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Model-based Control of Vapor-recompressed Batch Distillation Column⁎
Proceedings, 10th IFAC International Symposium on Proceedings, 10th IFAC International Symposium on Advanced Control Chemical Processes Proceedings, 10th of IFAC International Symposium on Advanced Control of China, Chemical Processes Available online at www.sciencedirect.com Shenyang, Liaoning, July 25-27, 2018 Advanced Chemical Processes Proceedings, 10th of IFAC International Symposium on Shenyang,Control Liaoning, China, July 25-27, 2018 Shenyang,Control Liaoning, July 25-27, 2018 Advanced of China, Chemical Processes Shenyang, Liaoning, China, July 25-27, 2018
ScienceDirect
IFAC PapersOnLine 51-18 (2018) 554–559
Model-based Control of Model-based Control of Model-based Control of Vapor-recompressed Batch Distillation Vapor-recompressed Batch Distillation Model-based Control of Vapor-recompressed Batch Distillation Column Column Vapor-recompressed Batch Distillation Column Column
Madhuri Madhuri M. M. Vibhute Vibhute and and Sujit Sujit S. S. Jogwar Jogwar Madhuri M. Vibhute and Sujit S. Jogwar Madhuri Vibhute and Sujit S. Jogwar Indian Institute Institute of M. Technology Bombay, Mumbai, 400076, India India Indian of Technology Bombay, Mumbai, 400076, Indian(e-mail: [email protected], of Technology Bombay, Mumbai, 400076, India (e-mail: [email protected], [email protected]). [email protected]). [email protected]). Indian(e-mail: [email protected], of Technology Bombay, Mumbai, 400076, India (e-mail: [email protected], [email protected]). Abstract: Abstract: This This article article provides provides a a comparison comparison of of control control strategies strategies for for an an economically economically attractive attractive Abstract: This article provides a comparison of control forcolumn an economically vapor-recompressed batch distillation (VRBD) column.strategies A VRBD exhibits attractive nonlinear vapor-recompressed batch distillation (VRBD) column. A VRBD column exhibits nonlinear A VRBD exhibits nonlinear vapor-recompressed batch distillation (VRBD) column. dynamics with inter-stream interactions due to strategies energy-integration, which canattractive give rise Abstract: Thisstrong article provides a comparison of control forcolumn an economically dynamics with with strong strong inter-stream inter-stream interactions interactions due due to which can give to energy-integration, energy-integration, cannonlinear give rise rise dynamics to the using controllers. In vapor-recompressed batch distillation (VRBD) column. A linear VRBD columnwhich exhibits to difficulties difficulties in in controlling controlling the operation operation using traditional traditional linear controllers. In this this paper, paper, we we to difficulties instrong controlling the operation using traditional In this we propose and compare model-based control strategies such aslinear linearcontrollers. quadratic regulator (LQR), dynamics with inter-stream interactions due to energy-integration, which canpaper, give rise propose and compare model-based control strategies such as linear quadratic regulator (LQR), propose and compare model-based control strategies such aslinear linear quadratic regulator linear model predictive control and Globally linearizing controller (GLC) forpaper, a (LQR), VRBD to difficulties in controlling the (LMPC) operation using traditional controllers. In this we linear model model predictive predictive control control (LMPC) (LMPC) and and Globally Globally linearizing linearizing controller controller (GLC) (GLC) for for aa VRBD VRBD linear column to achieve desired distillate purity minimum consumption. The effectiveness propose and compare model-based controlwith strategies suchenergy as linear quadratic regulator (LQR), The effectiveness column to to achieve achieve desired desired distillate distillate purity purity with with minimum minimum energy energy consumption. consumption. The column effectiveness of control strategies is using aa simulation case study of linear model predictive control (LMPC) and Globally linearizing controller for a VRBD of these these control strategies is illustrated illustrated using simulation case study (GLC) of benzene/toluene benzene/toluene of thesetocontrol strategies is illustrated usingminimum a simulation study of The benzene/toluene separation in a VRBD column. column achieve desired distillate purity with energycase consumption. effectiveness separation in in aa VRBD VRBD column. column. separation of these control strategies is illustrated using a simulation case study of benzene/toluene © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. separation in a VRBD column. Keywords: Keywords: Energy-integration, Energy-integration, heat heat pump, pump, batch batch distillation, distillation, model-based model-based control, control, Keywords: Energy-integration, heat pump, batch distillation, model-based control, input/output linearization, linear quadratic regulator, model predictive control. input/output linearization, linear quadratic regulator, model predictive control. input/output linearization, linear quadratic regulator, model predictive control. Keywords: Energy-integration, heat pump, batch distillation, model-based control, input/output linearization, linear quadratic regulator, model predictive control. 1. INTRODUCTION Vapor-recompressed Batch Distillation (VRBD), as 1. INTRODUCTION as dedeVapor-recompressed Batch Distillation (VRBD), 1. INTRODUCTION Vapor-recompressed Distillation (VRBD),configuas depicted one energy-integrated picted in in Figure Figure 1, 1, is is Batch one such such energy-integrated configu1. INTRODUCTION picted in batch Figuredistillation 1, is Batch one such energy-integrated ration of (Babu and Jana, 2014).configuAs Vapor-recompressed Distillation (VRBD), as the deAs As the the chemical chemical and and allied allied industries industries are are growing growing at at ration of batch distillation (Babu and 2014). As distillation (Babu and Jana, Jana, 2014). As the the productof withdrawn fromsuch the energy-integrated VRBD column, similar to picted inisbatch Figure 1, is one configuAs the chemical allied industries growing are at ration a faster rate andand non-renewable energyareresources product is withdrawn from the column, similar to a faster rate and non-renewable energy resources are withdrawn from(Babu the VRBD VRBD column, similar to adepleting faster rate andday, non-renewable energy conventional batch distillation, the product purity starts ration of isbatch distillation and Jana, 2014). As the day by itallied is necessary to perform mostare of product As the chemical and industries areresources growing at conventional batch distillation, the product purity starts depleting day by day, it is necessary to perform most of conventional batch distillation, the product purity starts by it in is necessary to perform of product to drop from the desired value. In order to maintain the is withdrawn from the VRBD column, similar to depleting day operations industrial an energy saver mode.most Oneare athefaster rate andday, non-renewable energy resources drop from the desired value. In order to maintain the the industrial industrial operations operations in an energy saver mode. One of to to drop from the desired value. In order to maintain the in anthermally energy to saver mode.most One of product purity, a feedback control system is needed. The conventional batch distillation, the product purity starts the ways to achieve this is to integrate process depleting day by day, it is necessary perform purity, a feedback control system is needed. The the ways to achieve this is to thermally integrate process product purity, feedback control needed. major challenge comes from fact thatThe the to dropoperational from thea desired value. In system orderthe tois maintain the waysand to achieve this is integrate process streams get economic benefits. an integration industrial operations in to anthermally energySuch saver mode. One of product major operational challenge comes from the fact that the streams and get economic benefits. Such an integration major operational challenge comes from the fact the streams and get economic benefits. Such an integration deviations in product purity disturb the thermal balance product purity, a feedback control system is needed. The involves of energy sources and sinks within the waysidentification to achieve this is to thermally integrate processa deviations in product purity disturb the thermal that balance