Journal of Process Control 24 (2014) 415–421

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Journal of Process Control

j ourna l ho me pa ge: www.elsev ier .com/ locate / jprocont

JITL-based concentration control for semi-batch pH-shift reactivecrystallization of l-glutamic acid

Qing-Lin Sua, Richard D. Braatzb,∗, Min-Sen Chiua,∗

a Department of Chemical and Biomolecular Engineering, National University of Singapore, Singapore 117585, Singaporeb Department of Chemical Engineering, Massachusetts Institute of Technology, Cambridge, MA 02139, USA

a r t i c l e i n f o

Article history:Received 3 January 2013Accepted 20 July 2013Available online 27 December 2013

Keywords:Concentration controlpH-shift reactive crystallizationSemi-batch processJust-in-Time Learning

a b s t r a c t

Although concentration control (C-control) strategy has been shown to give effective and robust controlperformance for batch cooling and semi-batch antisolvent crystallizations in recent years, no researchwork was reported concerning the potential application of conventional C-control for the more challeng-ing semi-batch pH-shift reactive crystallization that is common in the process industries. To this end, thispaper presents detailed analysis to find out that it is not feasible to apply the C-control to semi-batchpH-shift reactive crystallization. To circumvent this problem, a variant of C-control strategy by incorpo-rating the Just-in-Time Learning (JITL) method to cope with strong process nonlinearity inherent in thepH-shift reactive crystallization is developed in this paper. Simulation results are presented to illustratethe proposed design and a comparison with conventional optimal control is made.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

The prevalence and high value-added of batch and semi-batchcrystallization processes in the pharmaceutical, fine chemical, andfood industries have motivated the development of many controlstrategies [1–5]. The solute concentration is a critical state vari-able for controlling crystallization processes, as the crystallizationkinetics are usually written in terms of the supersaturation, whichis the difference between the solute concentration and a saturatedconcentration.

A control strategy for batch and semi-batch crystallizations thathas become popular in recent years is to determine an optimalsolute concentration or supersaturation trajectory against othermanipulated system state throughout the run, and then designa feedback control system to maintain the optimal relationshipbetween the states [6,7]. Similar studies can also be found intracking of necessary conditions of optimality [8]. Detailed uncer-tainty and disturbance analyses carried out both experimentallyand in simulations have shown that the approach ensures theconsistent production of large crystals by suppressing excessivenucleation and the formation of undesired polymorphs [9,10]. Thisso-called concentration control (C-control) approach, in which thetrajectories of concentration vs. temperature or concentration vs.antisolvent mass fraction are tracked throughout the batch, has

∗ Corresponding author. Tel.: +65 6516 2223; fax: +65 6779 1936.E-mail addresses: braatz@mit.edu (R.D. Braatz), checms@nus.edu.sg (M.-S. Chiu).

been implemented in many cooling and antisolvent crystallizations[6–11].

However, application of C-control to the more challengingsemi-batch pH-shift reactive crystallization processes that are alsocommon in industrial practice receives little attention. This moti-vates this paper to investigate whether conventional C-controlstrategy can be applied to a semi-batch pH-shift reactive crys-tallization using l-glutamic acid as a model compound. Sinceour analysis shows that straightforward extension of C-controlis not feasible due to highly nonlinearity of the correspondingdesired concentration trajectory, which has a dome-shaped pro-file resulting from the combined effects of reaction, crystallization,and dilution, an enhanced C-control strategy by incorporating theJust-in-Time Learning (JITL) method [12–15], which has good pre-dictive performance to provide useful information for C-controldesign to track the dome-shaped concentration trajectory closelyfor improved control performance, is developed in this paper. Sim-ulation results are presented to illustrate the proposed design anda comparison with conventional optimal control is made.

This paper is organized as follows. The next section reviews theconventional C-control strategy applied to batch cooling crystal-lization. Section 3 gives detailed account of the proposed JITL-basedC-control strategy, followed by the simulation studies discussed inSection 4. Finally, concluding remarks were made.

