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Neural network-based optimal control of a batch crystallizer
Neurocomputing 83 (2012) 158–164
Contents lists available at SciVerse ScienceDirect
Neurocomputing journal homepage: www.elsevier.com/locate/neucom
Neural network-based optimal control of a batch crystallizer Woranee Paengjuntuek a, Linda Thanasinthana b, Amornchai Arpornwichanop b,c,n a b c
Department of Chemical Engineering, Faculty of Engineering, Thammasat University, Patumthani 12120, Thailand Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand Computational Process Engineering, Chulalongkorn University, Bangkok 10330, Thailand
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 October 2010 Received in revised form 18 November 2011 Accepted 5 December 2011 Available online 29 December 2011
In batch crystallization, the control of size and shape distributions of crystal product is known to be a difficult and challenging task. Although various model-based control strategies have been widely implemented, the effectiveness of such the control strategies depends heavily on the exact knowledge of crystallization of which the dynamic behavior is complicated and highly nonlinear. In this study, a neural network-based optimal control was proposed to regulate the batch crystallization of potassium sulfate chosen as a case study. A neural network model of the batch crystallizer was first developed to capture the nonlinear dynamics of crystallization in terms of the solution concentration within the batch crystallizer and the moment variables that relate to a crystal product quality over a prediction horizon. Then, the developed neural network model was incorporated in an optimal control framework to find an optimal operating temperature profile for improving the quality of the crystal product. The simulation results showed that the neural network can predict the final product properties and the optimal control integrated with the developed neural network gives a better control performance compared to a conventional linear cooling control technique. & 2011 Elsevier B.V. All rights reserved.
Keywords: Batch crystallization Neural network Optimal control Simulation
1. Introduction Crystallization is an economically important separation and purification process, which has been widely applied for chemical, pharmaceutical, microelectronic, and food industries. Generally, the operating condition of crystallization processes has direct effect on not only product qualities, i.e., crystal purity, shape and size distribution, but also downstream operations, i.e., filtration, drying, and formulation [1]. However, the primary bottleneck to the efficient operation of a crystallizer is associated with difficulties in controlling the size and shape distributions of crystals produced. If a crystal size distribution (CSD) is not controlled properly, it can cause the off-specification product and difficulties in the subsequent operations, leading to long filtration or drying time [2]. Batch crystallizations are often used in the production of lowvolume and high-value chemicals. Moreover, the operation of crystallizers in a batch mode offers the advantage of achieving products with a narrow CSD and a large mean crystal size. In general, the final CSD of batch crystallization is closely related to the supersaturation condition, a non-equilibrium driving force for crystallizations, which is a function of crystallizer temperature. As a consequence, the control of the operating temperature at an
n Corresponding author at: Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand. Tel.: þ66 2 2186878; fax: þ66 2 2186877. E-mail address: [email protected] (A. Arpornwichanop).
0925-2312/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2011.12.008
optimal condition is crucial for obtaining the crystal product with desired quality. In the past years, various traditional cooling methods such as linear cooling and natural cooling were widely investigated [3]. Ward et al. [4] described an operating policy for control of seeded batch crystallizations. Presently, there is a growing interest in the implementation of an optimal control approach to determine an optimal operation policy in terms of crystallization temperatures. The aim is to improve the crystal product quality at the final batch time, which is usually represented by the CSD or other related properties such as mean crystal size, seeded crystal size, mass of seeded or nucleated crystals, and the variance of the product CSD [2]. Many previous works have been performed on modelbased optimization and control of crystallization processes. Miller and Rawlings [5] proposed an open-loop optimal control strategy for a bench-scale potassium nitrate–water system. The implementation of the optimal cooling policy leads to an increase in the weight mean size of crystal product. Zhang and Rohani [6] presented an on-line optimal control methodology for the optimal quality control. With the proposed control approach, a much better CSD of the final product can be achieved, compared to the off-line optimal cooling policy. Hu et al. [7] studied the optimization of batch-seeded crystallizer. The results show that the optimal cooling profile is able to reduce the volume of fine crystals. Shi et al. [8] focused on an optimization-based predictive control strategy of a batch crystallizer. The objective is to achieve a desired particle size distribution under control and product quality constraints. Hermanto et al. [9] considered the control of polymorphism in a pharmaceutical
W. Paengjuntuek et al. / Neurocomputing 83 (2012) 158–164
Nomenclature b B C Cm Cs E n g G kb kg kv
nucleation rate exponent nucleation rate, no. crystal s 1 g solvent 1 solution concentration, g solute g solvent 1 metastable concentration, g solute g solvent 1 saturation concentration, g solute g solvent 1 activation energy population density of crystals, no. of crystals mm 1 g solvent 1 growth rate exponent growth rate, mm s 1 birth rate coefficient, s 1 mm 3 growth rate coefficient, mm s 1 volumetric shape factor
