2 presents and explains thermally coupled distillation columns, making emphasis in DWC columns. Section 3 presents the control strategies used in the paper. Section 4 applies decentralized (PID controllers) control and MPC to a ternary systems separation. Finally, Section 5 presents a performance comparison, Section 6 draws conclusions and Section 7 introduces further work. 2. Energy integration in distillation Distillation systems have evolved from direct, indirect, or distributed column sequences to thermally coupled systems and eventually to Petlyuk configurations [4] and DWC schemes (Fig. 1).
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Fig. 1. Evolution from a distributed sequence (a) to a Petlyuk configuration (b) and eventually to the DWC (c).
Intermediate steps in this path include systems with heat pumps, prefractionators and side-stripers or side-rectifiers. The Petlyuk configuration and the DWC were aimed at the reduction of thermodynamic losses due to mixing streams, especially at the feed tray location. DWC has more degrees of freedom (DOF) compared to a binary distillation column. This entails a complex design, but also presents extended optimization capabilities. If three product specifications are taken into account, DWC has 7 DOF’s: distillate and bottoms flowrate, reflux ratio, reboiler duty, sidestream flowrate, and vapor and liquid internal split ratios. 5 DOF’s are used to stabilize 2 levels and 3 compositions while the remaining 2 DOF’s are used for optimization purposes. Traditionally, liquid split ratio (˛L = LP /LM ) and vapor split ratio (˛V = VP /VM ) are optimization variables (see Fig. 1). Vapor split ratio is usually fixed during the design stage because it
is given by the pressure drop across both sides of the wall, which in turn depends on the stages type and geometry. The liquid split ratio is used as a control variable during operation by manipulating the flowrates leaving the bottom tray of the rectifying section. The optimal design is given by the number of stages in the different sections of the DWC. The number of stages at both sides of the wall is usually the same but approaches with different number of plates have been reported. Olujic´ et al. presents a review on the different design approaches of DWC [5].
3. Control strategies for divided-wall columns Past and recent distrust on DWC controllability and flexibility is mainly due to the complex design of a control strategy.
Table 1 Survey on control studies applied to DWC. Date
1995 1998 1998 1998 1999 2001 2002 2003 2004 2007 2007 2007 2008 2008 2009 2009 2010 2010 2010 2011 2011 2011 2012
Ref.
Wolff and Skogestad [6] Mutalib and Smith [7] Mutalib and Smith [8] Mizsey et al. [17] Puigjaner et al. [9] Puigjaner et al. [11] Kim [12] Puigjaner et al. [10] Adrian [13] Hernández et al. [18] Wang and Wong [19] Cho et al. [20] Hernández et al. [21] Wang et al. [14] Luyben and Ling [22] Han et al. [23] Kiss et al. [24] Luyben and Ling [25] Woinaroschy et al. [26] Kiss and Bildea [27] Buck et al. [28] Buck et al. [29] Kiss and Rewagad [30]
Steady state optimization
√ √ √ √ √ √ √
RGA
√ √ √ √ √
√
Dynamic simulation
PID control
SM/TF based √
SM/TF based √
RCM based √ √ √
√ √ √ √
MPC
RCM based
Exp
SM/TF based
RCM based
√ √ √ √ √
√ √
√ √
√ √ √ √ √
√ √
√ √ √ √ √ √ √
√ √ √ √
√
√ √ √ √ √
√ √
√ √
√
√ √
√ √
√ √
√ √
Exp
√ √
√ √
Acronyms: RGA, Relative Gain Analysis; SM, shortcut modeling; TF, transfer functions; RCM, rigorous computer modeling; Exp, experimental.
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Date
Ref.
Chemical system
Composition control
1995
Wolff and Skogestad [6]
Ethanol
Propanol
Butanol
1998
Mutalib and Smith [7]
Methanol
Isopropanol
Butanol
1998
Mutalib and Smith [8]
Methanol
Isopropanol
Butanol
1998
Mizsey et al. [17]
Hexane Pentane ibutanol
Heptane Hexane Butanol
2002
Kim [12]
Pentane i-Pentane 2Butanol
2003
Puigjaner et al. [10]
Benzene
Toluene
o-Xylene
2004 2007 2007 2008 2009 2009
Adrian [13] Wang and Wong [19] Cho et al. [20] Wang et al. [14] Luyben and Lin [22] Han et al. [23]
Butanol Ethanol Benzene Water Benzene Benzene
Pentanol Propanol Toluene Methyl-acetate Toluene Toluene
Hexanol Butanol Xylene Isobutyl-acetate o-Xylene Xylene
2010
Kiss et al. [24]
Benzene
Toluene
Xylene
2010
Luyben and Lin [25] Woinaroschy and Isopescu [26]
Benzene Benzene Methanol Benzene Pentane n-Hexanol Benzene
Toluene Toluene Ethanol Toluene Hexane n-Octanol Toluene
Xylene Ethylbenzene Propanol Xylene Heptane n-Decanol Xylene
2010 2011
Kiss and Bildea [27]
2011 2012
Buck et al. [29] Kiss and Rewagad [30]
Level control
Top
Side-stream
Bottoms
L L D L ML D
S S S Const Const S
L L L/V D D L D L S D L L L L L L D L
S S S ML S V S S L S S S S Const S S S S
V D V D V L V D V D V L No successful structure B D V D ML D S L B L S D V L V D V D V L V D V D V D V D V D V D V L V D
Acronyms: L, reflux flowrate; S, sidestream; V, boilup rate; D, distillate; B, bottoms flowrate; Const, constant; TPC, temperature profile control.
Top
Bottoms B B B B B B V B B B V B B B B B B B B B B B B B
TPC
√ √
√ √ √ √ √
√
√
M. Rodríguez Hernández, J.A. Chinea-Herranz / Journal of Process Control 22 (2012) 1582–1592
Table 2 Summary of control strategies used in previous references.
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Fig. 2. Reboiler duty optimization results for the case studied.
Maintaining product specifications while rejecting disturbances and loop interaction are the key concerns together with achieving significant energy savings. Otherwise, DWC advantages to column sequences might disappear. Early references on DWC control were focused mainly on decentralized control. The first approaches extended PID control structures of traditional distillation columns by including liquid or even vapor split ratio among the manipulated
variables. Wolff and Skogestad [6] demonstrated that threepoint control structures were feasible using PID controllers. Mutalib and Smith reported the first experimental application of decentralized control using temperature profile instead of composition measurements [7,8]. Puigjaner et al. follow a research line in which multiple decentralized control studies are compared by using transfer functions obtained from shortcut modeling and apply dynamic matrix
Fig. 3. Aspen Dynamics flowsheet.