2. Conventional C-control strategy

Two methods for implementing conventional C-control havebeen employed for batch cooling crystallization with main

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416 Q.-L. Su et al. / Journal of Process Control 24 (2014) 415–421

Fig. 1. Implementation of conventional C-control using a concentration (top) ortemperature (bottom) feedback controller.

difference in the choice of set point for a lower-level PID controlloop, i.e., concentration set point [7] or temperature set point [6],as outlined in Fig. 1. It was argued that the controller tuning ismuch more difficult for the former, particularly for complicatedcrystallization systems [16], so this paper considers only the latterapproach.

For illustration purpose, the implementation of conventional C-control for batch cooling crystallization [6] is schematically shownin Fig. 2, where the solid curve represents the desired concentra-tion vs. temperature trajectory tracked by the C-control withinthe batch. Suppose the process is operated at point A with cur-rent solute concentration C(k) and temperature T(k), C-controldetermines new set point Tset(k) for the temperature controllerby drawing a horizontal line from point A to intersect the tar-get trajectory at point B as shown in Fig. 2, from which Tset(k) isspecified to be the abscissa of point B. The physical significance ofhorizontal line aforementioned is that C-control assumes negligi-ble crystallization effect on the solution concentration when thesolution is cooled from the current temperature T(k) to new setpoint Tset(k). In practice, although the lower-level PID temperaturecontroller can track new set points by the next sampling instant,

Fig. 2. Conventional C-control for a batch cooling crystallization.

Fig. 3. Applications of (a) conventional C-control and (b) proposed C-control for asemi-batch pH-shift reactive crystallization.

i.e., T(k + 1) = Tset(k), the process cannot reach to point B as soluteconcentration at the next sample, C(k + 1), should be smaller thanC(k) due to crystallization effect, which is shown by the vertical lineconnecting point B to point E in Fig. 2. Hence, by repeating the pro-cedure of A → B → E, the desired trajectory can be tracked fairlyclosely by implementing C-control provided that the deviationbetween B and E is small, which is the case when the crystallizationkinetics are slow within one sampling instant. This control strategycan be similarly applied to antisolvent crystallization by replacingthe concentration vs. temperature trajectory by the concentrationvs. antisolvent mass fraction trajectory [6] and taking into accountthe dilution effect [17].

Although conventional C-control has received successfulapplications for both batch/semi-batch cooling and antisolventcrystallizations, it cannot be applied to control a more compli-cated semi-batch pH-shift reactive crystallization whose desiredconcentration vs. volume trajectory to be tracked by the C-controlis dome-shaped (see Fig. 3) resulting from the combined effectsof reaction, crystallization, and dilution. Consequently, the imple-mentation of conventional C-control is not feasible [18–20] becausewhen the process is operated at the left-hand side of the dome-shape trajectory, for example point A in Fig. 3(a) with current soluteconcentration C(k) and corresponding solution volume V(k), theimplementation of conventional C-control is to draw a horizon-tal line from point A to intersect with the dome-shape curve atpoint B and the set point Vset(k) is specified to be the corresponding

Q.-L. Su et al. / Journal of Process Control 24 (2014) 415–421 417

abscissa of point B. However, as can be seen from Fig. 3(a), Vset(k)is smaller than V(k), which is not possible to be implemented assolution volume increases monotonically since the start-up of pro-cess operation. On the other end, when the process operation liesat the right-hand side of the trajectory, for example at point E, it ispossible to implement the conventional C-control in a similar fash-ion as what is practiced for cooling and antisolvent crystallization.Therefore, to cope with challenging process characteristics inher-ent in semi-batch pH-shift reactive crystallization that impede theperformance of conventional C-control strategy, a variant of con-ventional C-control to achieve improved performance is developedin the next section.