crystallization process. The robustness and performance of the proposed T-control and C-control strategies integrated with a nonlinear state feedback control were studied. Paengjuntuek et al. [10] implemented the on-line dynamic optimization integrated with a generic model control strategy to improve the product quality of seeded batch cooling crystallization under plant-model mismatch and external disturbance cases. The results demonstrated that the on-line optimal control has more robustness than the off-line optimal policy. Nagy et al. [11] proposed the model-based and direct design control approaches to control the combined cooling and antisolvent crystallization of pharmaceuticals. As mentioned, there is a significant body of recent papers dealing with the model-based optimization and control using complex process models, whereas the application of neural networks (NNs) in crystallization to make the optimization more efficient is relatively small. Furthermore, such the control approaches require the real-time solution of the optimization problem, and hence efficient models such as the neural networks can increase computational performance significantly. Considering the model-based control approach, it is found that the effectiveness of the optimal control depends heavily on the exact knowledge of the system’s model. With the limited understanding of complex and highly nonlinear systems like a crystallization process, the optimal control would not perform as expected due to model mismatch. One of the most effective techniques to handle with such a situation is a neural network (NN). An obvious advantage of NN is its universal character in approximating different physical phenomena with similar computational structure. Moreover, the ability to approximate complex nonlinear relationships from process data without prior knowledge of the model structure makes the NN a very attractive alternative to the classical modeling techniques [12]. There are a number of studies concerning about various applications of NN such as sensor data analysis, fault detection, nonlinear process identification and chemical process control including predictive control, inverse-model-based control and adaptive control [13]. Georgieva and de Azevedo [12] applied a predictive control based on a feed forward NN model to control a fed-batch evaporative sugar crystallization. The feed flow rate of sugar liquor/syrup was considered as the control input. Mjalli et al. [14] presented the study on the use of NN model to predict the performance of a wastewater treatment plant. The results indicated that the NNbased model has many favorable features such as efficiency, generalization, and simplicity, which makes it an attractive choice for modeling complex systems. Moreover, NN has been applied successfully in the identification and control of dynamic systems. Nagy [15] demonstrated the ability of NN to model and control complex nonlinear biochemical processes. The simulation results
r R t T
159
characteristic crystal length, mm gas constant time, min reactor temperature, 1C
Greek symbols
r m
density of crystals, g mm 3 moment variable of crystal size distribution (CSD)
Superscripts n s
nucleated crystal seeded crystal
were presented to demonstrate that the NN model can achieve a good generalization and integrate with a model predictive control. Arpornwichanop and Shomchoam [16] presented the application of a feedforward NN for on-line estimation of unmeasured substrate concentration, which is employed for determining the optimal substrate feed rate for a fed-batch fermentation process. The simulation results showed that the NN model is capable of capturing the essential features of the process Nagy et al. [17]. also used the NN for sensor calibration in crystallization process. Due to the predictive capability of NN for complex systems, the aim of this work is focused on the utilization of NN for modeling and control of a batch crystallization process. To attain such a goal, a NN model of the batch crystallization is first developed. In this study, process data for NN training are assumed to be generated from simulations of batch crystallization in which the production of potassium sulfate is chosen as a case study [8]. An optimal control problem is then formulated using the developed NN model to determine an optimal operating policy of the crystallizer in terms of cooling temperature. The performance of the proposed optimal control strategy is compared with other conventional control methodologies.
2. Batch crystallization process Crystallization occurs only if the system is supersaturated. For the formation of crystals, two steps are required: (1) the birth of a new crystal called nucleation and (2) the growth of the nucleated crystal. The driving potential for such the processes is the nonequilibrium state of the system, which is measured by a relative supersaturation (S): S¼
CC s ðTÞ C s ðTÞ
ð1Þ
where C is the solution concentration and Cs is the saturation concentration depending on the solution temperature (T). To represent a batch crystallization process, a reduced-order moment model of the nuclei and seed classes of crystals was employed to explain the dynamic behavior of the process as follows [18]: dmn0 ¼ BðtÞ, dt n dmi ¼ iGðtÞmni1 ðtÞ, dt
ms0 ¼ constant,
i ¼ 1,2,3
ð2Þ
160
W. Paengjuntuek et al. / Neurocomputing 83 (2012) 158–164
dmsi ¼ iGðtÞmsi1 ðtÞ, dt
i ¼ 1,2,3
ð3Þ
where B(t) and G(t) are, respectively, the nucleation and growth rates of crystals and mi (i¼0,y,3), which is the summation of mni and msi , represents the average product quality in terms of the total of number, length, surface area, and volume of crystals, respectively. Without consideration of crystal agglomeration or breakage phenomena, mass balance described the changes in the concentration of solution in the batch crystallizer can be expressed as: @C ¼ 3rkv GðtÞm2 ðtÞ @t
ð4Þ
where r is the density of crystals and kv is the volumetric shape factor. The model of crystallization is completed by defining the kinetic processes that relate the dynamics of crystal population to the state of the bulk system. This involves the determination of rate expressions for crystal nucleation and growth. These processes are related to the relative supersaturation (S) as follows: BðtÞ ¼ kb eEb =RT Sb m3 ðtÞ
ð5Þ
GðtÞ ¼ kg eEg =RT Sg
ð6Þ
where Eb is the nucleation activation energy, Eg is the growth activation energy, and b and g are the exponent terms relating the nucleation rate and the growth rate to the supersaturation, respectively. The control purpose of a crystallization process is to manage the nucleation and growth rates of crystal to achieve a desired crystal size. Well-controlled crystallization process is usually operated in the metastable zone bounded by the saturation concentration and the metastable limit, Cs rCrCm, in order to avoid uncontrolled nucleation of crystals. In this study, the seeded batch crystallizer of potassium sulfate studied by Shi et al. [8] is considered. The process parameters are shown in Table 1. The following equations are used to calculate the saturation and metastable concentrations corresponding to the solution temperature, T, as: C s ðTÞ ¼ 6:29 102 þ2:46 103 T7:14 106 T 2
ð7Þ
C m ðTÞ ¼ 7:76 102 þ 2:46 103 T8:10 106 T 2
ð8Þ
The distribution of seeded crystals in the batch crystallizer at initial condition was assumed to be a parabolic distribution, which is a function of the crystal characteristic length (r) varying from 250 to 300 mm as ( 0:0032ð300rÞðr250Þ for 250 mmr r r 300 mm nðr,0Þ ¼ 0 for r o250 mm and r 4 300 mm ð9Þ It is noted that the ith moment of the crystal population density at the start of batch run can be determined as Z 1 mi ð0Þ ¼ r i nðr,0Þdr ð10Þ 0
Table 1 Model parameters for the seeded batch crystallizer of potassium sulfate. b ¼1.45 kb ¼ 285 s 1 mm 3 Eb/R¼ 7517 K kv ¼1.5 r ¼2.66 10 12 g mm 3
g¼ 1.5 kg ¼ 1.44 108 mm s 1 Eg/R¼ 4859 K C(t ¼ 0)¼ 0.1742 g solute g solvent 1 tf ¼30 min
Since the crystal breakage or agglomeration was not considered in the proposed crystallizer model, a total number of the crystals growing from seeds, which is determined by the initial seed size distribution, remains constant.