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Fig. 4. Decentralized control response to a +10% feed composition disturbance in C5 (a), C6 (b), and C7 (c).
Table 3 Summary of tuning parameters for decentralized control.
Distillate composition control Sidestream composition control Bottoms composition control Prefractionator composition control
Manipulated variable
Proportional gain
Integral time (min)
Set point (mole fraction)
Reflux ratio Sidestream rate Reboiler duty Liquid split ratio
7.144 121.37 4.745 0.379
63.36 38.28 35.64 29.04
0.980 0.980 0.980 0.004
Table 4 MPC tuning parameters. Control interval size
Control horizon
Prediction horizon
Output weight
(s)
(intervals)
(intervals)
Distillate purity
Sidestream purity
Bottoms purity
Liquid ratio
360
2
10
2.2572
1.4974
1.8221
1.0191
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Fig. 5. Decentralized control manipulated variable responses for the +10% feed composition disturbance in C7.
control to DWC [9–11]. Kim [12] and Adrian [13] are among the first to use model predictive control but their approach is either experimental or shortcut modeling based. DWC has also been applied to complex distillation systems. Wang extended DWC to azeotropic
distillation [14], while other references deal with extractive and reactive DWC [15,16]. A wide range of control strategies is reported in the literature, Table 1 presents a survey on previous references dealing
Fig. 6. Decentralized control response to a simultaneous set point change in product purity from 98 to 98.5%.
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4. Case study The separation of n-pentane, n-hexane, and n-heptane is carried out in a DWC. The rectifying, prefractionator, and stripping sections have respectively 7, 12, and 10 stages. The number of stages at both sides of the wall is the same. The feeding stage and sidestream withdraw are located at stage 12 in the prefractionator and main column respectively. The feed is assumed to be 180 kmol/h of a mixture 0.4/0.2/0.4 (C5/C6/C7) in mole fraction at 300 K and product specifications are set at 98%. Condenser pressure is set at 1 atm and stage pressure drop is 0.0068 atm, feed pressure is equal to the feed stage pressure. A simulation and optimization has been conducted in order to calculate the operation conditions that provide minimum energy consumption, results of this simulation are shown in Fig. 2. It can be observed that minimum energy consumption occurs with a liquid split ratio of 0.48 and a vapor split ratio of 0.625. The resulting reflux and boilup ratios are 2.521 and 3.445 respectively. The steady state simulations are performed in Aspen Plus using the rigorous Radfrac model with a Chao-Seader property package. Sizing rules for reflux drum, column bottoms, and tray geometry are taken from Luyben [31]. The performance of PID and MPC control structures is studied using ±10% disturbances in feed flowrate and temperature as well as in feed mole fraction of each component. Aspen Dynamics is used for decentralized control study and the non-linear model is exported for its use in Matlab. With the Systems Identification toolbox the non-linear model is converted in a Plant Model suitable for its use in the MPC toolbox. 4.1. Decentralized control
Fig. 7. Controlled variables responses when using PSBS signal on manipulates variables.
with DWC control. Most of the references study columns whose design is obtained by steady state optimization and use Relative Gain Analysis to analyze the controllability of the process. Rigorous simulation is mostly used in dynamic simulations and PID control schemes but not in MPC studies. It is important to highlight the absence of experimental studies on MPC applied to DWC, besides most of the references are based on shortcut modeling. Some early references on this topic demonstrate the superiority of MIMO systems against decentralized multi-loop controllers while others claim a better response of PID controllers, this may be due to the different chemical systems studied. The absence of previous references comparing decentralized to MPC control with the same chemical system using rigorous computer modeling justifies the work here done. The study on decentralized control is done with Aspen Dynamics using a flowsheet built in Aspen Plus. MPC control study is done with Matlab.
The main advantage of decentralized control lies in its simple design and tuning. As less time and effort is needed on its development, it might be convenient for simple applications. However, PID control ability to reduce interaction among control loops is reduced. As a result settling times and oscillation during disturbances might compromise stable operation. In decentralized control, the choice of variable pairings plays a fundamental role in the performance of the system. There are numerous references dealing with the best pairing, Table 2 presents a summary on the control structures. Variable pairing depends highly on the chemical system studied, the design and the product specification level. Nevertheless, the best result is traditionally associated to the strategy L/S/V–D/B. In this strategy distillate composition is controlled by reflux ratio, sidestream purity is tied to sidestream rate and bottoms specifications is guaranteed by manipulating reboiler duty. Condenser drum and bottoms levels are maintained by distillate and bottoms rates respectively. A special reference must be done on a paper by Luyben and Lin applying a four composition PID control scheme [22], which is eventually extended to temperature profile control [25]. This last reference treats standard temperature control strategies as well as differential temperature control loops to maintain 4 compositions across the column. Luyben’s control scheme minimizes indirectly energy consumption by maintaining heavy component concentration on top of the prefractionator at a minimum value. It is widely accepted that any minimal amount of heaviest component going out the top of the prefractionator causes an irreversible decrease on the sidestream purity [6]. The same idea applies if the lightest component crosses the dividing wall at the bottom of the prefractionator, however the influence on product specification is not so important as this component will be present mainly in the vapor phase. As L/S/V–D/B gives the best performance according to most of the references and Luyben’s control scheme accomplishes and
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Fig. 8. Aspen Dynamics output (dash-dot black lines) and linear parametric model prediction (solid green line for arx442 linear model and dashed red line for n4s4 state space model) for PRBS disturbances on feed composition. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
indirect energy optimization, both approaches will be used. A PI controller is designed for each control loop; tuning parameters are shown in Table 3. PI controllers were tunned using the closed loop ATV method available in Aspen Dynamics with Tyreus–Luyben tunning rules. A caption of the flowsheet designed in Aspen Dynamics is shown in Fig. 3, it corresponds to the same approach used by Luyben and Lin [22]. 4.1.1. System performance The decentralized control scheme has been tested to ±10% disturbances in feed composition as well as a simultaneous set point change in all product purities from 98 to 98.5% (mole fraction). Fig. 4 presents the evolution of product purities for feed composition disturbances. The largest loop interaction and settling time appears in composition disturbances of C5, C7 feed composition disturbances affect to a lesser extent, and C6 composition variations barely affect column stability. Fig. 5 shows the manipulated variables responses for the +10% feed composition disturbance in C7. Fig. 6 depicts product purity when a simultaneous set point change from 98% to 98.5% is carried out. It is clear the existence of loop interaction, affecting especially on distillate and bottoms purities. 4.2. Model predictive control MPC is assumed to be the next control standard in the industry, however its widespread is still limited in some integrated unit
operations such as DWC. Qin and Badgwell’s paper [32] presents a survey on MPC applications along industrial practice. Some authors claim that relevant experience on the superiority of MPC is still limited [28]. Some references highlight the enhanced performance of predictive controllers while for others PID control gives better results. Theoretical and experimental comparisons between MPC and PID controllers should be done for a wide variety of chemical systems in order to give a universal solution. Model predictive controllers present enhanced performance reducing oscillations, loop interactions, and settling times. Besides the ability to include optimization constraints allows for a safety improvement. Energy efficiency and economic optimization are feasible as well, representing a major advantage. Nevertheless, MPC present several disadvantages: (1) it entails larger development cost and time, (2) it requires a deep knowledge of the process, and (3) it requires the availability of a dynamic model representing the main features of the unit operation. The performance of MPC is directly proportional on the accuracy of the dynamic model and the adequate tuning of its parameters. For complex operations, PID controllers might be directly tunned on-site while MPC might entail an expensive development to generate an adequate model and on-site tunning will still be a challenge. MPC uses a dynamic model of the process to predict its behavior and adapt sequentially the manipulated variables in order to minimize the objective function while fulfilling the constraints. The
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Fig. 9. Model predictive controller response to a +10% feed composition disturbance in C5 (a), C6 (b), and C7 (c).