involves identification identification of of energy energy sources sources and and sinks sinks within within aa major deviations in product purity disturb the thermal balance between the heat source and sink, and can easily destabioperational challenge comes from the fact that the involves system and establishing transfer between them to streams and get economic benefits. Such an integration system and establishing energy transfer between them to between the heat source and sink, and can easily destabibetween the heat source and sink, and can easily destabilize the system. In order to address this control problem deviations in product purity disturb the thermal balance system and establishing transfer between them to reduce the use of external utilities. involves identification of energy sources and sinks within a lize the system. In order to address this control problem reduce the use of external utilities. the system. Insource orderand to address this control problem utilities. in we to use model-based between the heatmanner, sink, and destabireduce of externalenergy system the anduse establishing transfer between them to lize in aa systematic systematic manner, we propose propose tocan useeasily model-based Due to operational flexibility and repeatability, batch proin a systematic manner, we propose to use model-based control configurations to achieve product purity control lize the system. In order to address this control problem Due to operational flexibility and repeatability, batch proreduce the use of external utilities. control configurations to achieve product purity control Due operational flexibilityof repeatability, batchyears pro- in cesses getting researchers in control configurations to achieve product purity control while ensuring stability and optimality of operation. a systematic manner, we propose to use model-based cessestoare are getting attention attention ofand researchers in recent recent years while ensuring stability and optimality of operation. cesses are getting researchers in attractive recent (Fern´ andez et al., attention 2012). It of isand economically to control Due to operational flexibility repeatability, batchyears prowhile ensuring stabilitytoand optimality of operation. configurations achieve product purity control (Fern´ a ndez et al., 2012). It is economically attractive to (Fern´ andez et al., attention 2012). It of is researchers economically attractive to In this paper, model-based control strategies incorporate energy integration in batch in processes, but cesses are getting recent years thisensuring paper, several several control strategies are are while stabilitymodel-based and optimality of operation. incorporate energy energy integration integration in in batch batch processes, processes, but but In In this paper, several model-based control strategies are explored for efficient operation of a VRBD column. Firstly, incorporate strong coupling between process streams resulting from (Fern´ a ndez et al., 2012). It is economically attractive to strong coupling between process streams resulting from explored for efficient operation of a VRBD column. Firstly, explored for efficient operation of a VRBD column. Firstly, linear quadratic regulator (LQR) which is the simplest this paper, several model-based control strategies are strong coupling between resulting+from such integration gives riseprocess to hybrid (continuous disincorporate energy integration instreams batch processes, but In quadratic regulator (LQR) which is the simplest such integration integration gives gives rise rise to to hybrid hybrid (continuous (continuous + + disdis- linear quadratic regulator (LQR) which is the simplest form of optimal control is considered. Linear model preexplored for efficient operation of a VRBD column. Firstly, such crete) two-time dynamics (Jogwar Daoutidis, strong coupling scale between process streams and resulting from linear of optimal control is considered. Linear model precrete) two-time two-time scale scale dynamics dynamics (Jogwar (Jogwar and and Daoutidis, Daoutidis, form form optimal control is considered. Linear model predictive controller (LMPC) is to regulator (LQR) which the simplest crete) 2015).integration In such a gives case, rise control system(continuous design to achieve such to hybrid + dis- linear dictiveofquadratic controller (LMPC) is designed designed toissystematically systematically 2015). In such a case, control system design to achieve dictive controller (LMPC) is designed to systematically handle operating constraints. Lastly, a nonlinear control form of optimal control is considered. Linear model pre2015). In such a case, control system design to achieve desired performance of the process is a challenging task. crete) two-time scale dynamics (Jogwar and Daoutidis, handle operating constraints. Lastly, a nonlinear control desired performance of the process is a challenging task. handle operating constraints. Lastly, a nonlinear control scheme is designed with the help of input/output linearizadictive controller (LMPC) is designed to systematically desired performance of the process is a challenging task. 2015). In such a case, control system design to achieve is designed with the help of input/output linearizaDistillation is one of the most widely used separation scheme scheme is designed with the helpLastly, of input/output linearization for nonlinearity in the phase. handle operating nonlinear control desired performance the process is a challenging task. Distillation is one one of ofof the the most widely widely used separation separation tion to to account account forconstraints. nonlinearity in the aproduction production phase. Distillation is most used processes with high energy consumption and low thertion to account for with nonlinearity the production phase. is designed the help in of input/output linearizaprocesses with high energy consumption and low ther- scheme of is as follows. Section 2 processes with highofenergy consumption and thermodylow ther- The modynamic efficiency. The low Distillation is one the disadvantage most widely ofused separation The rest rest of the the paper paper is organized organized follows. Section 2 dedeto account for nonlinearity inas the production phase. modynamic efficiency. The of thermody- tion rest of the paper is organized as follows. Section 2 demodynamic efficiency. The disadvantage disadvantage of low low scribes the configuration and operating principle of VRBD. namic efficiency of distillation can be overcome by incorprocesses with high energy consumption and thermodylow ther- The scribes the configuration and operating principle of VRBD. namic efficiency of distillation can be overcome by incorscribes configuration and principle of VRBD. Section 33ofpresents design of various model-based control restthe the paper is organized as follows. Section 2 denamic efficiency of distillation can be overcome bycoupled incor- The porating energy-integration. Numerous thermally modynamic efficiency. The disadvantage of low thermodypresents design of operating various model-based control porating energy-integration. energy-integration. Numerous Numerous thermally thermally coupled coupled Section Section 3 presents design of various model-based control strategies for a VRBD column. Closed-loop performances scribes the configuration and operating principle of VRBD. porating configurations and control strategies have been developed namic efficiency of distillation can be overcome by incorfor a VRBD column. Closed-loop performances configurations and control strategies have been developed strategies a column VRBD column. Closed-loop performances been economics developed of the VRBD with above control strategies Section 3 for presents design of the various model-based control configurations and control strategies for continuous distillation column tohave improve porating energy-integration. Numerous thermally coupled strategies of the VRBD column with the above control strategies for continuous distillation column to improve economics of the VRBD column with the above control strategies for continuous distillation column to improve economics are presented in Section 4 for a simulation case study for a VRBD column. Closed-loop performances and lower energy (see Jogwar and developed Daoutidis strategies configurations andconsumption control strategies have been presented in Section 44 for aa simulation case study and lower lower energy energy consumption consumption (see (see Jogwar Jogwar and and Daoutidis Daoutidis are are presented in Section for simulation case study benzene-toluene separation and concluding remarks are the VRBD column with the above control strategies and (2010) for a review), whereas limitedto literature available of for continuous distillation column improve iseconomics of benzene-toluene separation and concluding remarks are (2010) for a review), whereas limited literature is available of benzene-toluene separation and concluding remarks are drawn in Section 5. are presented in Section 4 for a simulation case study (2010) for a review), whereas limited literature is available on energy-integrated batch distillation (Babu and Jana, and lower energy consumption (see Jogwar and Daoutidis in Section 5. on energy-integrated batch distillation (Babu and Jana, drawn in Section 5.separation and concluding remarks are of benzene-toluene on energy-integrated batch distillation (Babu isand Jana, drawn 2014). (2010) for a review), whereas limited literature available 2014). 