3. Neural network-based optimal control 3.1. Optimal control problem Considering the practical operation of industrial crystallizers, fine crystals usually cause difficulties in downstream processing equipment and affect both product quality and process economics. A very detailed overview of the optimization objectives used for crystallization control was provided by Ward et al. [4]. This study focuses on the development of an optimal control system to achieve a desired final CSD. The control objective is to determine the optimal temperature profile that minimizes the total volume of nucleated fine crystals, which is represented by the third moment of crystals formed by nucleation (mn3), and at the same time maximizes the total volume of the desired crystals growing from seeds (ms3) at the end of batch operation (tf ¼30 min). Thus, the optimal control problem takes the form as follows [8]: Minimize TðtÞ
mn3 ðt f Þ ms3 ðt f Þ
ð11Þ
subject to Dynamic crystallizer model (Eqs. (2)–(6)) 30 o C r TðtÞ r50 o C C S r CðtÞ r C m dT rk dt
ms3 ðtf Þ ZV where the constant k is the maximum gradient of the reactor temperature, which was chosen to be 2 oC/min, corresponding to a ability of a cooling control system and V denotes the lower bound on the total volume of the crystals growing from seeded crystals. It is noted that the constraint on ms3(tf) indicates a desirable quality of the final crystal product. In this study, the lower bound of ms3(tf) was chosen as 8.33 109 mm3 g solvent 1. 3.2. Neural network model of batch crystallizer The first step of implementing NN in an optimal control algorithm is to train the NN to predict the dynamics of the batch crystallizer to be controlled, i.e., the total volume of fine and seeded crystals, when the operating temperature of the crystallizer changes. With the limited availability of actual experimental data, the detailed theoretical model of batch crystallization as mentioned earlier was numerical solved and implemented in Matlab to generate data for NN training. The solution concentration and the total volume of fine and seeded crystals represented by the third moments of crystals (mn3 and ms3) as outputs were predicted by using the current values of solution temperature and concentration as inputs since they have direct effect on the predicted outputs. However, it was found that only the inputs at the current time may not be enough to predict the future outputs. For this reason, the input data consists of the reactor temperatures at time (t), (t 1) and (t 2) and the solution concentration at time (t) and (t 1). Training and validation data sets for NN training were generated by performing various simulations of batch crystallizer operated under random changes in the cooling temperature profile in ranges of 30–50 1C. The operational time was kept constant at 30 min and the sampling time of data was 0.1 min. These data sets were further normalized
W. Paengjuntuek et al. / Neurocomputing 83 (2012) 158–164
by Z-score standardization for achieving a good performance of NN model. It is noted that, in general, experimental data are used for NN training; however, with their limited availability for a wide range of operational conditions, the simulated data obtained from numerical simulations of the theoretical crystallizer model were assumed to be used instead.
161
Fig. 1 shows the detailed training procedure to find the NN model. To train the multilayer feedforward NN, the Levenberg– Marquardt backpropagation algorithm with an early stopping mechanism was used as shown in Fig. 2. Minimizing a mean square error (MSE) between the NN predicted value and the actual targeted value of C, mn3 and ms3 was used as a criterion for
Fig. 1. Detailed procedure for neural network modeling.
C µin µis
T
Ct Ct Tt Tt Tt
C predict (t + 1)
µ3n,predict (t + 1)
µ3s ,predict (t + 1)
Fig. 2. Training algorithm of feedforward NN.
C (t + 1) µ3n (t + 1) µ3s (t + 1)
162
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weights and biases adjustment and also for NN structure selection. From simulation results, the optimum architecture of the NN for the prediction of the solution concentration and the third moment variables consists of three hidden layers with the log-sigmoid transfer
Tt
function and one output layer with a linear transfer function. The number of nodes in the 1st, 2nd, and 3rd hidden layers are 3, 7 and 5, respectively, as shown in Fig. 3. Table 2 summarizes the MSE value of the NN model with three-hidden layers.
C (t + 1)
Tt
µ (t + 1)
Tt Ct
µ (t + 1)
Ct
Fig. 3. Optimum structure of trained NN model.
Table 2 MSE of NN with three-hidden layers. Number of nodes
Mean square error (MSE) ( 10 4)
First hidden layer
Second hidden layer
Third hidden layer
3
3
3 5 7 9 3 5 7 9 3 5 7 9 3 5 7 9
5
7
9
293.646 5.8851 6.3296 26.6982 6.2416 248.198 6.3224 6.9727 6.4698 5.3558 6.6531 6.7970 6.5793 6.3281 5.6535 6.4608
Random Temperature Profile 50 48 46 44
T (°C)
42 40 38 36 34 32 30
0
5
10
15 time (min)
20
Fig. 4. Example of cooling temperature profile.
25
30 Fig. 5. Comparison of simulation results obtained from NN and theoretical model: (a) solution concentration (b) mn3 and (c) ms3.
W. Paengjuntuek et al. / Neurocomputing 83 (2012) 158–164
163
of mn3 and ms3 at the final batch time when three different control strategies: (1) linear cooling control, (2) optimal cooling control based on mathematical model (Shi et al. [8]), and (3) optimal cooling control based on neural network model (this study), were applied to the control of the batch crystallizer. It is noted that for the linear cooling control, the crystallizer temperature is linearly decreased from 50 1C to 30 1C. Comparing the simulation results, it is clear that the optimal control strategy can yield the lower volume of fine crystals, compared to the linear cooling strategy, while the seeded crystals still satisfy the product quality requirement. The proposed optimal control strategy incorporating the NN model shows good control performance in term of reducing the total volume of fine crystals by 94.65% compared to the linear cooling strategy and by 73.25% compared to the optimal control strategy based on mathematical model.