objective function is usually the sum of the quadratic differences between the process variable and its set point. The optimization constraints are introduced as limit values defining feasible regions of operation. The optimization problem is performed in a receding horizon fashion in order to obtain feedback from the system response. The main issue when designing a MPC system is to obtain a model that represents all the features of the process. There are several approaches to generate such a model. Linear MPC controllers use the simplest approach as the model is created by means of step disturbances responses. These MPC applications (using linear dynamic models), however simple its development is, may not correctly represent complex systems with high non-linearities and large loop interactions. Another approach is to generate the model by linearization of a rigorous dynamic model around the operating point. A recent reference by Kiss and Rewagad [30] follows this approach by linearization of an approximate model. This approach gives very good results but its development cost and time might be unaffordable in an industrial environment, especially when dealing with complex systems. Here we discuss the generation of the controller model by means of system identification tools. Using the dynamic responses on the rigorous model implemented in Aspen Dynamics one can create a linear parametric or state space model. The identification experiments are carried out with Aspen Dynamics simulation by attaching a Pseudo-Random Binary Sequence (PRBS) signal generator to each of the disturbances or manipulated variables. Fig. 7 shows the response of the controlled variables when the manipulated variables are modified randomly in Aspen Dynamics. The resulting output is treated using Matlab’s Systems Identification toolbox. Arx and state space models seem to describe the process accordingly. Fig. 8 represents the prediction of an
arx442 model and an n4s4 state space model. The state space model is used in the system performance experiments here presented. The process here described of system identification using Aspen Dynamics output might be very convenient during the first development stages of an industrial project. The identified model is used with Matlab’s MPC Toolbox to represent the controller responses to disturbances or set point change experiments. The Integrated Square Error function is used as the performance function for tuning. Table 4 summarizes MPC tuning parameters. 4.2.1. System performance The model predictive control scheme has also been tested to ±10% disturbances in feed composition as well as a simultaneous set point change in all product purities from 98 to 98.5% (mole fraction). Fig. 9 presents the evolution of product purities for feed composition disturbances. Feed composition disturbances barely affect product purities. Fig. 10 shows the manipulated variables responses for the +10% feed composition disturbance in C7. Fig. 11 depicts product purity for a simultaneous set point change from 98% to 98.5%. Loop interaction is significantly reduced, though some oscillation is still present, besides settling times are also lower. In the same way as for decentralized control, the largest column disturbances appear for C5 and C7 feed composition disturbances. 5. Performance comparison By comparing Fig. 9 to Fig. 4 and Fig. 11 to Fig. 6, it is clear how the predictive controller eliminates all loop interactions and guarantees lower settling times. Column disturbances are higher in distillate and bottoms purity. In the case of sidestream purity the
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Fig. 10. MPC manipulated variable responses for the +10% feed composition disturbance in C7.
Fig. 11. Model predictive controller response to a simultaneous set point change in product purity from 98% to 98.5%.
lower disturbance may be due to the lesser content of C6 fraction in the feed. Prefractionator may also act as a buffer by protecting sidestream purity against feed disturbances. System identification seem to present some inaccuracy in some of the responses presented on Fig. 8. Nevertheless, given the moving horizon nature of MPC these inaccuracies are compensated and the output is clearly superior to the decentralized control scheme performance. No constraints or blocking are used when testing the predictive controller as the purpose of this study is to show the potential of MPC based on identified models against model based controllers.
6. Conclusions MPC superiority in eliminating loop coupling has been demonstrated comparing it to a decentralized control scheme. The same comparison has to be done with a decentralized control with decoupling strategies. Another interesting feature of predictive controllers is the possibility of creating a model for each of the operating points. This results in a greater flexibility in changing from one operating point to another. The results here presented match up with most of the previous references on predictive control of DWC. Nevertheless, this kind of comparison should be extended to other chemical systems. Data
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regarding development time and cost should be taken into account to perform a fair comparison between decentralized control and identified model predictive control, especially when dealing with practical implementations. 7. Future work Temperature based MPC is the next step for the successful industrial application of DWC control at affordable costs and adequate response times by eliminating the use of expensive on-line analyzers. Nevertheless, it entails a big challenge as the accuracy of the model to represent the composition of a ternary system only by using temperature values is very difficult. Either by using temperatures or differential temperatures the model has to infer product compositions as well as represent process dynamics. Complex identification approach should be used for the model to include composition inference capabilities. The future of DWC design points to developing complex schemes such as Kaibel columns, double-wall distillation columns (Sargent arrangements) or Agrawal columns. This foreseeable future should force control engineers to develop a research line on control strategies based either on composition or temperature measurements applied to these new schemes. References [1] G. Soave, J.A. Feliu, Saving energy in distillation towers by feed splitting, Applied Thermal Engineering 22 (2002) 889. [2] H.Z. Kister, Distillation Design, McGraw-Hill, Alhambra, California, 1992. [3] E.Y. Kenig, O. Yildirim, A.A. Kiss, Dividing wall columns in chemical process industry: a review on current activities, Separation and Purification Technology 80 (2011) 403. [4] F.B. Petlyuk, V.M. Platonov, V.M. Slavinskii, Thermodynamically optimal method for separating multicomponent mixtures, International Chemical Engineering 5 (1965) 555. ´ I. Dejanovicˇı, L. Matijasevicˇı, Dividing wall column—a breakthrough [5] Z. Olujic, towards sustainable distilling, Chemical Engineering and Processing 49 (2010) 559. [6] E.A. Wolff, S. Skogestad, Operation of integrated three-product (Petlyuk) distillation columns, Industrial and Engineering Chemistry Research 34 (1995) 2094. [7] M. Mutalib, R. Smith, Operation and control of dividing wall distillation columns. Part 1: degrees of freedom and dynamic simulation, Transactions of IChemE 76 (Part A) (1998) 308. [8] M. Mutalib, R. Smith, Operation and control of dividing wall distillation columns. Part 2: simulation and pilot plant studies using temperature control, Transactions of IChemE 76 (Part A) (1998) 319. ˜ Control and optimization of the divided wall [9] L. Puigjaner, M. Serra, A. Espuna, column, Chemical Engineering and Processing 38 (1999) 549. ˜ Controllability of different multicomponent [10] L. Puigjaner, M. Serra, A. Espuna, distillation arrangements, Industrial and Engineering Chemistry Research 42 (2003) 1773.