2. RECOMPRESSED BATCH 2014). in Section 5. on energy-integrated batch distillation (Babu and Jana, drawn 2. VAPOR VAPOR RECOMPRESSED BATCH DISTILLATION DISTILLATION Partial financial support for this work by the Government of India, 2. VAPOR RECOMPRESSED BATCH DISTILLATION 2014). Partial financial support for this work by the Government of India, Vapor-recompressed batch is 2. VAPOR RECOMPRESSED BATCH DISTILLATION Department of Science andfor Technology grant IFAPartial financial support this work (DST)-INSPIRE by the Government of India, Vapor-recompressed batch distillation distillation is an an energyenergyDepartment of Science and Technology (DST)-INSPIRE grant IFAVapor-recompressed batch distillation is an energy Partial integrated configuration which works on the 13 ENG-61 isofgratefully acknowledged. Department Science and Technology (DST)-INSPIRE grant IFAfinancial support for this work by the Government of India, integrated configuration which works on the principle principle of of 13 ENG-61 is gratefully acknowledged. integrated configuration which works on the principle of 13 ENG-61 is gratefully acknowledged. Vapor-recompressed batch distillation is an energyDepartment of Science and Technology (DST)-INSPIRE grant IFAintegrated configuration which works on the principle of 13 ENG-61 is gratefully acknowledged. 2405-8963 © 2018 2018, IFAC IFAC (International Federation of Automatic Control) Copyright 548 Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 548 Peer review© under responsibility of International Federation of Automatic Copyright 2018 IFAC 548 Control. 10.1016/j.ifacol.2018.09.366 Copyright © 2018 IFAC 548
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555
xD
1
0.5 R = 0.06 R = 0.05 R = 0.04
0 0
500
1000
1500
2000
Time [min]
Fig. 2. Open-loop dynamics of the VRBD column for step changes in the reflux rate Fig. 1. Vapor-recompressed batch distillation a heat pump. Figure 1 shows a schematic configuration of a VRBD column. The overhead vapor from the column acts as a heat source and the reboiler liquid acts as a heat sink. Note that the heat source is colder than the heat sink which is thermodynamically infeasible. To ensure feasibility of heat transfer, the top vapor is compressed in a compressor to raise its condensation temperature. A thermal driving force (∆T ) is to be maintained between the temperature of the compressed top vapor (TC ) and the reboiler liquid (TB ) throughout the batch. As the operation of a VRBD column is dynamic, the top tray temperature (TT ) and the reboiler temperature vary with time. The compressor therefore operates at a variable speed to maintain constant ∆T throughout the batch operation. The corresponding compression ratio (CR) required is estimated as: µ ( µ−1 ) TC (1) CR = TT where µ is the specific heat ratio. As the thermal energy associated with the condensing vapor may not always be sufficient to generate the required amount of vapor, an auxiliary reboiler is installed to cover for any deficit amount of heating duty. The overall operation of VRBD consists of two phases: • Start-up phase: At first, the column is operated at total reflux conditions and no product is withdrawn. The start-up phase ends when a steady state with the desired product purity is reached. • Production phase: This phase starts with the withdrawal of distillate as a product. As mentioned earlier, this causes the purities as well as the dew/bubble point temperature of the top vapor and the reboiler liquid to deviate from the start-up phase values, requiring continuous intervention (through control) to achieve sustained product withdrawal at the desired purity. The production phase ends when either the average distillate purity (xD,avg ) or the reflux drum holdup (MD ) falls below its minimum value (xD,avg,min or MD,min , respectively).
Additionally, there is a need to maintain sufficient reflux drum holdup. Available manipulated inputs are the reflux rate (R) and the auxiliary reboiler duty (Qaux ). In order to investigate the dynamic properties of the VRBD column, we performed open loop simulations in the production phase. Step changes are given to the reflux rate and the corresponding response of the distillate purity is depicted in figure 2. It can be seen that the relationship between the reflux rate (one of the key manipulated inputs) and the product purity (the primary controlled variable) is nonlinear. Furthermore, the use of Qaux as a manipulated input necessitates that the overall energy consumption of the system be optimized otherwise the primary objective of energy integration is compromised. This motivated us to explore control strategies beyond conventional PID control. In what follows, we develop several model-based control strategies to achieve these operational objectives. 3.1 Linear Quadratic Regulator (LQR) As there is a requirement of optimal use of one of the manipulated inputs, we start with LQR, the simplest of the optimal controllers. The original nonlinear dynamic system is linearized around the steady state obtained at the end of the startup phase and discretized with a sampling time of 30 s. This results in the following discrete state-space representation of the system. xk+1 = φxk + γuk yk = Cxk
(2)
where the states x, inputs u and the outputs y represent deviations from the steady state. For this system, a state feedback law of the form (3) uk = −Kxk can be obtained (Kumar and Jerome, 2013) to minimize a performance index J defined as: ∞ T J= x Qx + uT Ru dt (4) 0
The two tuning parameters Q and R are adjusted so as to balance control performance and energy utilization. 3.2 Linear Model Predictive Control (LMPC)
3. MODEL-BASED CONTROL STRATEGIES The primary control objective of this system is to maintain xD,avg above the desired value. This is accomplished by regulating the instantaneous distillate purity (xD ). 549
The LQR indirectly penalizes excessive use of auxiliary reboiler duty. Linear MPC scheme is therefore designed to handle input constraints in a systematic way. Even though
2018 IFAC ADCHEM 556 Madhuri Vibhute et al. / IFAC PapersOnLine 51-18 (2018) 554–559 Shenyang, Liaoning, China, July 25-27, 2018
the input/output relationship is nonlinear, we explore the potential of linear MPC as it is shown to yield acceptable results even for nonlinear processes (Darby and Nikolaou, 2012). The discrete-time state space model in Eq. (2) developed earlier is used for the controller design. For this LMPC, the following objective function is considered: J=
Np i=1
(yset − yi )Wy (yset − yi )T + ui Wu uTi
α2 α1 + (xD,avg − xD,avg,min ) (MD − MD,min ) alongwith the following operating constraints: +
(5)
response, the following external integral action is added in the GLC control scheme. KC0 t (x1,set − x1 ) dt v = β10 x1,set + KC0 (x1,set − x1 ) + τ0 0 The other objective of controlling the reflux drum hold-up by manipulating auxiliary reboiler duty is achieved using a PI controller: Qaux = Qaux,nom + KC1 (MD,set − MD ) + KC1 t (MD,set − MD ) dt τ1 0
(7)
3.4 Multi-loop PI controller
Qaux ≤ Qaux,max