It should be noted that in order to compute the third moments of crystals (mn3 and ms3) at the final batch time (tf), the trained NN model can be recursively employed to predict future outputs over the prediction horizon (n). With the given cooling temperature profile (the value of temperature at each time interval) as shown in Fig. 4, the NN can predict the value of future outputs (i.e., C, mn3 and ms3) at time tþ1. Based on the first output prediction and the current value of temperature, the NN is then recall for the next prediction of the outputs at t þ2. This step is repeated until the end of batch run; the multiple outputs for n time intervals can be predicted. Fig. 5 compares the predicted values of the solution concentration and the third moment variable obtained from NN and theoretical models.
4. Computational results In this section, the optimal control technique based on NN model is implemented to determine an optimal temperature profile for a batch crystallizer. Fig. 6 shows the proposed optimal control structure integrated with NN. The NN was used as a state predictor to predict the values of the solution concentration and the third moment of crystals formed by nucleation (mn3) and seeds (ms3). The optimal control problem as mentioned in Section 3 was numerically solved by a sequential optimization and control approach [19]. In such an approach, the control variable (i.e. crystallizer temperature) is discretized by a piecewise constant function with equally spaced time intervals. This transforms the optimal control problem into a nonlinear programming problem (NLP). In this work, the temperature profile was assumed to be divided into 10 intervals. With the initial guess of the decision variables (the value of temperature at each time interval), the recursive NN is implemented to compute the value of outputs (i.e., C, mn3 and ms3) over the prediction horizon as earlier mentioned. Then, the outputs at the final batch time are passed to the optimization solver, which is based on a sequential quadratic programming algorithm, to compute a new temperature profile. These steps are iterative until the optimal temperature profile is found, satisfying the objective function and constraints. Fig. 7 shows the optimal temperature profile obtained for controlling the batch crystallizer. It is found that under the proposed optimal operation, the crystallizer system is operated within the metastable limit (Fig. 8), which is bounded by the saturation concentration and the metastable limit to avoid uncontrolled nucleation of crystals. Table 3 presents the values
5. Conclusions An optimal control based on a neural network model for a batch crystallizer was studied in this work. The optimal control Temperature Profile 50 48 46 44
T (°C)
42 40 38 36 34 32 30
0
5
10
15 time (min)
Fig. 7. Optimal cooling temperature profile.
Controller
µ 3n (t+1) µ 3s (t+1) T’(t)
Initial Condition Optimization
20
T(t-1) T(t-2)
Neural Network Model
C(t+1)
C(t-1)
C(t)
T(t) Crystallizer Fig. 6. Optimal control incorporating with NN model predictor.
25
30
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W. Paengjuntuek et al. / Neurocomputing 83 (2012) 158–164
Concentration Profile
0.2 0.19 0.18
C (g/g)
0.17 0.16 0.15 0.14 Cm (t)
0.13 0.12
C(t) Cs(t)
0
5
10
15 time (min)
20
25
30
Fig. 8. Concentration profile under the optimal operation of batch crystallizer.
Table 3 Performance of batch crystallization under different control strategies. Control strategies
mn3(tf)
ms3(tf)
Linear cooling control Optimal control based on theoretical crystallization model [7] Optimal control based on NN model
8.917 109 9.1121 109 1.7828 109 1.0545 1010
[5] S.M. Miller, J.B. Rawlings, Model identification and control strategies for batch cooling crystallizers, AIChE. J. 40 (1994) 1312–1327. [6] G. Zhang, S. Rohani, On-line optimal control of a seeded batch cooling crystallizer, Chem. Eng. Sci. 58 (2003) 1887–1896. [7] Q. Hu, S. Rohani, A. Jutan, Modeling and optimization of seeded batch crystallizers, Comput. Chem. Eng. 29 (2005) 911–918. [8] D. Shi, N.H. El-Farra, M. Li, P. Mhaskar, P.D. Christofides, Predictive control of particle size distribution in particulate processes, Chem. Eng. Sci. 61 (2006) 268–281. [9] M.W. Hermanto, M. Chiu, X. Woo, R.D. Braatz, Robust optimal control of polymorphic transformation in batch crystallization, AIChE J. 53 (2007) 2643–2650. [10] W. Paengjuntuek, P. Kittisupakorn, A. Arpornwichanop, On-line dynamic optimization integrated with generic model control of a batch crystallizer, J. Ind. Eng. Chem. 14 (2008) 442–448. [11] Z.K. Nagy, J.W. Chew, M. Fujiwara, R.D. Braatz, Comparative performance of concentration and temperature controlled batch crystallizations, J. Process Control 18 (2008) 399–407. [12] P. Georgieva, S.F. De Azevedo, Application of feed forward neural networks in modeling and control of a fed-batch crystallization process, Trans. Eng. Comput. Tech. 12 (2006). [13] M.A. Hussain, Review of the application of neural networks in chemical process control-simulation and online implementation, Artif. Intel. Eng. 13 (1999) 55–68. [14] F.S. Mjalli, S. Al-Asheh, H.E. Alfadala, Use of artificial neural network blackbox modeling for the prediction of wastewater treatment plants performance, J. Environ. Manage. 83 (2007) 329–338. [15] Z.K. Nagy, Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks, Chem. Eng. J. 127 (2007) 95–109. [16] A. Arpornwichanop, N. Shomchoam, Control of fed-batch bioreactors by a hybrid on-line optimal control strategy and neural network estimator, Neurocomputing 72 (2009) 2297–2302. [17] Z.K. Nagy, M Fujiwara, R.D. Braatz, Modeling and control of combined cooling and antisolvent crystallization processes, J. Process Control 18 (2008) 856–864. [18] H.B. Matthews, Model identification and control of batch crystallization for an industrial chemical system, PhD Thesis, University of Wisconsin at Madison, 1997. [19] A. Arpornwichanop, N. Shomchoam, Studies on optimal control approach in a fed-batch fermentation, Korean J. Chem. Eng. 24 (2007) 11–15.