3. JITL-based C-control strategy

Before we discuss the proposed C-control strategy, it is worth-while pointing out that the conventional C-control strategy is infact a model-based controller design method, which motivates thedevelopment of proposed C-control strategy. Suppose the desiredconcentration vs. temperature trajectory for cooling crystallizationin Fig. 2 is given by

C(k) = f [T(k)] (1)

where f denotes the nonlinear function describing the desired tra-jectory between process output C and process input T. Furthermore,given the nonlinear function g representing input and output rela-tionship for cooling crystallization system, the following equationholds.

C(k + 1) = C(k) +∫ T(k+1)

T(k)

g(T)dT (2)

The implementation of C-control is to solve the following opti-mization problem subject to constraints, if any, to track the desiredtrajectory of Eq. (1).

Tset(k) = arg min∥∥f [T(k + 1)] − C(k + 1)

∥∥

= arg min

∥∥∥∥∥f [T(k + 1)] − C(k) −∫ T(k+1)

T(k)

g(T)dT

∥∥∥∥∥= arg min

∥∥∥∥∥f [Tset(k)] − C(k) −∫ Tset (k)

T(k)

g(T)dT

∥∥∥∥∥

(3)

where a lower level PID temperature controller is assumed to reachnew set point within one sampling instant, i.e., T(k + 1) = Tset(k).

As discussed previously, conventional C-control strategy illus-trated in Fig. 2 neglects the crystallization effect when temperaturedecreases from T(k) to Tset(k), meaning that g(T) = 0 or equivalently,C(k + 1) = C(k) based on Eq. (2). Therefore, the optimal solution forEq. (3) can be obtained by solving Eqs. (1) and (2) simultaneously,which is equivalent to the conditions inferred by the intersect Bin Fig. 2. In the case of semi-batch antisolvent crystallization, theC-control problem can be analogously formulated by replacing T inEqs. (1)–(3) by W which is the mass fraction of antisolvent. In thiscase, the corresponding g(W) only considers the dilution of soluteconcentration resulting from the addition of antisolvent [17].

Motivated by the on-going analysis, a model-based C-controlapproach by incorporating a process model capable of predictingsolute concentration in complicated pH-shift reactive crystalliza-tion is developed in the ensuing discussion. Suppose the processis operated at point A in Fig. 3(b) with current volume V(k) andsolute concentration C(k), the proposed C-control determines newset point Vset(k) for the flow controller by drawing the dotted lineA → D to intersect the desired trajectory at point D and the set pointVset(k) is specified to be the corresponding abscissa of point D, i.e.,

V(k + 1). Therefore one key step to determine the intersect is to pre-dict future concentration at point D, C(k + 1), by the process modelincorporated into the proposed C-control strategy using currentand past process data V(k) and C(k) as well as a pre-specified V(k + 1).The intersect D is then obtained when the point [V(k + 1), C(k + 1)]discussed above is located at desired trajectory.

In this paper, a data-based Just-in-Time Learning (JITL) mod-elling method [12–15] is adopted for the proposed C-controlstrategy. There are three main steps in the JITL methods to predictfuture process output corresponding to the query data: (a) rele-vant data samples in the reference database are searched to matchthe query data by some nearest neighbourhood criterion; (b) a localmodel is built based on the relevant data; (c) model output is calcu-lated based on the chosen local model and the query data. The localmodel is then discarded right after the prediction is obtained. Whenthe next query data comes, a new local model will be built accordingto the aforementioned procedure. In the proposed C-control design,future solute concentration C(k + 1) discussed above is predicted bythe JITL method using the following ARX model:

C(k + 1) = ˛k1C(k) + ˇk

1V(k) + ˇk2V(k + 1) (4)

In summary, the implementation of proposed JITL-based C-control is given in the following:

(1) At sampling instant k, both C(k) and V(k) are measured;(2) For a chosen value of Vset(k), which by definition is the solution

volume at the k + 1 sampling instant, i.e., V(k + 1) = Vset(k);(3) The predicted concentration at the k + 1 sampling instant,

C(k + 1), is obtained by the JITL method using query dataq = [C(k), V(k), V(k + 1)]; while the solute concentration C̃(k + 1)in the target trajectory corresponding to V(k + 1) is readilyobtained;

(4) By comparing C(k + 1) and C̃(k + 1), the bisection method is usedto update Vset(k) subject to constraints due to the minimum andmaximum flowrates;

(5) Repeat Steps 2–4 until Vset(k) converges and this correspondingVset(k) is set as the set point for the lower-level PID controller.