˜ M. Perrier, Analysis of different control pos[11] L. Puigjaner, M. Serra, A. Espuna, sibilities for the divided wall column: feedback diagonal and dynamic matrix control, Computers and Chemical Engineering 25 (2001) 859. [12] Y.H. Kim, Structural design and operation of a fully thermally coupled distillation column, Chemical Engineering Journal 85 (2002) 289. [13] T. Adrian, H. Schoenmakers, M. Boll, Model predictive control of integrated unit operations: control of a divided wall column, Chemical Engineering and Processing 43 (2004) 347. [14] S. Wang, C. Lee, S. Jang, S. Shieh, Plant-wide design and control of acetic acid dehydration system via heterogeneous azeotropic distillation and divided wall distillation, Journal of Process Control 18 (2008) 45. [15] C.C. Bravo-Bravo, J.G. Segovia-Hernández, C. Gutiérrez-Antonio, A.L. Duran, A. Bonilla-Petriciolet, A. Briones-Ramírez, Extractive dividing wall column: design and optimization, Industrial and Engineering Chemistry Research 49 (2010) 3672. [16] A.A. Kiss, H. Pragt, C. van Strien, Reactive dividing-wall columns, how to get more with less resources? Chemical Engineering Communications 196 (2009) 1366. [17] P. Mizsey, N.T. Hau, N. Benko, I. Kalmar, Z. Fonyo, Process control for energy integrated distillation schemes, Computers and Chemical Engineering 22 (Suppl.) (1998) S427. [18] S. Hernández, J.G. Segovia-Hernández, M. Ledezma-Martínez, M. CarreraRodríguez, Controllability analysis of thermally coupled distillation systems: five-component mixtures, Industrial and Engineering Chemistry Research 46 (2007) 211. [19] S. Wang, D. Wong, Controllability and energy efficiency of a high-purity divided wall column, Chemical Engineering Science 62 (2007) 1010. [20] Y. Cho, B. Kim, D. Kim, M. Han, Operation of divided wall column using profile position control, in: International Conference on Control, Automation and Systems, Seoul, Korea, 2007. [21] S. Hernández, J.G. Segovia-Hernández, F. Gómez-Castro, C. GutiérrezAntonio, A. Briones-Ramírez, Dividing wall distillation columns: optimization and control properties, Chemical Engineering and Technology 31 (2008) 1246. [22] W.L. Luyben, H. Lin, New control structure for divided-wall columns, Industrial and Engineering Chemistry Research 48 (2009) 6034. [23] Y. Cho, B. Kim, D. Kim, M. Han, M. Lee, Operation of divided wall column with vapor sidedraw using profile position control, Journal of Process Control 19 (2009) 932. [24] A. Kiss, R.C. van Diggelen, A.W. Heemink, Comparison of control strategies for dividing-wall columns, Industrial and Engineering Chemistry Research 49 (2010) 288. [25] W.L. Luyben, H. Lin, Temperature control of the BTX divided-wall column, Industrial and Engineering Chemistry Research 49 (2010) 189. [26] A. Woinaroschy, R. Isopescu, Time-optimal control of dividing-wall distillation columns, Industrial and Engineering Chemistry Research 49 (2010) 9195. [27] A.A. Kiss, C.S. Bildea, A control perspective on process intensification in dividing-wall columns, Chemical Engineering and Processing 50 (2011) 281. [28] C. Buck, C. Hiller, G. Fieg, Applying model predictive control to dividing wall columns, Chemical Engineering and Technology 34 (2011) 663. [29] C. Buck, C. Hiller, G. Fieg, Decentralized temperature control of a pilot dividing wall column, Chemical Engineering and Processing 50 (2011) 167. [30] A.A. Kiss, R.R. Rewagad, Dynamic optimization of a dividing-wall column using model predictive control, Chemical Engineering Science 68 (2012) 132. [31] W.L. Luyben, Distillation Design and Control using AspenTM Simulation, AIChE Wiley Inter-science, Bethlehem, Pennsylvania, 2006. [32] S.J. Qin, T.A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice 11 (2003) 733.
Contents lists available at SciVerse ScienceDirect
Journal of Process Control journal homepage: www.elsevier.com/locate/jprocont
Decentralized control and identified-model predictive control of divided wall columns Manuel Rodríguez Hernández ∗ , José A. Chinea-Herranz Autonomous System Laboratory, Universidad Politécnica de Madrid, José Gutierrez Abascal, 2, Madrid 28006, Spain
a r t i c l e
i n f o
Article history: Received 2 February 2012 Received in revised form 22 June 2012 Accepted 22 June 2012 Available online 22 July 2012 Keywords: Integrated process control Divided wall column Model predictive control System identification
a b s t r a c t As a thermal separation method, distillation is one of the most important separation technologies in the chemical industry. Given its importance, it is no surprise that increasing efforts have been made in reducing its energy inefficiencies. A great deal of research is focused in the design and optimization of the divided-wall column (DWC). Its applications are still reduced due to distrust of its controllability and robustness. Previous references have studied the decentralized control of DWC but still few papers deal about model predictive control (MPC) applied to DWC. In this work we present a decentralized control of both a divided-wall column along with its equivalent MPC schema, both approaches are compared. Instead of building a rigorous model or performing the step test to an existing plant, the MPC model is obtained by identification of a rigorous simulation. An ARX model is demonstrated to represent adequately the DWC column behavior. This approach might be very convenient if plant testing is not available. © 2012 Elsevier Ltd. All rights reserved.