R ≤ Rmax The last two terms of the objective function in Eq. (5) act as soft constraints to maintain the average distillate purity and reflux drum holdup above their critical values. The process behavior is predicted over the prediction horizon of Np = 40 and control horizon of Nc = 5 is used. Optimal inputs are calculated by solving a constrained optimization problem and the first control move is implemented (Garcia et al., 1989). 3.3 Globally Linearizing Control (GLC) The previous two control schemes used an approximate linearized model of the VRBD column which is valid only in the neighborhood of the considered steady state. Let us now design a controller based on the description of the underlying nonlinear dynamics. Globally Linearizing Control is an efficient and one of the most widely used nonlinear control techniques of feedback linearization (Kravaris and Kantor, 1990). Here, a nonlinear state feedback law is synthesized to linearize the input-output map. We considered top tray purity x1 as the controlled variable as this is equivalent to controlling the distillate purity for a complete condenser (xD = y1 (x1 )). For a 2 × 2 GLC controller with x1 and MD as outputs and R and Qaux as inputs, the characteristic matrix is singular and the design of GLC controller is tricky (Soroush and Kravaris, 1994). In order to simplify controller design, we consider a GLC controller with x1 and R as output and input, respectively. The corresponding input-output relative degree is 1. The GLC controller would achieve the following closed-loop response dx1 + β10 x1 = v = β10 x1,set (6) β11 dt using the following nonlinear state feedback law v − β11 Lf h(x) − β10 x1 u= β11 Lg h(x) with x D − x1 M V (y2 − y1 ) Lf h(x) = M To further simplify the controller implementation, we approximate the instantaneous vapor flow by the steady state vapor flow (V = Vss ). This approximation results in plant-model mismatch. In order to achieve offset-free Lg h(x) =
550
Lastly, we also compare the effectiveness of these proposed optimal and nonlinear model-based control strategies with two conventional PI controllers. Here, the reflux rate and the auxiliary reboiler duty are manipulated as: R = Rnom + KC2 (x1,set − x1 ) +
KC2 τ2
t 0
(x1,set − x1 )dt
Qaux = Qaux,nom + KC3 (MD,set − MD ) + KC3 τ3
t
0
MD,set − MD dt
(8)
In order to compare these control strategies, we define two performance indices. Specifically, • Production Performance Index (PPI): This index captures separation yield and is defined as the total distillate collected as a fraction of the total product present in the feed. Dtotal (9) PPI = M 0 zF where Dtotal is the total distillate collected, M0 is the total charge in the reboiler and zF is the feed composition. • Energetic Performance Index (EPI): This index captures the energy efficiency of the operation and is defined as the amount of product collected per unit energy consumption. Dtotal (10) EP I = Qaux,total where Qaux,total is the total auxiliary reboiler duty used for separation. 4. SIMULATION CASE STUDY Let us now consider a case study of benzene/toluene separation in a VRBD column. This VRBD column has total 8 trays. For simplicity, pressure drop in the column is assumed to be negligible. Constant tray holdup (M) is considered and Hildebrand model is used to predict the vapor-liquid equilibrium. We also assume constant specific heats and liquid flow rate from tray to tray. The nominal operating information of this system is given in Table 1. It is considered that the product is withdrawn at a rate of 0.02 kmol/min in the production phase only if the distillate purity is above a threshold value (0.985). In the first simulation, we implemented the LQR-based state feedback
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5. CONCLUSION
Table 1. VRBD column specifications Parameter Number of stages Total fresh feed M0 Feed composition Tray holdup Reflux drum holdup Distillate composition (xD ) Auxiliary duty (Qaux,nom ) Tray efficiency
Value 8 100 kmol 0.5 0.25 kmol 1.1 kmol 0.99 273.5 kJ/min 59.5%
Table 2. Comparison of controller performance Controller
xD,avg
LQR LMPC GLC PI
0.985 0.985 0.985 0.985
Production phase [min] 2750 2760 3450 4430
PPI 0.3276 0.3372 0.3572 0.3836
557
EPI [kmol/GJ] 19.07 21.46 17.14 12.38
law of Eq. (3) and the corresponding responses are shown in figure 3. It can be seen that the auxiliary heat duty given by the controller is just sufficient to maintain the reflux ratio, and thus the drum hold-up, during product withdrawal by increasing vapor generation in the column. As no constraint is inserted on minimum product purity, the closed-loop system gives a PPI of 0.3276 and an EPI of 19.07 kmol/GJ. In the next simulation, the performance of LMPC is analyzed and figure 4 shows the corresponding closed-loop dynamics. The optimized inputs given by the LMPC are strictly within the bounds and the reflux drum hold-up is also maintained within its limits. Due to the soft constraint on minimum product purity, the LMPC is able to handle trade off between production and energy consumption, resulting in higher values of PPI (0.3372) and EPI (21.46 kmol/GJ) compared to unconstrained LQR. For the next simulation, the closed-loop dynamics of the VRBD column with the GLC scheme is considered and the corresponding responses are depicted in figure 5. The manipulations in the reflux rate are better handled due to the nonlinear control law, resulting in higher values of PPI (0.3572). As this controller does not penalize energy consumption, the EPI (17.14 kmol/GJ) is lower than LMPC. In the last simulation run, multi-loop PI controllers are used during the production phase. Figure 6 depicts the corresponding closed-loop dynamics. The reflux rate given by PI controller in conventional control strategy increases almost linearly to maintain distillate purity at the desired value by consuming auxiliary reboiler duty. Interestingly, this scheme gives the best PPI of 0.3836 (which is even better than the nonlinear controller). However, this is accomplished by compromising benefits of energy integration and results in a small value of EPI (12.38 kmol/GJ). Table 2 gives the comparison of performance for these control strategies. The LMPC has the highest EPI but a low value of PPI as it resulted in less amount of distillate. The PI controller, on the other hand, gave the highest PPI, but resulted in the least energy-efficient operation. The LMPC and GLC provided good trade-off between separation performance and energy efficiency. 551
In this paper, a comparison of model-based control strategies is presented for an energy-integrated batch distillation column. The operational objective of this system is to produce the maximum possible product at the desired purity with minimum energy consumption. We explored various model-based feedback control strategies and studied their closed-loop dynamics. Two key performance indicators were defined to compare separation yield and energy efficiency obtained during closed-loop response. All the model-based control strategies resulted in stable operation and satisfied the purity criteria. The LQR gave the most energy efficient operation (but with poor separation yield), whereas the multi-loop PI strategy resulted in the highest separation yield (with poor energy efficiency). The nonlinear GLC and linear MPC provided high values of both the performance indices. Motivated by this, to further improve these performance indices, we are currently working on the development of a nonlinear model predictive controller (NMPC) for this system. ACKNOWLEDGEMENTS Partial financial support for this work by the Government of India, DST-INSPIRE grant (IFA-13, ENG-61) is gratefully acknowledged. REFERENCES Babu, G.U.B. and Jana, A.K. (2014). Impact of vapor recompression in batch distillation on energy consumption, cost and co2 emission: Open-loop versus closedloop operation. Appl. Therm. Eng., 62(2), 365–374. Darby, M.L. and Nikolaou, M. (2012). Mpc: Current practice and challenges. Control Eng. Pract., 20(4), 328– 342. Fern´ andez, I., Renedo, C.J., P´erez, S.F., Ortiz, A., and Ma˜ nana, M. (2012). A review: Energy recovery in batch processes. Renew. Sust. Energ. Rev., 16(4), 2260–2277. Garcia, C.E., Prett, D.M., and Morari, M. (1989). Model predictive control: theory and practice - a survey. Automatica, 25(3), 335–348. Jogwar, S.S. and Daoutidis, P. (2010). Energy flow patterns and control implications for integrated distillation networks. Ind. Eng. Chem. Res., 49(17), 8048–8061. Jogwar, S.S. and Daoutidis, P. (2015). Dynamic characteristics of energy-integrated batch process systems: Insights from two case studies. Ind. Eng. Chem. Res., 54(16), 4326–4336. Kravaris, C. and Kantor, J.C. (1990). Geometric methods for nonlinear process control. 2. controller synthesis. Ind. Eng. Chem. Res., 29(12), 2310–2323. Kumar, E.V. and Jerome, J. (2013). Robust lqr controller design for stabilizing and trajectory tracking of inverted pendulum. Procedia Eng., 64, 169–178. Soroush, M. and Kravaris, C. (1994). Nonlinear control of a polymerization cstr with singular characteristic matrix. AIChE J., 40(6), 980–990.