4. Results and discussion

In this study, a first-principles mathematical model developedfrom the published data [19,20] was used to simulate the semi-batch pH-shift reactive crystallization of l-glutamic acid [21]. Forease of reference, the experimental procedure is briefly summa-rized here. The 0.97 L crystallizer is initially filled with 0.65 L ofmonosodium glutamate (MSG) of 1.0 mol/L and the default batchtime is 40 min. The manipulated variable is the addition flowrateof sulfuric acid (SA) of 1.0 mol/L, which is constrained between 0and 16 ml/min while adjusted every minute to achieve the max-imum polymorphic purity of �-form, volume-based mean crystalsize, and product yield of the final crystalline product at the batchend. The Pareto-optimality front for this multi-objective optimiza-tion is shown in Fig. 4, which is solved using the Non-dominatedSorting Genetic Algorithm-II (NSGA-II) [22]. The chosen optimaloperating point is denoted by the star symbol in Fig. 4 and thecorresponding optimal state trajectories are shown in Figs. 5 and 6.

To proceed to the proposed JITL-based C-control strategy, refer-ence database for the JITL method is generated using fifty batchesprocess data obtained by perturbing optimal flowrate profile cor-responding to the optimal volume profile given in Fig. 5(a) with anormal distribution of N(0, 1.0) at each sampling instant and vary-ing initial concentrations of monosodium glutamate and sulfuricacid with N(0, 0.02) for each batch. The resulting concentration dataused to construct reference database are shown in Fig. 7. To evalu-ate prediction accuracy of the JITL method with local model given

418 Q.-L. Su et al. / Journal of Process Control 24 (2014) 415–421

Fig. 4. Pareto-optimality front obtained for optimal control of a semi-batch pH-shiftreactive crystallization.

in Eq. (4), ten additional batches of process data are used in the vali-dation test. As can be seen from Fig. 8, JITL method gives accurateprediction of solute concentration.

To evaluate the robustness of the proposed JITL-based C-control,uncertainties in the kinetics of crystal growth and nucleation of thepolymorphic crystallization system, i.e., ˛- and ˇ-form polymorphsof l-glutamic acid, as well as the disturbances in feeding concen-trations are considered. For the purpose of comparison, optimalflowrate control obtained by solving the multi-objective optimiza-tion aforementioned is used as the benchmark design.

The first case study considers a 20% reduction of the growth rateof ˛-form crystal. Fig. 9 shows that the JITL-based C-control givesexcellent tracking performance of the desired concentration vs.

Fig. 5. Optimal profiles for (a) solution volume, (b) solute concentration, and (c)concentration vs. volume trajectory.

Fig. 6. Optimal profile for the three performance indices.

Fig. 7. Solute concentration data generated to construct reference database for theJITL method.

Fig. 8. Validation result for the JITL method (root mean squared error = 0.0012).

Q.-L. Su et al. / Journal of Process Control 24 (2014) 415–421 419

Table 1Summary of the three case studies.