4.7681 108 9.6841 109
strategy was implemented to find an optimal temperature profile with the aim to minimize a total volume of nucleated fine particles (mn3) and to maximize a total volume of the crystals growing from seeds (ms3) at the end of the operation. The neural network model of batch crystallizer was developed to predict the future process response in terms of the solution concentration and the moment variables that represent a crystal product quality and then employed as a predictor in the optimal control algorithm. It was found that the neural network shows a good state predictor and the optimal control with the neural network model provides a superior control performance compared to a conventional control methodologies.
Acknowledgment Support from The Thailand Research Fund and Commission on Higher Education (MRG5280109), Thammasat University and the Special Task Force for Activating Research (STAR), Chulalongkorn University Centenary Academic Development Project is gratefully acknowledged. References [1] P.A. Larsen, D.B. Patience, J.B. Rawlings, Industrial crystallization process and control, IEEE Control Syst. Mag. (2006) 70–80. [2] C.B.B. Costa, A.C. Da Costa, R.M. Filho, Mathematical modeling and optimal control strategy development for an adipic acid crystallization process, Chem. Eng. Proc ess. 44 (2005) 737–753. [3] H. Hojjati, S. Rohani, Cooling and seeding effect on supersaturation and final crystal size distribution of ammonium sulphate in a batch crystallizer, Chem. Eng. Process. 44 (2005) 949–957. [4] J.D. Ward, D.A. Mellichamp, M.F. Doherty, Choosing an operating policy for seeded batch crystallization, AIChE J. 52 (2006) 2046–2054.
Woranee Paengjuntuek received the B.Eng. degree (first class honours) in chemical engineering from Khon Kaen University (Thailand) in 2004 and the D.Eng. degree in chemical engineering from Chulalongkorn University (Thailand) in 2008. Since 2008, she has been a lecturer at the department of chemical engineering, faculty of engineering, Thammasat University. Her research fields of interest include process control and optimization and their applications in chemical processes and crystallization.
Linda Thanasinthana received B.Eng and M.Eng degrees in chemical engineering from Chulalongkorn University (Thailand) in 2006 and 2008, respectively. Her past research focused on the control of batch crystallization, optimal control and neural network. She is presently a consulting engineer at Invensys Process System, Thailand.
Amornchai Arpornwichanop received B.Eng. and D. Eng. degrees in chemical engineering from Chulalongkorn University (Thailand) in 1997 and 2003, respectively. Since 2003, he has been with the department of chemical engineering, faculty of engineering, Chulalongkorn University. His current research interests include modeling and optimization, optimal control and model predictive control, neural network. Presently, his research projects mainly focus on systems such as reactive distillation, solid oxide fuel cell, crystallizer, membrane reactor and batch and fedbatch biochemical reactor.
Contents lists available at SciVerse ScienceDirect
Neurocomputing journal homepage: www.elsevier.com/locate/neucom
Neural network-based optimal control of a batch crystallizer Woranee Paengjuntuek a, Linda Thanasinthana b, Amornchai Arpornwichanop b,c,n a b c
Department of Chemical Engineering, Faculty of Engineering, Thammasat University, Patumthani 12120, Thailand Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand Computational Process Engineering, Chulalongkorn University, Bangkok 10330, Thailand
a r t i c l e i n f o
a b s t r a c t
Article history: Received 3 October 2010 Received in revised form 18 November 2011 Accepted 5 December 2011 Available online 29 December 2011
In batch crystallization, the control of size and shape distributions of crystal product is known to be a difficult and challenging task. Although various model-based control strategies have been widely implemented, the effectiveness of such the control strategies depends heavily on the exact knowledge of crystallization of which the dynamic behavior is complicated and highly nonlinear. In this study, a neural network-based optimal control was proposed to regulate the batch crystallization of potassium sulfate chosen as a case study. A neural network model of the batch crystallizer was first developed to capture the nonlinear dynamics of crystallization in terms of the solution concentration within the batch crystallizer and the moment variables that relate to a crystal product quality over a prediction horizon. Then, the developed neural network model was incorporated in an optimal control framework to find an optimal operating temperature profile for improving the quality of the crystal product. The simulation results showed that the neural network can predict the final product properties and the optimal control integrated with the developed neural network gives a better control performance compared to a conventional linear cooling control technique. & 2011 Elsevier B.V. All rights reserved.
Keywords: Batch crystallization Neural network Optimal control Simulation
1. Introduction Crystallization is an economically important separation and purification process, which has been widely applied for chemical, pharmaceutical, microelectronic, and food industries. Generally, the operating condition of crystallization processes has direct effect on not only product qualities, i.e., crystal purity, shape and size distribution, but also downstream operations, i.e., filtration, drying, and formulation [1]. However, the primary bottleneck to the efficient operation of a crystallizer is associated with difficulties in controlling the size and shape distributions of crystals produced. If a crystal size distribution (CSD) is not controlled properly, it can cause the off-specification product and difficulties in the subsequent operations, leading to long filtration or drying time [2]. Batch crystallizations are often used in the production of lowvolume and high-value chemicals. Moreover, the operation of crystallizers in a batch mode offers the advantage of achieving products with a narrow CSD and a large mean crystal size. In general, the final CSD of batch crystallization is closely related to the supersaturation condition, a non-equilibrium driving force for crystallizations, which is a function of crystallizer temperature. As a consequence, the control of the operating temperature at an
n Corresponding author at: Department of Chemical Engineering, Faculty of Engineering, Chulalongkorn University, Bangkok 10330, Thailand. Tel.: þ66 2 2186878; fax: þ66 2 2186877. E-mail address: [email protected] (A. Arpornwichanop).