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Fig. 3. Closed-loop response of the VRBD system with LQR in the production phase
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ScienceDirect
IFAC PapersOnLine 51-18 (2018) 554–559
Model-based Control of Model-based Control of Model-based Control of Vapor-recompressed Batch Distillation Vapor-recompressed Batch Distillation Model-based Control of Vapor-recompressed Batch Distillation Column Column Vapor-recompressed Batch Distillation Column Column
Madhuri Madhuri M. M. Vibhute Vibhute and and Sujit Sujit S. S. Jogwar Jogwar Madhuri M. Vibhute and Sujit S. Jogwar Madhuri Vibhute and Sujit S. Jogwar Indian Institute Institute of M. Technology Bombay, Mumbai, 400076, India India Indian of Technology Bombay, Mumbai, 400076, Indian(e-mail: [email protected], of Technology Bombay, Mumbai, 400076, India (e-mail: [email protected], [email protected]). [email protected]). [email protected]). Indian(e-mail: [email protected], of Technology Bombay, Mumbai, 400076, India (e-mail: [email protected], [email protected]). Abstract: Abstract: This This article article provides provides a a comparison comparison of of control control strategies strategies for for an an economically economically attractive attractive Abstract: This article provides a comparison of control forcolumn an economically vapor-recompressed batch distillation (VRBD) column.strategies A VRBD exhibits attractive nonlinear vapor-recompressed batch distillation (VRBD) column. A VRBD column exhibits nonlinear A VRBD exhibits nonlinear vapor-recompressed batch distillation (VRBD) column. dynamics with inter-stream interactions due to strategies energy-integration, which canattractive give rise Abstract: Thisstrong article provides a comparison of control forcolumn an economically dynamics with with strong strong inter-stream inter-stream interactions interactions due due to which can give to energy-integration, energy-integration, cannonlinear give rise rise dynamics to the using controllers. In vapor-recompressed batch distillation (VRBD) column. A linear VRBD columnwhich exhibits to difficulties difficulties in in controlling controlling the operation operation using traditional traditional linear controllers. In this this paper, paper, we we to difficulties instrong controlling the operation using traditional In this we propose and compare model-based control strategies such aslinear linearcontrollers. quadratic regulator (LQR), dynamics with inter-stream interactions due to energy-integration, which canpaper, give rise propose and compare model-based control strategies such as linear quadratic regulator (LQR), propose and compare model-based control strategies such aslinear linear quadratic regulator linear model predictive control and Globally linearizing controller (GLC) forpaper, a (LQR), VRBD to difficulties in controlling the (LMPC) operation using traditional controllers. In this we linear model model predictive predictive control control (LMPC) (LMPC) and and Globally Globally linearizing linearizing controller controller (GLC) (GLC) for for aa VRBD VRBD linear column to achieve desired distillate purity minimum consumption. The effectiveness propose and compare model-based controlwith strategies suchenergy as linear quadratic regulator (LQR), The effectiveness column to to achieve achieve desired desired distillate distillate purity purity with with minimum minimum energy energy consumption. consumption. The column effectiveness of control strategies is using aa simulation case study of linear model predictive control (LMPC) and Globally linearizing controller for a VRBD of these these control strategies is illustrated illustrated using simulation case study (GLC) of benzene/toluene benzene/toluene of thesetocontrol strategies is illustrated usingminimum a simulation study of The benzene/toluene separation in a VRBD column. column achieve desired distillate purity with energycase consumption. effectiveness separation in in aa VRBD VRBD column. column. separation of these control strategies is illustrated using a simulation case study of benzene/toluene © 2018, IFAC (International Federation of Automatic Control) Hosting by Elsevier Ltd. All rights reserved. separation in a VRBD column. Keywords: Keywords: Energy-integration, Energy-integration, heat heat pump, pump, batch batch distillation, distillation, model-based model-based control, control, Keywords: Energy-integration, heat pump, batch distillation, model-based control, input/output linearization, linear quadratic regulator, model predictive control. input/output linearization, linear quadratic regulator, model predictive control. input/output linearization, linear quadratic regulator, model predictive control. Keywords: Energy-integration, heat pump, batch distillation, model-based control, input/output linearization, linear quadratic regulator, model predictive control. 1. INTRODUCTION Vapor-recompressed Batch Distillation (VRBD), as 1. INTRODUCTION as dedeVapor-recompressed Batch Distillation (VRBD), 1. INTRODUCTION Vapor-recompressed Distillation (VRBD),configuas depicted one energy-integrated picted in in Figure Figure 1, 1, is is Batch one such such energy-integrated configu1. INTRODUCTION picted in batch Figuredistillation 1, is Batch one such energy-integrated ration of (Babu and Jana, 2014).configuAs Vapor-recompressed Distillation (VRBD), as the deAs As the the chemical chemical and and allied allied industries industries are are growing growing at at ration of batch distillation (Babu and 2014). As distillation (Babu and Jana, Jana, 2014). As the the productof withdrawn fromsuch the energy-integrated VRBD column, similar to picted inisbatch Figure 1, is one configuAs the chemical allied industries growing are at ration a faster rate andand non-renewable energyareresources product is withdrawn from the column, similar to a faster rate and non-renewable energy resources are withdrawn from(Babu the VRBD VRBD column, similar to adepleting faster rate andday, non-renewable energy conventional batch distillation, the product purity starts ration of isbatch distillation and Jana, 2014). As the day by itallied is necessary to perform mostare of product As the chemical and industries areresources growing at conventional batch distillation, the product purity starts depleting day by day, it is necessary to perform most of conventional batch distillation, the product purity starts by it in is necessary to perform of product to drop from the desired value. In order to maintain the is withdrawn from the VRBD column, similar to depleting day operations industrial an energy saver mode.most Oneare athefaster rate andday, non-renewable energy resources drop from the desired value. In order to maintain the the industrial industrial operations operations in an energy saver mode. One of to to drop from the desired value. In order to maintain the in anthermally energy to saver mode.most One of product purity, a feedback control system is needed. The conventional batch distillation, the product purity starts the ways to achieve this is to integrate process depleting day by day, it is necessary perform purity, a feedback control system is needed. The the ways to achieve this is to thermally integrate process product purity, feedback control needed. major challenge comes from fact thatThe the to dropoperational from thea desired value. In system orderthe tois maintain the waysand to achieve this is integrate process streams get economic benefits. an integration industrial operations in to anthermally energySuch saver mode. One of product major operational challenge comes from the fact that the streams and get economic benefits. Such an integration major operational challenge comes from the fact the streams and get economic benefits. Such an integration deviations in product purity disturb the thermal balance product purity, a feedback control system is needed. The involves of energy sources and sinks within the waysidentification to achieve this is to thermally integrate processa deviations in product purity disturb the thermal that balance involves identification identification of of energy energy sources sources and and sinks sinks within within aa major deviations in product purity disturb the thermal balance between the heat source and sink, and can easily destabioperational challenge comes from the fact that the involves system and establishing transfer between them to streams and get economic benefits. Such an integration system and establishing energy transfer between them