Case study Controller Polymorphic purity Mean crystal size (�m) Product yield

20% reduction of growth rate for the �-formcrystals

Flowrate control 0.707 210.839 0.804JITL-based C-control 0.736 219.721 0.816

20% reduction of nucleation rate for the �-formcrystals

Flowrate control 0.793 247.389 0.808JITL-based C-control 0.799 249.311 0.815

Excess sulfuric acid (MSG = 0.95, SA = 1.05) Flowrate control 0.798 241.818 0.820JITL-based C-control 0.797 243.240 0.818

Fig. 9. Concentration vs. volume trajectories obtained for 20% reduction of growthrate for the �-form crystal.

volume trajectory, which is denoted by nominal optimal trajectoryin Fig. 9, compared with the flowrate control. This demonstratesthe capability of proposed C-control to handle nonlinearity in thenominal optimal trajectory. However, the improvement of threeimportant performance indices for crystallization, i.e., mean crys-tal size, polymorphic purity, and product yield, attained by theproposed C-control is modest as shown in Table 1 and Fig. 10,where the evolution of three performance indices is shown. The

Fig. 10. Profiles of the three performance indices obtained for 20% reduction ofgrowth rate for the �-form crystal.

corresponding control actions or flowrate profiles of the two con-trollers are given in Fig. 11. This finding is in sharp contrast tobatch cooling or antisolvent crystallization processes, where con-ventional C-control strategy has produced robust performance.The degraded performance of C-control in this particular pH-shiftreactive crystallization process is because the glutamic acid con-centration is affected by competing polymorphic crystallizationsand the relative rates of these competing processes cannot beobserved by measuring only the glutamic acid concentration. For

Fig. 11. Flowrate profiles obtained for 20% reduction of growth rate for the �-form crystal.

420 Q.-L. Su et al. / Journal of Process Control 24 (2014) 415–421

Fig. 12. Profiles of the three performance indices obtained for 20% reduction ofnucleation rate for the �-form crystal.

example, the stable ˇ-form polymorph can consume the solute atthe expense of the ˛-form that is less active than normal for a 20%decrease in crystal growth rate. In contrast, applications of con-ventional C-control to the cooling and antisolvent crystallizationprocesses are operated under condition that either the formationof alternative polymorphic forms is suppressed or only one poly-morph can grow and other polymorphs dissolve [9,10].

Next, performance of the two controller designs is comparedwhen 20% reduction of nucleation rate for the �-form crystal isconsidered. In this case, the JITL-based C-control also gives bet-ter tracking of the nominal optimal concentration vs. volumetrajectory [23], but with only slight improvement in the three per-formance indices as indicated in Table 1 and Fig. 12.

Lastly, the capability of proposed C-control to suppress dis-turbances in the initial concentration of MSG and the feedconcentration of SA is evaluated as shown in Fig. 13. It is assumedthat the former is decreased to 0.95 mol/L and the latter increased to1.05 mol/L so that higher supersaturation is generated at the initialphase of the batch but less durable at the later phase of the batch.

Fig. 13. Concentration vs. volume trajectories obtained for step disturbances ininitial MSG and sulfuric acid feed concentrations.

High supersaturation favours growth of the ˛-form polymorph,which increases the crystal product yield, as seen in Table 1.

In summary, case studies are investigated to evaluate the effectsof variations in the crystallization kinetics and disturbances inthe initial and feed concentrations are all summarized in Table 1.Although the JITL-based C-control is more robust in tracking thepre-defined concentration vs. volume trajectory than the flowratecontrol, the performance improvement gained in terms of the threekey product quality indices is either modest or marginal. This mayimply that the solute concentration measurement cannot fullyreflect the complexity of competitive polymorphic crystallization.Hence, tracking of the concentration vs. volume trajectory alonemay not be adequate to obtain good control performance underprocess uncertainties.

5. Conclusions

This paper extends the idea of C-control strategy to semi-batchpH-shift reactive crystallization process by incorporating a processmodel to better cope with highly nonlinear dynamics inherent inthe reactive crystallization process. Case studies of a pH-shift reac-tive crystallization show that the JITL-based C-control strategy isable to track closely the pre-specified concentration vs. volumetrajectory, however, it is less promising as that enjoyed by theconventional C-control for batch cooling crystallization. This resultsuggests the development of control strategies incorporating mea-surements that are more directly linked to the product quality.

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