0925-2312/$ - see front matter & 2011 Elsevier B.V. All rights reserved. doi:10.1016/j.neucom.2011.12.008
optimal condition is crucial for obtaining the crystal product with desired quality. In the past years, various traditional cooling methods such as linear cooling and natural cooling were widely investigated [3]. Ward et al. [4] described an operating policy for control of seeded batch crystallizations. Presently, there is a growing interest in the implementation of an optimal control approach to determine an optimal operation policy in terms of crystallization temperatures. The aim is to improve the crystal product quality at the final batch time, which is usually represented by the CSD or other related properties such as mean crystal size, seeded crystal size, mass of seeded or nucleated crystals, and the variance of the product CSD [2]. Many previous works have been performed on modelbased optimization and control of crystallization processes. Miller and Rawlings [5] proposed an open-loop optimal control strategy for a bench-scale potassium nitrate–water system. The implementation of the optimal cooling policy leads to an increase in the weight mean size of crystal product. Zhang and Rohani [6] presented an on-line optimal control methodology for the optimal quality control. With the proposed control approach, a much better CSD of the final product can be achieved, compared to the off-line optimal cooling policy. Hu et al. [7] studied the optimization of batch-seeded crystallizer. The results show that the optimal cooling profile is able to reduce the volume of fine crystals. Shi et al. [8] focused on an optimization-based predictive control strategy of a batch crystallizer. The objective is to achieve a desired particle size distribution under control and product quality constraints. Hermanto et al. [9] considered the control of polymorphism in a pharmaceutical
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Nomenclature b B C Cm Cs E n g G kb kg kv
nucleation rate exponent nucleation rate, no. crystal s 1 g solvent 1 solution concentration, g solute g solvent 1 metastable concentration, g solute g solvent 1 saturation concentration, g solute g solvent 1 activation energy population density of crystals, no. of crystals mm 1 g solvent 1 growth rate exponent growth rate, mm s 1 birth rate coefficient, s 1 mm 3 growth rate coefficient, mm s 1 volumetric shape factor
crystallization process. The robustness and performance of the proposed T-control and C-control strategies integrated with a nonlinear state feedback control were studied. Paengjuntuek et al. [10] implemented the on-line dynamic optimization integrated with a generic model control strategy to improve the product quality of seeded batch cooling crystallization under plant-model mismatch and external disturbance cases. The results demonstrated that the on-line optimal control has more robustness than the off-line optimal policy. Nagy et al. [11] proposed the model-based and direct design control approaches to control the combined cooling and antisolvent crystallization of pharmaceuticals. As mentioned, there is a significant body of recent papers dealing with the model-based optimization and control using complex process models, whereas the application of neural networks (NNs) in crystallization to make the optimization more efficient is relatively small. Furthermore, such the control approaches require the real-time solution of the optimization problem, and hence efficient models such as the neural networks can increase computational performance significantly. Considering the model-based control approach, it is found that the effectiveness of the optimal control depends heavily on the exact knowledge of the system’s model. With the limited understanding of complex and highly nonlinear systems like a crystallization process, the optimal control would not perform as expected due to model mismatch. One of the most effective techniques to handle with such a situation is a neural network (NN). An obvious advantage of NN is its universal character in approximating different physical phenomena with similar computational structure. Moreover, the ability to approximate complex nonlinear relationships from process data without prior knowledge of the model structure makes the NN a very attractive alternative to the classical modeling techniques [12]. There are a number of studies concerning about various applications of NN such as sensor data analysis, fault detection, nonlinear process identification and chemical process control including predictive control, inverse-model-based control and adaptive control [13]. Georgieva and de Azevedo [12] applied a predictive control based on a feed forward NN model to control a fed-batch evaporative sugar crystallization. The feed flow rate of sugar liquor/syrup was considered as the control input. Mjalli et al. [14] presented the study on the use of NN model to predict the performance of a wastewater treatment plant. The results indicated that the NNbased model has many favorable features such as efficiency, generalization, and simplicity, which makes it an attractive choice for modeling complex systems. Moreover, NN has been applied successfully in the identification and control of dynamic systems. Nagy [15] demonstrated the ability of NN to model and control complex nonlinear biochemical processes. The simulation results
r R t T
159
characteristic crystal length, mm gas constant time, min reactor temperature, 1C
Greek symbols
r m
density of crystals, g mm 3 moment variable of crystal size distribution (CSD)
Superscripts n s
nucleated crystal seeded crystal
were presented to demonstrate that the NN model can achieve a good generalization and integrate with a model predictive control. Arpornwichanop and Shomchoam [16] presented the application of a feedforward NN for on-line estimation of unmeasured substrate concentration, which is employed for determining the optimal substrate feed rate for a fed-batch fermentation process. The simulation results showed that the NN model is capable of capturing the essential features of the process Nagy et al. [17]. also used the NN for sensor calibration in crystallization process. Due to the predictive capability of NN for complex systems, the aim of this work is focused on the utilization of NN for modeling and control of a batch crystallization process. To attain such a goal, a NN model of the batch crystallization is first developed. In this study, process data for NN training are assumed to be generated from simulations of batch crystallization in which the production of potassium sulfate is chosen as a case study [8]. An optimal control problem is then formulated using the developed NN model to determine an optimal operating policy of the crystallizer in terms of cooling temperature. The performance of the proposed optimal control strategy is compared with other conventional control methodologies.