to between the heat source and sink, and can easily destabibetween the heat source and sink, and can easily destabilize the system. In order to address this control problem deviations in product purity disturb the thermal balance system and establishing transfer between them to reduce the use of external utilities. involves identification of energy sources and sinks within a lize the system. In order to address this control problem reduce the use of external utilities. the system. Insource orderand to address this control problem utilities. in we to use model-based between the heatmanner, sink, and destabireduce of externalenergy system the anduse establishing transfer between them to lize in aa systematic systematic manner, we propose propose tocan useeasily model-based Due to operational flexibility and repeatability, batch proin a systematic manner, we propose to use model-based control configurations to achieve product purity control lize the system. In order to address this control problem Due to operational flexibility and repeatability, batch proreduce the use of external utilities. control configurations to achieve product purity control Due operational flexibilityof repeatability, batchyears pro- in cesses getting researchers in control configurations to achieve product purity control while ensuring stability and optimality of operation. a systematic manner, we propose to use model-based cessestoare are getting attention attention ofand researchers in recent recent years while ensuring stability and optimality of operation. cesses are getting researchers in attractive recent (Fern´ andez et al., attention 2012). It of isand economically to control Due to operational flexibility repeatability, batchyears prowhile ensuring stabilitytoand optimality of operation. configurations achieve product purity control (Fern´ a ndez et al., 2012). It is economically attractive to (Fern´ andez et al., attention 2012). It of is researchers economically attractive to In this paper, model-based control strategies incorporate energy integration in batch in processes, but cesses are getting recent years thisensuring paper, several several control strategies are are while stabilitymodel-based and optimality of operation. incorporate energy energy integration integration in in batch batch processes, processes, but but In In this paper, several model-based control strategies are explored for efficient operation of a VRBD column. Firstly, incorporate strong coupling between process streams resulting from (Fern´ a ndez et al., 2012). It is economically attractive to strong coupling between process streams resulting from explored for efficient operation of a VRBD column. Firstly, explored for efficient operation of a VRBD column. Firstly, linear quadratic regulator (LQR) which is the simplest this paper, several model-based control strategies are strong coupling between resulting+from such integration gives riseprocess to hybrid (continuous disincorporate energy integration instreams batch processes, but In quadratic regulator (LQR) which is the simplest such integration integration gives gives rise rise to to hybrid hybrid (continuous (continuous + + disdis- linear quadratic regulator (LQR) which is the simplest form of optimal control is considered. Linear model preexplored for efficient operation of a VRBD column. Firstly, such crete) two-time dynamics (Jogwar Daoutidis, strong coupling scale between process streams and resulting from linear of optimal control is considered. Linear model precrete) two-time two-time scale scale dynamics dynamics (Jogwar (Jogwar and and Daoutidis, Daoutidis, form form optimal control is considered. Linear model predictive controller (LMPC) is to regulator (LQR) which the simplest crete) 2015).integration In such a gives case, rise control system(continuous design to achieve such to hybrid + dis- linear dictiveofquadratic controller (LMPC) is designed designed toissystematically systematically 2015). In such a case, control system design to achieve dictive controller (LMPC) is designed to systematically handle operating constraints. Lastly, a nonlinear control form of optimal control is considered. Linear model pre2015). In such a case, control system design to achieve desired performance of the process is a challenging task. crete) two-time scale dynamics (Jogwar and Daoutidis, handle operating constraints. Lastly, a nonlinear control desired performance of the process is a challenging task. handle operating constraints. Lastly, a nonlinear control scheme is designed with the help of input/output linearizadictive controller (LMPC) is designed to systematically desired performance of the process is a challenging task. 2015). In such a case, control system design to achieve is designed with the help of input/output linearizaDistillation is one of the most widely used separation scheme scheme is designed with the helpLastly, of input/output linearization for nonlinearity in the phase. handle operating nonlinear control desired performance the process is a challenging task. Distillation is one one of ofof the the most widely widely used separation separation tion to to account account forconstraints. nonlinearity in the aproduction production phase. Distillation is most used processes with high energy consumption and low thertion to account for with nonlinearity the production phase. is designed the help in of input/output linearizaprocesses with high energy consumption and low ther- scheme of is as follows. Section 2 processes with highofenergy consumption and thermodylow ther- The modynamic efficiency. The low Distillation is one the disadvantage most widely ofused separation The rest rest of the the paper paper is organized organized follows. Section 2 dedeto account for nonlinearity inas the production phase. modynamic efficiency. The of thermody- tion rest of the paper is organized as follows. Section 2 demodynamic efficiency. The disadvantage disadvantage of low low scribes the configuration and operating principle of VRBD. namic efficiency of distillation can be overcome by incorprocesses with high energy consumption and thermodylow ther- The scribes the configuration and operating principle of VRBD. namic efficiency of distillation can be overcome by incorscribes configuration and principle of VRBD. Section 33ofpresents design of various model-based control restthe the paper is organized as follows. Section 2 denamic efficiency of distillation can be overcome bycoupled incor- The porating energy-integration. Numerous thermally modynamic efficiency. The disadvantage of low thermodypresents design of operating various model-based control porating energy-integration. energy-integration. Numerous Numerous thermally thermally coupled coupled Section Section 3 presents design of various model-based control strategies for a VRBD column. Closed-loop performances scribes the configuration and operating principle of VRBD. porating configurations and control strategies have been developed namic efficiency of distillation can be overcome by incorfor a VRBD column. Closed-loop performances configurations and control strategies have been developed strategies a column VRBD column. Closed-loop performances been economics developed of the VRBD with above control strategies Section 3 for presents design of the various model-based control configurations and control strategies for continuous distillation column tohave improve porating energy-integration. Numerous thermally coupled strategies of the VRBD column with the above control strategies for continuous distillation column to improve economics of the VRBD column with the above control strategies for continuous distillation column to improve economics are presented in Section 4 for a simulation case study for a VRBD column. Closed-loop performances and lower energy (see Jogwar and developed Daoutidis strategies configurations andconsumption control strategies have been presented in Section 44 for aa simulation case study and lower lower energy energy consumption consumption (see (see Jogwar Jogwar and and Daoutidis Daoutidis are are presented in Section for simulation case study benzene-toluene separation and concluding remarks are the VRBD column with the above control strategies and (2010) for a review), whereas limitedto literature available of for continuous distillation column improve iseconomics of benzene-toluene separation and concluding remarks are (2010) for a review), whereas limited literature is available of benzene-toluene separation and concluding remarks are drawn in Section 5. are presented in Section 4 for a simulation case study (2010) for a review), whereas limited literature is available on energy-integrated batch distillation (Babu and Jana, and lower energy consumption (see Jogwar and Daoutidis in Section 5. on energy-integrated batch distillation (Babu and Jana, drawn in Section 5.separation and concluding remarks are of benzene-toluene on energy-integrated batch distillation (Babu isand Jana, drawn 2014). (2010) for a review), whereas limited literature available 2014). 