1. Introduction Basically, in every production process some of the chemicals go through at least one distillation column on their way from raw species to final product. Distillation is and will remain the separation method of choice in the chemical industry (by the year 2002 there were more than 40,000 columns in operation around the world [1]). Despite its flexibility and widespread use, this unit operation is very energy demanding, which constitutes one important drawback. Distillation can generate more than 50% of plant operating costs and it is responsible of 3% of the energy usage in the U.S. [1] (notice that thermodynamic efficiency of a typical distillation column is around 10% [2]). In order to reduce this drawback new approaches and configurations have appeared. The divided-wall column (the name is given because the middle part of the column is split into two sections by a wall) is an important example of process intensification and integration. Both energy consumption and capital cost can be reduced in some systems compared to a conventional two-column direct separation sequence when using these types of columns. DWC is very appealing to the chemical industry, with Montz and BASF as the leading companies. Kenig et al. state that there are more than 125 industrial applications nowadays and if the exponential trend continues there will be more than 350 by 2015 [3].
∗ Corresponding author. E-mail address: [email protected] (M. Rodríguez Hernández). 0959-1524/$ – see front matter © 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.jprocont.2012.06.015
DWC can separate three or more components in one vessel using a single condenser and reboiler, hence reducing capital and operating costs. In fact, using dividing-wall columns can save up to 30% in the capital invested and up to 40% in the energy costs [3], particularly for close boiling species. DWC is considered to be on the path for energy conservation and green house gases emissions decrease. The control of a divided-wall column is more difficult than the control of a conventional schema with two columns for the separation of ternary mixtures because there is more interaction among control loops. Besides, the absence of controllability could mean the absence of energy savings if the optimal operation is not accomplished. The paper is organized as follows. Section 1 introduces the importance of the separation operation and its relation with energy consumption, the problem of control in integrated solutions as well as the state of the art in the field. Section 2 presents and explains thermally coupled distillation columns, making emphasis in DWC columns. Section 3 presents the control strategies used in the paper. Section 4 applies decentralized (PID controllers) control and MPC to a ternary systems separation. Finally, Section 5 presents a performance comparison, Section 6 draws conclusions and Section 7 introduces further work. 2. Energy integration in distillation Distillation systems have evolved from direct, indirect, or distributed column sequences to thermally coupled systems and eventually to Petlyuk configurations [4] and DWC schemes (Fig. 1).
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Fig. 1. Evolution from a distributed sequence (a) to a Petlyuk configuration (b) and eventually to the DWC (c).
Intermediate steps in this path include systems with heat pumps, prefractionators and side-stripers or side-rectifiers. The Petlyuk configuration and the DWC were aimed at the reduction of thermodynamic losses due to mixing streams, especially at the feed tray location. DWC has more degrees of freedom (DOF) compared to a binary distillation column. This entails a complex design, but also presents extended optimization capabilities. If three product specifications are taken into account, DWC has 7 DOF’s: distillate and bottoms flowrate, reflux ratio, reboiler duty, sidestream flowrate, and vapor and liquid internal split ratios. 5 DOF’s are used to stabilize 2 levels and 3 compositions while the remaining 2 DOF’s are used for optimization purposes. Traditionally, liquid split ratio (˛L = LP /LM ) and vapor split ratio (˛V = VP /VM ) are optimization variables (see Fig. 1). Vapor split ratio is usually fixed during the design stage because it
is given by the pressure drop across both sides of the wall, which in turn depends on the stages type and geometry. The liquid split ratio is used as a control variable during operation by manipulating the flowrates leaving the bottom tray of the rectifying section. The optimal design is given by the number of stages in the different sections of the DWC. The number of stages at both sides of the wall is usually the same but approaches with different number of plates have been reported. Olujic´ et al. presents a review on the different design approaches of DWC [5].
3. Control strategies for divided-wall columns Past and recent distrust on DWC controllability and flexibility is mainly due to the complex design of a control strategy.
Table 1 Survey on control studies applied to DWC. Date
1995 1998 1998 1998 1999 2001 2002 2003 2004 2007 2007 2007 2008 2008 2009 2009 2010 2010 2010 2011 2011 2011 2012
Ref.
Wolff and Skogestad [6] Mutalib and Smith [7] Mutalib and Smith [8] Mizsey et al. [17] Puigjaner et al. [9] Puigjaner et al. [11] Kim [12] Puigjaner et al. [10] Adrian [13] Hernández et al. [18] Wang and Wong [19] Cho et al. [20] Hernández et al. [21] Wang et al. [14] Luyben and Ling [22] Han et al. [23] Kiss et al. [24] Luyben and Ling [25] Woinaroschy et al. [26] Kiss and Bildea [27] Buck et al. [28] Buck et al. [29] Kiss and Rewagad [30]
Steady state optimization
√ √ √ √ √ √ √
RGA
√ √ √ √ √
√
Dynamic simulation
PID control
SM/TF based √
SM/TF based √
RCM based √ √ √
√ √ √ √
MPC
RCM based
Exp
SM/TF based
RCM based
√ √ √ √ √
√ √
√ √
√ √ √ √ √
√ √
√ √ √ √ √ √ √
√ √ √ √
√
√ √ √ √ √
√ √
√ √
√
√ √
√ √
√ √
√ √
Exp
√ √
√ √
Acronyms: RGA, Relative Gain Analysis; SM, shortcut modeling; TF, transfer functions; RCM, rigorous computer modeling; Exp, experimental.
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Date
Ref.
Chemical system
Composition control
1995
Wolff and Skogestad [6]
Ethanol
Propanol
Butanol
1998
Mutalib and Smith [7]
Methanol
Isopropanol
Butanol
1998
Mutalib and Smith [8]
Methanol
Isopropanol
Butanol
1998
Mizsey et al. [17]
Hexane Pentane ibutanol
Heptane Hexane Butanol
2002
Kim [12]
Pentane i-Pentane 2Butanol
2003
Puigjaner et al. [10]
Benzene
Toluene
o-Xylene
2004 2007 2007 2008 2009 2009
Adrian [13] Wang and Wong [19] Cho et al. [20] Wang et al. [14] Luyben and Lin [22] Han et al. [23]
Butanol Ethanol Benzene Water Benzene Benzene
Pentanol Propanol Toluene Methyl-acetate Toluene Toluene
Hexanol Butanol Xylene Isobutyl-acetate o-Xylene Xylene
2010
Kiss et al. [24]
Benzene
Toluene
Xylene
2010
Luyben and Lin [25] Woinaroschy and Isopescu [26]
Benzene Benzene Methanol Benzene Pentane n-Hexanol Benzene
Toluene Toluene Ethanol Toluene Hexane n-Octanol Toluene
Xylene Ethylbenzene Propanol Xylene Heptane n-Decanol Xylene
2010 2011
Kiss and Bildea [27]
2011 2012
Buck et al. [29] Kiss and Rewagad [30]
Level control
Top
Side-stream
Bottoms
L L D L ML D
S S S Const Const S
L L L/V D D L D L S D L L L L L L D L
S S S ML S V S S L S S S S Const S S S S
V D V D V L V D V D V L No successful structure B D V D ML D S L B L S D V L V D V D V L V D V D V D V D V D V D V L V D
Acronyms: L, reflux flowrate; S, sidestream; V, boilup rate; D, distillate; B, bottoms flowrate; Const, constant; TPC, temperature profile control.