2. Batch crystallization process Crystallization occurs only if the system is supersaturated. For the formation of crystals, two steps are required: (1) the birth of a new crystal called nucleation and (2) the growth of the nucleated crystal. The driving potential for such the processes is the nonequilibrium state of the system, which is measured by a relative supersaturation (S): S¼
CC s ðTÞ C s ðTÞ
ð1Þ
where C is the solution concentration and Cs is the saturation concentration depending on the solution temperature (T). To represent a batch crystallization process, a reduced-order moment model of the nuclei and seed classes of crystals was employed to explain the dynamic behavior of the process as follows [18]: dmn0 ¼ BðtÞ, dt n dmi ¼ iGðtÞmni1 ðtÞ, dt
ms0 ¼ constant,
i ¼ 1,2,3
ð2Þ
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dmsi ¼ iGðtÞmsi1 ðtÞ, dt
i ¼ 1,2,3
ð3Þ
where B(t) and G(t) are, respectively, the nucleation and growth rates of crystals and mi (i¼0,y,3), which is the summation of mni and msi , represents the average product quality in terms of the total of number, length, surface area, and volume of crystals, respectively. Without consideration of crystal agglomeration or breakage phenomena, mass balance described the changes in the concentration of solution in the batch crystallizer can be expressed as: @C ¼ 3rkv GðtÞm2 ðtÞ @t
ð4Þ
where r is the density of crystals and kv is the volumetric shape factor. The model of crystallization is completed by defining the kinetic processes that relate the dynamics of crystal population to the state of the bulk system. This involves the determination of rate expressions for crystal nucleation and growth. These processes are related to the relative supersaturation (S) as follows: BðtÞ ¼ kb eEb =RT Sb m3 ðtÞ
ð5Þ
GðtÞ ¼ kg eEg =RT Sg
ð6Þ
where Eb is the nucleation activation energy, Eg is the growth activation energy, and b and g are the exponent terms relating the nucleation rate and the growth rate to the supersaturation, respectively. The control purpose of a crystallization process is to manage the nucleation and growth rates of crystal to achieve a desired crystal size. Well-controlled crystallization process is usually operated in the metastable zone bounded by the saturation concentration and the metastable limit, Cs rCrCm, in order to avoid uncontrolled nucleation of crystals. In this study, the seeded batch crystallizer of potassium sulfate studied by Shi et al. [8] is considered. The process parameters are shown in Table 1. The following equations are used to calculate the saturation and metastable concentrations corresponding to the solution temperature, T, as: C s ðTÞ ¼ 6:29 102 þ2:46 103 T7:14 106 T 2
ð7Þ
C m ðTÞ ¼ 7:76 102 þ 2:46 103 T8:10 106 T 2
ð8Þ
The distribution of seeded crystals in the batch crystallizer at initial condition was assumed to be a parabolic distribution, which is a function of the crystal characteristic length (r) varying from 250 to 300 mm as ( 0:0032ð300rÞðr250Þ for 250 mmr r r 300 mm nðr,0Þ ¼ 0 for r o250 mm and r 4 300 mm ð9Þ It is noted that the ith moment of the crystal population density at the start of batch run can be determined as Z 1 mi ð0Þ ¼ r i nðr,0Þdr ð10Þ 0
Table 1 Model parameters for the seeded batch crystallizer of potassium sulfate. b ¼1.45 kb ¼ 285 s 1 mm 3 Eb/R¼ 7517 K kv ¼1.5 r ¼2.66 10 12 g mm 3
g¼ 1.5 kg ¼ 1.44 108 mm s 1 Eg/R¼ 4859 K C(t ¼ 0)¼ 0.1742 g solute g solvent 1 tf ¼30 min
Since the crystal breakage or agglomeration was not considered in the proposed crystallizer model, a total number of the crystals growing from seeds, which is determined by the initial seed size distribution, remains constant.
3. Neural network-based optimal control 3.1. Optimal control problem Considering the practical operation of industrial crystallizers, fine crystals usually cause difficulties in downstream processing equipment and affect both product quality and process economics. A very detailed overview of the optimization objectives used for crystallization control was provided by Ward et al. [4]. This study focuses on the development of an optimal control system to achieve a desired final CSD. The control objective is to determine the optimal temperature profile that minimizes the total volume of nucleated fine crystals, which is represented by the third moment of crystals formed by nucleation (mn3), and at the same time maximizes the total volume of the desired crystals growing from seeds (ms3) at the end of batch operation (tf ¼30 min). Thus, the optimal control problem takes the form as follows [8]: Minimize TðtÞ
mn3 ðt f Þ ms3 ðt f Þ
ð11Þ
subject to Dynamic crystallizer model (Eqs. (2)–(6)) 30 o C r TðtÞ r50 o C C S r CðtÞ r C m dT rk dt
ms3 ðtf Þ ZV where the constant k is the maximum gradient of the reactor temperature, which was chosen to be 2 oC/min, corresponding to a ability of a cooling control system and V denotes the lower bound on the total volume of the crystals growing from seeded crystals. It is noted that the constraint on ms3(tf) indicates a desirable quality of the final crystal product. In this study, the lower bound of ms3(tf) was chosen as 8.33 109 mm3 g solvent 1. 3.2. Neural network model of batch crystallizer The first step of implementing NN in an optimal control algorithm is to train the NN to predict the dynamics of the batch crystallizer to be controlled, i.e., the total volume of fine and seeded crystals, when the operating temperature of the crystallizer changes. With the limited availability of actual experimental data, the detailed theoretical model of batch crystallization as mentioned earlier was numerical solved and implemented in Matlab to generate data for NN training. The solution concentration and the total volume of fine and seeded crystals represented by the third moments of crystals (mn3 and ms3) as outputs were predicted by using the current values of solution temperature and concentration as inputs since they have direct effect on the predicted outputs. However, it was found that only the inputs at the current time may not be enough to predict the future outputs. For this reason, the input data consists of the reactor temperatures at time (t), (t 1) and (t 2) and the solution concentration at time (t) and (t 1). Training and validation data sets for NN training were generated by performing various simulations of batch crystallizer operated under random changes in the cooling temperature profile in ranges of 30–50 1C. The operational time was kept constant at 30 min and the sampling time of data was 0.1 min. These data sets were further normalized
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by Z-score standardization for achieving a good performance of NN model. It is noted that, in general, experimental data are used for NN training; however, with their limited availability for a wide range of operational conditions, the simulated data obtained from numerical simulations of the theoretical crystallizer model were assumed to be used instead.
161
Fig. 1 shows the detailed training procedure to find the NN model. To train the multilayer feedforward NN, the Levenberg– Marquardt backpropagation algorithm with an early stopping mechanism was used as shown in Fig. 2. Minimizing a mean square error (MSE) between the NN predicted value and the actual targeted value of C, mn3 and ms3 was used as a criterion for
Fig. 1. Detailed procedure for neural network modeling.
C µin µis
T
Ct Ct Tt Tt Tt
C predict (t + 1)
µ3n,predict (t + 1)
µ3s ,predict (t + 1)
Fig. 2. Training algorithm of feedforward NN.