2. RECOMPRESSED BATCH 2014). in Section 5. on energy-integrated batch distillation (Babu and Jana, drawn 2. VAPOR VAPOR RECOMPRESSED BATCH DISTILLATION DISTILLATION Partial financial support for this work by the Government of India, 2. VAPOR RECOMPRESSED BATCH DISTILLATION 2014). Partial financial support for this work by the Government of India, Vapor-recompressed batch is 2. VAPOR RECOMPRESSED BATCH DISTILLATION Department of Science andfor Technology grant IFAPartial financial support this work (DST)-INSPIRE by the Government of India, Vapor-recompressed batch distillation distillation is an an energyenergyDepartment of Science and Technology (DST)-INSPIRE grant IFAVapor-recompressed batch distillation is an energy Partial integrated configuration which works on the 13 ENG-61 isofgratefully acknowledged. Department Science and Technology (DST)-INSPIRE grant IFAfinancial support for this work by the Government of India, integrated configuration which works on the principle principle of of 13 ENG-61 is gratefully acknowledged. integrated configuration which works on the principle of 13 ENG-61 is gratefully acknowledged. Vapor-recompressed batch distillation is an energyDepartment of Science and Technology (DST)-INSPIRE grant IFAintegrated configuration which works on the principle of 13 ENG-61 is gratefully acknowledged. 2405-8963 © 2018 2018, IFAC IFAC (International Federation of Automatic Control) Copyright 548 Hosting by Elsevier Ltd. All rights reserved. Copyright © 2018 IFAC 548 Peer review© under responsibility of International Federation of Automatic Copyright 2018 IFAC 548 Control. 10.1016/j.ifacol.2018.09.366 Copyright © 2018 IFAC 548
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555
xD
1
0.5 R = 0.06 R = 0.05 R = 0.04
0 0
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1000
1500
2000
Time [min]
Fig. 2. Open-loop dynamics of the VRBD column for step changes in the reflux rate Fig. 1. Vapor-recompressed batch distillation a heat pump. Figure 1 shows a schematic configuration of a VRBD column. The overhead vapor from the column acts as a heat source and the reboiler liquid acts as a heat sink. Note that the heat source is colder than the heat sink which is thermodynamically infeasible. To ensure feasibility of heat transfer, the top vapor is compressed in a compressor to raise its condensation temperature. A thermal driving force (∆T ) is to be maintained between the temperature of the compressed top vapor (TC ) and the reboiler liquid (TB ) throughout the batch. As the operation of a VRBD column is dynamic, the top tray temperature (TT ) and the reboiler temperature vary with time. The compressor therefore operates at a variable speed to maintain constant ∆T throughout the batch operation. The corresponding compression ratio (CR) required is estimated as: µ ( µ−1 ) TC (1) CR = TT where µ is the specific heat ratio. As the thermal energy associated with the condensing vapor may not always be sufficient to generate the required amount of vapor, an auxiliary reboiler is installed to cover for any deficit amount of heating duty. The overall operation of VRBD consists of two phases: • Start-up phase: At first, the column is operated at total reflux conditions and no product is withdrawn. The start-up phase ends when a steady state with the desired product purity is reached. • Production phase: This phase starts with the withdrawal of distillate as a product. As mentioned earlier, this causes the purities as well as the dew/bubble point temperature of the top vapor and the reboiler liquid to deviate from the start-up phase values, requiring continuous intervention (through control) to achieve sustained product withdrawal at the desired purity. The production phase ends when either the average distillate purity (xD,avg ) or the reflux drum holdup (MD ) falls below its minimum value (xD,avg,min or MD,min , respectively).
Additionally, there is a need to maintain sufficient reflux drum holdup. Available manipulated inputs are the reflux rate (R) and the auxiliary reboiler duty (Qaux ). In order to investigate the dynamic properties of the VRBD column, we performed open loop simulations in the production phase. Step changes are given to the reflux rate and the corresponding response of the distillate purity is depicted in figure 2. It can be seen that the relationship between the reflux rate (one of the key manipulated inputs) and the product purity (the primary controlled variable) is nonlinear. Furthermore, the use of Qaux as a manipulated input necessitates that the overall energy consumption of the system be optimized otherwise the primary objective of energy integration is compromised. This motivated us to explore control strategies beyond conventional PID control. In what follows, we develop several model-based control strategies to achieve these operational objectives. 3.1 Linear Quadratic Regulator (LQR) As there is a requirement of optimal use of one of the manipulated inputs, we start with LQR, the simplest of the optimal controllers. The original nonlinear dynamic system is linearized around the steady state obtained at the end of the startup phase and discretized with a sampling time of 30 s. This results in the following discrete state-space representation of the system. xk+1 = φxk + γuk yk = Cxk
(2)
where the states x, inputs u and the outputs y represent deviations from the steady state. For this system, a state feedback law of the form (3) uk = −Kxk can be obtained (Kumar and Jerome, 2013) to minimize a performance index J defined as: ∞ T J= x Qx + uT Ru dt (4) 0
The two tuning parameters Q and R are adjusted so as to balance control performance and energy utilization. 3.2 Linear Model Predictive Control (LMPC)
3. MODEL-BASED CONTROL STRATEGIES The primary control objective of this system is to maintain xD,avg above the desired value. This is accomplished by regulating the instantaneous distillate purity (xD ). 549
The LQR indirectly penalizes excessive use of auxiliary reboiler duty. Linear MPC scheme is therefore designed to handle input constraints in a systematic way. Even though
2018 IFAC ADCHEM 556 Madhuri Vibhute et al. / IFAC PapersOnLine 51-18 (2018) 554–559 Shenyang, Liaoning, China, July 25-27, 2018
the input/output relationship is nonlinear, we explore the potential of linear MPC as it is shown to yield acceptable results even for nonlinear processes (Darby and Nikolaou, 2012). The discrete-time state space model in Eq. (2) developed earlier is used for the controller design. For this LMPC, the following objective function is considered: J=
Np i=1
(yset − yi )Wy (yset − yi )T + ui Wu uTi
α2 α1 + (xD,avg − xD,avg,min ) (MD − MD,min ) alongwith the following operating constraints: +
(5)
response, the following external integral action is added in the GLC control scheme. KC0 t (x1,set − x1 ) dt v = β10 x1,set + KC0 (x1,set − x1 ) + τ0 0 The other objective of controlling the reflux drum hold-up by manipulating auxiliary reboiler duty is achieved using a PI controller: Qaux = Qaux,nom + KC1 (MD,set − MD ) + KC1 t (MD,set − MD ) dt τ1 0
(7)
3.4 Multi-loop PI controller
Qaux ≤ Qaux,max