Top
Bottoms B B B B B B V B B B V B B B B B B B B B B B B B
TPC
√ √
√ √ √ √ √
√
√
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Table 2 Summary of control strategies used in previous references.
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Fig. 2. Reboiler duty optimization results for the case studied.
Maintaining product specifications while rejecting disturbances and loop interaction are the key concerns together with achieving significant energy savings. Otherwise, DWC advantages to column sequences might disappear. Early references on DWC control were focused mainly on decentralized control. The first approaches extended PID control structures of traditional distillation columns by including liquid or even vapor split ratio among the manipulated
variables. Wolff and Skogestad [6] demonstrated that threepoint control structures were feasible using PID controllers. Mutalib and Smith reported the first experimental application of decentralized control using temperature profile instead of composition measurements [7,8]. Puigjaner et al. follow a research line in which multiple decentralized control studies are compared by using transfer functions obtained from shortcut modeling and apply dynamic matrix
Fig. 3. Aspen Dynamics flowsheet.
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Fig. 4. Decentralized control response to a +10% feed composition disturbance in C5 (a), C6 (b), and C7 (c).
Table 3 Summary of tuning parameters for decentralized control.
Distillate composition control Sidestream composition control Bottoms composition control Prefractionator composition control
Manipulated variable
Proportional gain
Integral time (min)
Set point (mole fraction)
Reflux ratio Sidestream rate Reboiler duty Liquid split ratio
7.144 121.37 4.745 0.379
63.36 38.28 35.64 29.04
0.980 0.980 0.980 0.004
Table 4 MPC tuning parameters. Control interval size
Control horizon
Prediction horizon
Output weight
(s)
(intervals)
(intervals)
Distillate purity
Sidestream purity
Bottoms purity
Liquid ratio
360
2
10
2.2572
1.4974
1.8221
1.0191
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Fig. 5. Decentralized control manipulated variable responses for the +10% feed composition disturbance in C7.
control to DWC [9–11]. Kim [12] and Adrian [13] are among the first to use model predictive control but their approach is either experimental or shortcut modeling based. DWC has also been applied to complex distillation systems. Wang extended DWC to azeotropic
distillation [14], while other references deal with extractive and reactive DWC [15,16]. A wide range of control strategies is reported in the literature, Table 1 presents a survey on previous references dealing
Fig. 6. Decentralized control response to a simultaneous set point change in product purity from 98 to 98.5%.
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4. Case study The separation of n-pentane, n-hexane, and n-heptane is carried out in a DWC. The rectifying, prefractionator, and stripping sections have respectively 7, 12, and 10 stages. The number of stages at both sides of the wall is the same. The feeding stage and sidestream withdraw are located at stage 12 in the prefractionator and main column respectively. The feed is assumed to be 180 kmol/h of a mixture 0.4/0.2/0.4 (C5/C6/C7) in mole fraction at 300 K and product specifications are set at 98%. Condenser pressure is set at 1 atm and stage pressure drop is 0.0068 atm, feed pressure is equal to the feed stage pressure. A simulation and optimization has been conducted in order to calculate the operation conditions that provide minimum energy consumption, results of this simulation are shown in Fig. 2. It can be observed that minimum energy consumption occurs with a liquid split ratio of 0.48 and a vapor split ratio of 0.625. The resulting reflux and boilup ratios are 2.521 and 3.445 respectively. The steady state simulations are performed in Aspen Plus using the rigorous Radfrac model with a Chao-Seader property package. Sizing rules for reflux drum, column bottoms, and tray geometry are taken from Luyben [31]. The performance of PID and MPC control structures is studied using ±10% disturbances in feed flowrate and temperature as well as in feed mole fraction of each component. Aspen Dynamics is used for decentralized control study and the non-linear model is exported for its use in Matlab. With the Systems Identification toolbox the non-linear model is converted in a Plant Model suitable for its use in the MPC toolbox. 4.1. Decentralized control
Fig. 7. Controlled variables responses when using PSBS signal on manipulates variables.
with DWC control. Most of the references study columns whose design is obtained by steady state optimization and use Relative Gain Analysis to analyze the controllability of the process. Rigorous simulation is mostly used in dynamic simulations and PID control schemes but not in MPC studies. It is important to highlight the absence of experimental studies on MPC applied to DWC, besides most of the references are based on shortcut modeling. Some early references on this topic demonstrate the superiority of MIMO systems against decentralized multi-loop controllers while others claim a better response of PID controllers, this may be due to the different chemical systems studied. The absence of previous references comparing decentralized to MPC control with the same chemical system using rigorous computer modeling justifies the work here done. The study on decentralized control is done with Aspen Dynamics using a flowsheet built in Aspen Plus. MPC control study is done with Matlab.
The main advantage of decentralized control lies in its simple design and tuning. As less time and effort is needed on its development, it might be convenient for simple applications. However, PID control ability to reduce interaction among control loops is reduced. As a result settling times and oscillation during disturbances might compromise stable operation. In decentralized control, the choice of variable pairings plays a fundamental role in the performance of the system. There are numerous references dealing with the best pairing, Table 2 presents a summary on the control structures. Variable pairing depends highly on the chemical system studied, the design and the product specification level. Nevertheless, the best result is traditionally associated to the strategy L/S/V–D/B. In this strategy distillate composition is controlled by reflux ratio, sidestream purity is tied to sidestream rate and bottoms specifications is guaranteed by manipulating reboiler duty. Condenser drum and bottoms levels are maintained by distillate and bottoms rates respectively. A special reference must be done on a paper by Luyben and Lin applying a four composition PID control scheme [22], which is eventually extended to temperature profile control [25]. This last reference treats standard temperature control strategies as well as differential temperature control loops to maintain 4 compositions across the column. Luyben’s control scheme minimizes indirectly energy consumption by maintaining heavy component concentration on top of the prefractionator at a minimum value. It is widely accepted that any minimal amount of heaviest component going out the top of the prefractionator causes an irreversible decrease on the sidestream purity [6]. The same idea applies if the lightest component crosses the dividing wall at the bottom of the prefractionator, however the influence on product specification is not so important as this component will be present mainly in the vapor phase. As L/S/V–D/B gives the best performance according to most of the references and Luyben’s control scheme accomplishes and
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Fig. 8. Aspen Dynamics output (dash-dot black lines) and linear parametric model prediction (solid green line for arx442 linear model and dashed red line for n4s4 state space model) for PRBS disturbances on feed composition. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of the article.)
