phase diagram was highly robust to variations in the kinetic
parameters, while providing batch productivity nearly as high
as optimal control applied to batch crystallization with known
parameters, as illustrated in Figure 5c,g and many simulation
studies (not shown here) with variations in y
5 0). Although not explicitly included in
the optimization formulation, the operating constraints were
satisﬁed for the entire range of physicochemical parameters
(see Figure 5), except for a small constraint violation due to
variation in the solubility of a-form crystals that was removed
by slightly shifting the concentration setpoint trajectory away
from the a-solubility curve (Figure 6). Alternatively, shifts in
any solubility curve can be accounted for by updating meas-
urements of the solubility curve whenever there are signiﬁcant
changes in feedstocks between batch runs. Automated systems
exist for measuring such solubility curves.
as well as one of the author’s experi-
ence consulting with industry on their polymorphic crystalli-
zations suggest that the solubility curves of most polymorphs
are typically much closer together than for the a and b poly-
morphs of L-glutamic acid (Figure 1).
If this is true, then
the desired operating region for most polymorphic crystalli-
zations is typically much smaller than for the system investi-
gated in this study, making the robustness of batch control
strategies of much greater importance for most polymorphic
crystallizations. The results in this article indicate that the
design of operating procedures for future polymorphic crys-
tallizations should implement C-control.
1. De Anda JC, Wang XZ, Lai X, Roberts KJ. Classifying organic
crystals via in-process image analysis and the use of monitoring
charts to follow polymorphic and morphological changes. J Process
2. Blagden N, Davey R. Polymorphs take shape. Chem Brit.
3. Fujiwara M, Nagy ZK, Chew JW, Braatz RD. First-principles and
direct design approaches for the control of pharmaceutical crystalli-
zation. J Process Contr. 2005;15:493–504.
4. Rohani S, Horne S, Murthy K. Control of product quality in batch
crystallization of pharmaceuticals and ﬁne chemicals. Part 1: Design
of the crystallization process and the effect of solvent. Org Process
Res Dev. 2005;9:858–872.
5. Yu LX, Lionberger RA, Raw AS, D’Costa R, Wu HQ, Hussain AS.
Applications of process analytical technology to crystallization pro-
cesses. Adv Drug Delivery Rev. 2004;56:349–369.
6. Cardew PT, Davey RJ. The kinetics of solvent-mediated phase trans-
formations. Proc R Soc Lond A. 1985;398:415–428.
7. Hu Q, Rohani S, Jutan A. Modelling and optimization of seeded
batch crystallizers. Comput Chem Eng. 2005;29:911–918.
8. Larsen PA, Patience DB, Rawlings JB. Industrial crystallization pro-
cess control. IEEE Contr Syst Mag. 2006;26:70–80.
9. Rawlings JB, Miller SM, Witkowski WR. Model identiﬁcation and
control of solution crystallization processes: A review. Ind Eng
Chem Res. 1993;32:1275–1296.
10. Worlitschek J, Mazzotti M. Model-based optimization of particle
size distribution in batch-cooling crystallization of paracetamol.
Cryst Growth Des. 2004;4:891–903.
11. Zhang GP, Rohani S. On-line optimal control of a seeded batch
cooling crystallizer. Chem Eng Sci. 2003;58:1887–1896.
12. vvBraatz RD, Fujiwara M, Wubben T, Rusli E. Crystallization: Particle
size control. In: Swarbrick J, editor. Encyclopedia of Pharmaceutical
Technology, 3rd ed. New York: Marcel Dekker, 2006:858–871 (invited).
13. Rohani S, Horne S, Murthy K. Control of product quality in batch
crystallization of pharmaceuticals and ﬁne chemicals. Part 2: Exter-
nal control. Org Process Res Dev. 2005;9:873–883.
14. Diehl M, Bock HG, Kostina E. An approximation technique for robust
nonlinear optimization. Math Program Ser B. 2006;107:213–230.
15. Ma DL, Braatz RD. Worst-case analysis of ﬁnite-time control poli-
cies. IEEE Trans Contr Syst Technol. 2001;9:766–774.
16. Srinivasan B, Bonvin D, Visser E, Palanki S. Dynamic optimization
of batch processes – II. Role of measurements in handling uncer-
tainty. Comput Chem Eng. 2003;27:27–44.
17. Fujiwara M, Chow PS, Ma DL, Braatz RD. Paracetamol crystallization
using laser backscattering and ATR-FTIR spectroscopy: Metastability,
agglomeration and control. Cryst Growth Des. 2002;2:363–370.
18. Gron H, Borissova A, Roberts KJ. In-process ATR-FTIR spectro-
scopy for closed-loop supersaturation control of a batch crystallizer
producing monosodium glutamate crystals of deﬁned size. Ind Eng
Chem Res. 2003;42:198–206.
19. Liotta V, Sabesan V. Monitoring and feedback control of supersatu-
ration using ATR-FTIR to produce an active pharmaceutical ingredi-
ent of a desired crystal size. Org Process Res Dev. 2004;8:488–494.
20. Brittain HG. The impact of polymorphism on drug development: A
regulatory viewpoint. Am Pharmaceut Rev. 2000;3:67–70.
21. Ono T, Kramer HJM, Ter Horst JH, Jansens PJ. Process modeling of
the polymorphic transformation of L-glutamic acid. Cryst Growth
22. Miller SM, Rawlings JB. Model identiﬁcation and control strategies
for batch cooling crystallizers. AIChE J 1994;40:1312–1327.
23. Nagy ZK, Braatz RD. Worst-case and distributional robustness anal-
ysis of ﬁnite-time control trajectories for nonlinear distributed pa-
rameter systems. IEEE Trans Contr Syst Technol. 2003;11:694–704.
24. Hu Q, Rohani S, Wang DX, Jutan A. Optimal control of a batch
cooling seeded crystallizer. Powder Technol. 2005;156:170–176.
25. Matthews HB, Rawlings JB. Batch crystallization of a photochemi-
cal: Modeling, control, and ﬁltration. AIChE J. 1998;44:1119–1127.
26. Zhou GX, Fujiwara M, Woo XY, Rusli E, Tung HH, Starbuck C,
Davidson O, Ge Z, Braatz RD. Direct design of pharmaceutical anti-
solvent crystallization through concentration control. Cryst Growth
27. Kee N, Woo XY, Goh L, Chen K, He G, Bhamidi V, Rusli E, Nagy
ZK, Kenis PJA, Zukoski CF, Tan RBH, Braatz RD. Design of crys-
tallization processes from laboratory R&D to the manufacturing
scale. Am Pharmaceut Rev. 2008;11:to appear.
28. Seborg DE, Henson MA. Nonlinear Process Control. 1st ed. Piscat-
away, NJ: Prentice Hall; 1996.
29. Togkalidou T, Fujiwara M, Patel S, Braatz RD. Solute concentration
prediction using chemometrics and ATR-FTIR spectroscopy. J Cryst
Manuscript received Nov. 14, 2006, and ﬁnal revision received May 31, 2007.
This is especially true for enantiomeric polymorphs, in which the solubility
2650 DOI 10.1002/aic Published on behalf of the AIChE October 2007 Vol. 53, No. 10 AIChE Journal