R ≤ Rmax The last two terms of the objective function in Eq. (5) act as soft constraints to maintain the average distillate purity and reflux drum holdup above their critical values. The process behavior is predicted over the prediction horizon of Np = 40 and control horizon of Nc = 5 is used. Optimal inputs are calculated by solving a constrained optimization problem and the first control move is implemented (Garcia et al., 1989). 3.3 Globally Linearizing Control (GLC) The previous two control schemes used an approximate linearized model of the VRBD column which is valid only in the neighborhood of the considered steady state. Let us now design a controller based on the description of the underlying nonlinear dynamics. Globally Linearizing Control is an efficient and one of the most widely used nonlinear control techniques of feedback linearization (Kravaris and Kantor, 1990). Here, a nonlinear state feedback law is synthesized to linearize the input-output map. We considered top tray purity x1 as the controlled variable as this is equivalent to controlling the distillate purity for a complete condenser (xD = y1 (x1 )). For a 2 × 2 GLC controller with x1 and MD as outputs and R and Qaux as inputs, the characteristic matrix is singular and the design of GLC controller is tricky (Soroush and Kravaris, 1994). In order to simplify controller design, we consider a GLC controller with x1 and R as output and input, respectively. The corresponding input-output relative degree is 1. The GLC controller would achieve the following closed-loop response dx1 + β10 x1 = v = β10 x1,set (6) β11 dt using the following nonlinear state feedback law v − β11 Lf h(x) − β10 x1 u= β11 Lg h(x) with x D − x1 M V (y2 − y1 ) Lf h(x) = M To further simplify the controller implementation, we approximate the instantaneous vapor flow by the steady state vapor flow (V = Vss ). This approximation results in plant-model mismatch. In order to achieve offset-free Lg h(x) =
550
Lastly, we also compare the effectiveness of these proposed optimal and nonlinear model-based control strategies with two conventional PI controllers. Here, the reflux rate and the auxiliary reboiler duty are manipulated as: R = Rnom + KC2 (x1,set − x1 ) +
KC2 τ2
t 0
(x1,set − x1 )dt
Qaux = Qaux,nom + KC3 (MD,set − MD ) + KC3 τ3
t
0
MD,set − MD dt
(8)
In order to compare these control strategies, we define two performance indices. Specifically, • Production Performance Index (PPI): This index captures separation yield and is defined as the total distillate collected as a fraction of the total product present in the feed. Dtotal (9) PPI = M 0 zF where Dtotal is the total distillate collected, M0 is the total charge in the reboiler and zF is the feed composition. • Energetic Performance Index (EPI): This index captures the energy efficiency of the operation and is defined as the amount of product collected per unit energy consumption. Dtotal (10) EP I = Qaux,total where Qaux,total is the total auxiliary reboiler duty used for separation. 4. SIMULATION CASE STUDY Let us now consider a case study of benzene/toluene separation in a VRBD column. This VRBD column has total 8 trays. For simplicity, pressure drop in the column is assumed to be negligible. Constant tray holdup (M) is considered and Hildebrand model is used to predict the vapor-liquid equilibrium. We also assume constant specific heats and liquid flow rate from tray to tray. The nominal operating information of this system is given in Table 1. It is considered that the product is withdrawn at a rate of 0.02 kmol/min in the production phase only if the distillate purity is above a threshold value (0.985). In the first simulation, we implemented the LQR-based state feedback
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5. CONCLUSION
Table 1. VRBD column specifications Parameter Number of stages Total fresh feed M0 Feed composition Tray holdup Reflux drum holdup Distillate composition (xD ) Auxiliary duty (Qaux,nom ) Tray efficiency
Value 8 100 kmol 0.5 0.25 kmol 1.1 kmol 0.99 273.5 kJ/min 59.5%
Table 2. Comparison of controller performance Controller
xD,avg
LQR LMPC GLC PI
0.985 0.985 0.985 0.985
Production phase [min] 2750 2760 3450 4430
PPI 0.3276 0.3372 0.3572 0.3836
557
EPI [kmol/GJ] 19.07 21.46 17.14 12.38
law of Eq. (3) and the corresponding responses are shown in figure 3. It can be seen that the auxiliary heat duty given by the controller is just sufficient to maintain the reflux ratio, and thus the drum hold-up, during product withdrawal by increasing vapor generation in the column. As no constraint is inserted on minimum product purity, the closed-loop system gives a PPI of 0.3276 and an EPI of 19.07 kmol/GJ. In the next simulation, the performance of LMPC is analyzed and figure 4 shows the corresponding closed-loop dynamics. The optimized inputs given by the LMPC are strictly within the bounds and the reflux drum hold-up is also maintained within its limits. Due to the soft constraint on minimum product purity, the LMPC is able to handle trade off between production and energy consumption, resulting in higher values of PPI (0.3372) and EPI (21.46 kmol/GJ) compared to unconstrained LQR. For the next simulation, the closed-loop dynamics of the VRBD column with the GLC scheme is considered and the corresponding responses are depicted in figure 5. The manipulations in the reflux rate are better handled due to the nonlinear control law, resulting in higher values of PPI (0.3572). As this controller does not penalize energy consumption, the EPI (17.14 kmol/GJ) is lower than LMPC. In the last simulation run, multi-loop PI controllers are used during the production phase. Figure 6 depicts the corresponding closed-loop dynamics. The reflux rate given by PI controller in conventional control strategy increases almost linearly to maintain distillate purity at the desired value by consuming auxiliary reboiler duty. Interestingly, this scheme gives the best PPI of 0.3836 (which is even better than the nonlinear controller). However, this is accomplished by compromising benefits of energy integration and results in a small value of EPI (12.38 kmol/GJ). Table 2 gives the comparison of performance for these control strategies. The LMPC has the highest EPI but a low value of PPI as it resulted in less amount of distillate. The PI controller, on the other hand, gave the highest PPI, but resulted in the least energy-efficient operation. The LMPC and GLC provided good trade-off between separation performance and energy efficiency. 551
In this paper, a comparison of model-based control strategies is presented for an energy-integrated batch distillation column. The operational objective of this system is to produce the maximum possible product at the desired purity with minimum energy consumption. We explored various model-based feedback control strategies and studied their closed-loop dynamics. Two key performance indicators were defined to compare separation yield and energy efficiency obtained during closed-loop response. All the model-based control strategies resulted in stable operation and satisfied the purity criteria. The LQR gave the most energy efficient operation (but with poor separation yield), whereas the multi-loop PI strategy resulted in the highest separation yield (with poor energy efficiency). The nonlinear GLC and linear MPC provided high values of both the performance indices. Motivated by this, to further improve these performance indices, we are currently working on the development of a nonlinear model predictive controller (NMPC) for this system. ACKNOWLEDGEMENTS Partial financial support for this work by the Government of India, DST-INSPIRE grant (IFA-13, ENG-61) is gratefully acknowledged. REFERENCES Babu, G.U.B. and Jana, A.K. (2014). Impact of vapor recompression in batch distillation on energy consumption, cost and co2 emission: Open-loop versus closedloop operation. Appl. Therm. Eng., 62(2), 365–374. Darby, M.L. and Nikolaou, M. (2012). Mpc: Current practice and challenges. Control Eng. Pract., 20(4), 328– 342. Fern´ andez, I., Renedo, C.J., P´erez, S.F., Ortiz, A., and Ma˜ nana, M. (2012). A review: Energy recovery in batch processes. Renew. Sust. Energ. Rev., 16(4), 2260–2277. Garcia, C.E., Prett, D.M., and Morari, M. (1989). Model predictive control: theory and practice - a survey. Automatica, 25(3), 335–348. Jogwar, S.S. and Daoutidis, P. (2010). Energy flow patterns and control implications for integrated distillation networks. Ind. Eng. Chem. Res., 49(17), 8048–8061. Jogwar, S.S. and Daoutidis, P. (2015). Dynamic characteristics of energy-integrated batch process systems: Insights from two case studies. Ind. Eng. Chem. Res., 54(16), 4326–4336. Kravaris, C. and Kantor, J.C. (1990). Geometric methods for nonlinear process control. 2. controller synthesis. Ind. Eng. Chem. Res., 29(12), 2310–2323. Kumar, E.V. and Jerome, J. (2013). Robust lqr controller design for stabilizing and trajectory tracking of inverted pendulum. Procedia Eng., 64, 169–178. Soroush, M. and Kravaris, C. (1994). Nonlinear control of a polymerization cstr with singular characteristic matrix. AIChE J., 40(6), 980–990.
2018 IFAC ADCHEM 558 Madhuri Vibhute et al. / IFAC PapersOnLine 51-18 (2018) 554–559 Shenyang, Liaoning, China, July 25-27, 2018
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2018 IFAC ADCHEM Shenyang, Liaoning, China, July 25-27, 2018
Madhuri Vibhute et al. / IFAC PapersOnLine 51-18 (2018) 554–559
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