indirect energy optimization, both approaches will be used. A PI controller is designed for each control loop; tuning parameters are shown in Table 3. PI controllers were tunned using the closed loop ATV method available in Aspen Dynamics with Tyreus–Luyben tunning rules. A caption of the flowsheet designed in Aspen Dynamics is shown in Fig. 3, it corresponds to the same approach used by Luyben and Lin [22]. 4.1.1. System performance The decentralized control scheme has been tested to ±10% disturbances in feed composition as well as a simultaneous set point change in all product purities from 98 to 98.5% (mole fraction). Fig. 4 presents the evolution of product purities for feed composition disturbances. The largest loop interaction and settling time appears in composition disturbances of C5, C7 feed composition disturbances affect to a lesser extent, and C6 composition variations barely affect column stability. Fig. 5 shows the manipulated variables responses for the +10% feed composition disturbance in C7. Fig. 6 depicts product purity when a simultaneous set point change from 98% to 98.5% is carried out. It is clear the existence of loop interaction, affecting especially on distillate and bottoms purities. 4.2. Model predictive control MPC is assumed to be the next control standard in the industry, however its widespread is still limited in some integrated unit
operations such as DWC. Qin and Badgwell’s paper [32] presents a survey on MPC applications along industrial practice. Some authors claim that relevant experience on the superiority of MPC is still limited [28]. Some references highlight the enhanced performance of predictive controllers while for others PID control gives better results. Theoretical and experimental comparisons between MPC and PID controllers should be done for a wide variety of chemical systems in order to give a universal solution. Model predictive controllers present enhanced performance reducing oscillations, loop interactions, and settling times. Besides the ability to include optimization constraints allows for a safety improvement. Energy efficiency and economic optimization are feasible as well, representing a major advantage. Nevertheless, MPC present several disadvantages: (1) it entails larger development cost and time, (2) it requires a deep knowledge of the process, and (3) it requires the availability of a dynamic model representing the main features of the unit operation. The performance of MPC is directly proportional on the accuracy of the dynamic model and the adequate tuning of its parameters. For complex operations, PID controllers might be directly tunned on-site while MPC might entail an expensive development to generate an adequate model and on-site tunning will still be a challenge. MPC uses a dynamic model of the process to predict its behavior and adapt sequentially the manipulated variables in order to minimize the objective function while fulfilling the constraints. The
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Fig. 9. Model predictive controller response to a +10% feed composition disturbance in C5 (a), C6 (b), and C7 (c).
objective function is usually the sum of the quadratic differences between the process variable and its set point. The optimization constraints are introduced as limit values defining feasible regions of operation. The optimization problem is performed in a receding horizon fashion in order to obtain feedback from the system response. The main issue when designing a MPC system is to obtain a model that represents all the features of the process. There are several approaches to generate such a model. Linear MPC controllers use the simplest approach as the model is created by means of step disturbances responses. These MPC applications (using linear dynamic models), however simple its development is, may not correctly represent complex systems with high non-linearities and large loop interactions. Another approach is to generate the model by linearization of a rigorous dynamic model around the operating point. A recent reference by Kiss and Rewagad [30] follows this approach by linearization of an approximate model. This approach gives very good results but its development cost and time might be unaffordable in an industrial environment, especially when dealing with complex systems. Here we discuss the generation of the controller model by means of system identification tools. Using the dynamic responses on the rigorous model implemented in Aspen Dynamics one can create a linear parametric or state space model. The identification experiments are carried out with Aspen Dynamics simulation by attaching a Pseudo-Random Binary Sequence (PRBS) signal generator to each of the disturbances or manipulated variables. Fig. 7 shows the response of the controlled variables when the manipulated variables are modified randomly in Aspen Dynamics. The resulting output is treated using Matlab’s Systems Identification toolbox. Arx and state space models seem to describe the process accordingly. Fig. 8 represents the prediction of an
arx442 model and an n4s4 state space model. The state space model is used in the system performance experiments here presented. The process here described of system identification using Aspen Dynamics output might be very convenient during the first development stages of an industrial project. The identified model is used with Matlab’s MPC Toolbox to represent the controller responses to disturbances or set point change experiments. The Integrated Square Error function is used as the performance function for tuning. Table 4 summarizes MPC tuning parameters. 4.2.1. System performance The model predictive control scheme has also been tested to ±10% disturbances in feed composition as well as a simultaneous set point change in all product purities from 98 to 98.5% (mole fraction). Fig. 9 presents the evolution of product purities for feed composition disturbances. Feed composition disturbances barely affect product purities. Fig. 10 shows the manipulated variables responses for the +10% feed composition disturbance in C7. Fig. 11 depicts product purity for a simultaneous set point change from 98% to 98.5%. Loop interaction is significantly reduced, though some oscillation is still present, besides settling times are also lower. In the same way as for decentralized control, the largest column disturbances appear for C5 and C7 feed composition disturbances. 5. Performance comparison By comparing Fig. 9 to Fig. 4 and Fig. 11 to Fig. 6, it is clear how the predictive controller eliminates all loop interactions and guarantees lower settling times. Column disturbances are higher in distillate and bottoms purity. In the case of sidestream purity the
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Fig. 10. MPC manipulated variable responses for the +10% feed composition disturbance in C7.
Fig. 11. Model predictive controller response to a simultaneous set point change in product purity from 98% to 98.5%.
lower disturbance may be due to the lesser content of C6 fraction in the feed. Prefractionator may also act as a buffer by protecting sidestream purity against feed disturbances. System identification seem to present some inaccuracy in some of the responses presented on Fig. 8. Nevertheless, given the moving horizon nature of MPC these inaccuracies are compensated and the output is clearly superior to the decentralized control scheme performance. No constraints or blocking are used when testing the predictive controller as the purpose of this study is to show the potential of MPC based on identified models against model based controllers.
6. Conclusions MPC superiority in eliminating loop coupling has been demonstrated comparing it to a decentralized control scheme. The same comparison has to be done with a decentralized control with decoupling strategies. Another interesting feature of predictive controllers is the possibility of creating a model for each of the operating points. This results in a greater flexibility in changing from one operating point to another. The results here presented match up with most of the previous references on predictive control of DWC. Nevertheless, this kind of comparison should be extended to other chemical systems. Data
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regarding development time and cost should be taken into account to perform a fair comparison between decentralized control and identified model predictive control, especially when dealing with practical implementations. 7. Future work Temperature based MPC is the next step for the successful industrial application of DWC control at affordable costs and adequate response times by eliminating the use of expensive on-line analyzers. Nevertheless, it entails a big challenge as the accuracy of the model to represent the composition of a ternary system only by using temperature values is very difficult. Either by using temperatures or differential temperatures the model has to infer product compositions as well as represent process dynamics. Complex identification approach should be used for the model to include composition inference capabilities. The future of DWC design points to developing complex schemes such as Kaibel columns, double-wall distillation columns (Sargent arrangements) or Agrawal columns. This foreseeable future should force control engineers to develop a research line on control strategies based either on composition or temperature measurements applied to these new schemes. References [1] G. Soave, J.A. Feliu, Saving energy in distillation towers by feed splitting, Applied Thermal Engineering 22 (2002) 889. [2] H.Z. Kister, Distillation Design, McGraw-Hill, Alhambra, California, 1992. [3] E.Y. Kenig, O. Yildirim, A.A. Kiss, Dividing wall columns in chemical process industry: a review on current activities, Separation and Purification Technology 80 (2011) 403. [4] F.B. Petlyuk, V.M. Platonov, V.M. Slavinskii, Thermodynamically optimal method for separating multicomponent mixtures, International Chemical Engineering 5 (1965) 555. ´ I. Dejanovicˇı, L. Matijasevicˇı, Dividing wall column—a breakthrough [5] Z. Olujic, towards sustainable distilling, Chemical Engineering and Processing 49 (2010) 559. [6] E.A. Wolff, S. Skogestad, Operation of integrated three-product (Petlyuk) distillation columns, Industrial and Engineering Chemistry Research 34 (1995) 2094. [7] M. Mutalib, R. Smith, Operation and control of dividing wall distillation columns. Part 1: degrees of freedom and dynamic simulation, Transactions of IChemE 76 (Part A) (1998) 308. [8] M. Mutalib, R. Smith, Operation and control of dividing wall distillation columns. Part 2: simulation and pilot plant studies using temperature control, Transactions of IChemE 76 (Part A) (1998) 319. ˜ Control and optimization of the divided wall [9] L. Puigjaner, M. Serra, A. Espuna, column, Chemical Engineering and Processing 38 (1999) 549. ˜ Controllability of different multicomponent [10] L. Puigjaner, M. Serra, A. Espuna, distillation arrangements, Industrial and Engineering Chemistry Research 42 (2003) 1773.
˜ M. Perrier, Analysis of different control pos[11] L. Puigjaner, M. Serra, A. Espuna, sibilities for the divided wall column: feedback diagonal and dynamic matrix control, Computers and Chemical Engineering 25 (2001) 859. [12] Y.H. Kim, Structural design and operation of a fully thermally coupled distillation column, Chemical Engineering Journal 85 (2002) 289. [13] T. Adrian, H. Schoenmakers, M. Boll, Model predictive control of integrated unit operations: control of a divided wall column, Chemical Engineering and Processing 43 (2004) 347. [14] S. Wang, C. Lee, S. Jang, S. Shieh, Plant-wide design and control of acetic acid dehydration system via heterogeneous azeotropic distillation and divided wall distillation, Journal of Process Control 18 (2008) 45. [15] C.C. Bravo-Bravo, J.G. Segovia-Hernández, C. Gutiérrez-Antonio, A.L. Duran, A. Bonilla-Petriciolet, A. Briones-Ramírez, Extractive dividing wall column: design and optimization, Industrial and Engineering Chemistry Research 49 (2010) 3672. [16] A.A. Kiss, H. Pragt, C. van Strien, Reactive dividing-wall columns, how to get more with less resources? Chemical Engineering Communications 196 (2009) 1366. [17] P. Mizsey, N.T. Hau, N. Benko, I. Kalmar, Z. Fonyo, Process control for energy integrated distillation schemes, Computers and Chemical Engineering 22 (Suppl.) (1998) S427. [18] S. Hernández, J.G. Segovia-Hernández, M. Ledezma-Martínez, M. CarreraRodríguez, Controllability analysis of thermally coupled distillation systems: five-component mixtures, Industrial and Engineering Chemistry Research 46 (2007) 211. [19] S. Wang, D. Wong, Controllability and energy efficiency of a high-purity divided wall column, Chemical Engineering Science 62 (2007) 1010. [20] Y. Cho, B. Kim, D. Kim, M. Han, Operation of divided wall column using profile position control, in: International Conference on Control, Automation and Systems, Seoul, Korea, 2007. [21] S. Hernández, J.G. Segovia-Hernández, F. Gómez-Castro, C. GutiérrezAntonio, A. Briones-Ramírez, Dividing wall distillation columns: optimization and control properties, Chemical Engineering and Technology 31 (2008) 1246. [22] W.L. Luyben, H. Lin, New control structure for divided-wall columns, Industrial and Engineering Chemistry Research 48 (2009) 6034. [23] Y. Cho, B. Kim, D. Kim, M. Han, M. Lee, Operation of divided wall column with vapor sidedraw using profile position control, Journal of Process Control 19 (2009) 932. [24] A. Kiss, R.C. van Diggelen, A.W. Heemink, Comparison of control strategies for dividing-wall columns, Industrial and Engineering Chemistry Research 49 (2010) 288. [25] W.L. Luyben, H. Lin, Temperature control of the BTX divided-wall column, Industrial and Engineering Chemistry Research 49 (2010) 189. [26] A. Woinaroschy, R. Isopescu, Time-optimal control of dividing-wall distillation columns, Industrial and Engineering Chemistry Research 49 (2010) 9195. [27] A.A. Kiss, C.S. Bildea, A control perspective on process intensification in dividing-wall columns, Chemical Engineering and Processing 50 (2011) 281. [28] C. Buck, C. Hiller, G. Fieg, Applying model predictive control to dividing wall columns, Chemical Engineering and Technology 34 (2011) 663. [29] C. Buck, C. Hiller, G. Fieg, Decentralized temperature control of a pilot dividing wall column, Chemical Engineering and Processing 50 (2011) 167. [30] A.A. Kiss, R.R. Rewagad, Dynamic optimization of a dividing-wall column using model predictive control, Chemical Engineering Science 68 (2012) 132. [31] W.L. Luyben, Distillation Design and Control using AspenTM Simulation, AIChE Wiley Inter-science, Bethlehem, Pennsylvania, 2006. [32] S.J. Qin, T.A. Badgwell, A survey of industrial model predictive control technology, Control Engineering Practice 11 (2003) 733.