C (t + 1) µ3n (t + 1) µ3s (t + 1)
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weights and biases adjustment and also for NN structure selection. From simulation results, the optimum architecture of the NN for the prediction of the solution concentration and the third moment variables consists of three hidden layers with the log-sigmoid transfer
Tt
function and one output layer with a linear transfer function. The number of nodes in the 1st, 2nd, and 3rd hidden layers are 3, 7 and 5, respectively, as shown in Fig. 3. Table 2 summarizes the MSE value of the NN model with three-hidden layers.
C (t + 1)
Tt
µ (t + 1)
Tt Ct
µ (t + 1)
Ct
Fig. 3. Optimum structure of trained NN model.
Table 2 MSE of NN with three-hidden layers. Number of nodes
Mean square error (MSE) ( 10 4)
First hidden layer
Second hidden layer
Third hidden layer
3
3
3 5 7 9 3 5 7 9 3 5 7 9 3 5 7 9
5
7
9
293.646 5.8851 6.3296 26.6982 6.2416 248.198 6.3224 6.9727 6.4698 5.3558 6.6531 6.7970 6.5793 6.3281 5.6535 6.4608
Random Temperature Profile 50 48 46 44
T (°C)
42 40 38 36 34 32 30
0
5
10
15 time (min)
20
Fig. 4. Example of cooling temperature profile.
25
30 Fig. 5. Comparison of simulation results obtained from NN and theoretical model: (a) solution concentration (b) mn3 and (c) ms3.
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163
of mn3 and ms3 at the final batch time when three different control strategies: (1) linear cooling control, (2) optimal cooling control based on mathematical model (Shi et al. [8]), and (3) optimal cooling control based on neural network model (this study), were applied to the control of the batch crystallizer. It is noted that for the linear cooling control, the crystallizer temperature is linearly decreased from 50 1C to 30 1C. Comparing the simulation results, it is clear that the optimal control strategy can yield the lower volume of fine crystals, compared to the linear cooling strategy, while the seeded crystals still satisfy the product quality requirement. The proposed optimal control strategy incorporating the NN model shows good control performance in term of reducing the total volume of fine crystals by 94.65% compared to the linear cooling strategy and by 73.25% compared to the optimal control strategy based on mathematical model.
It should be noted that in order to compute the third moments of crystals (mn3 and ms3) at the final batch time (tf), the trained NN model can be recursively employed to predict future outputs over the prediction horizon (n). With the given cooling temperature profile (the value of temperature at each time interval) as shown in Fig. 4, the NN can predict the value of future outputs (i.e., C, mn3 and ms3) at time tþ1. Based on the first output prediction and the current value of temperature, the NN is then recall for the next prediction of the outputs at t þ2. This step is repeated until the end of batch run; the multiple outputs for n time intervals can be predicted. Fig. 5 compares the predicted values of the solution concentration and the third moment variable obtained from NN and theoretical models.
4. Computational results In this section, the optimal control technique based on NN model is implemented to determine an optimal temperature profile for a batch crystallizer. Fig. 6 shows the proposed optimal control structure integrated with NN. The NN was used as a state predictor to predict the values of the solution concentration and the third moment of crystals formed by nucleation (mn3) and seeds (ms3). The optimal control problem as mentioned in Section 3 was numerically solved by a sequential optimization and control approach [19]. In such an approach, the control variable (i.e. crystallizer temperature) is discretized by a piecewise constant function with equally spaced time intervals. This transforms the optimal control problem into a nonlinear programming problem (NLP). In this work, the temperature profile was assumed to be divided into 10 intervals. With the initial guess of the decision variables (the value of temperature at each time interval), the recursive NN is implemented to compute the value of outputs (i.e., C, mn3 and ms3) over the prediction horizon as earlier mentioned. Then, the outputs at the final batch time are passed to the optimization solver, which is based on a sequential quadratic programming algorithm, to compute a new temperature profile. These steps are iterative until the optimal temperature profile is found, satisfying the objective function and constraints. Fig. 7 shows the optimal temperature profile obtained for controlling the batch crystallizer. It is found that under the proposed optimal operation, the crystallizer system is operated within the metastable limit (Fig. 8), which is bounded by the saturation concentration and the metastable limit to avoid uncontrolled nucleation of crystals. Table 3 presents the values
5. Conclusions An optimal control based on a neural network model for a batch crystallizer was studied in this work. The optimal control Temperature Profile 50 48 46 44
T (°C)
42 40 38 36 34 32 30
0
5
10
15 time (min)
Fig. 7. Optimal cooling temperature profile.
Controller
µ 3n (t+1) µ 3s (t+1) T’(t)
Initial Condition Optimization
20
T(t-1) T(t-2)
Neural Network Model
C(t+1)
C(t-1)
C(t)
T(t) Crystallizer Fig. 6. Optimal control incorporating with NN model predictor.
25
30
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Concentration Profile
0.2 0.19 0.18
C (g/g)
0.17 0.16 0.15 0.14 Cm (t)
0.13 0.12
C(t) Cs(t)
0
5
10
15 time (min)
20
25
30
Fig. 8. Concentration profile under the optimal operation of batch crystallizer.
Table 3 Performance of batch crystallization under different control strategies. Control strategies
mn3(tf)
ms3(tf)
Linear cooling control Optimal control based on theoretical crystallization model [7] Optimal control based on NN model
8.917 109 9.1121 109 1.7828 109 1.0545 1010
[5] S.M. Miller, J.B. Rawlings, Model identification and control strategies for batch cooling crystallizers, AIChE. J. 40 (1994) 1312–1327. [6] G. Zhang, S. Rohani, On-line optimal control of a seeded batch cooling crystallizer, Chem. Eng. Sci. 58 (2003) 1887–1896. [7] Q. Hu, S. Rohani, A. Jutan, Modeling and optimization of seeded batch crystallizers, Comput. Chem. Eng. 29 (2005) 911–918. [8] D. Shi, N.H. El-Farra, M. Li, P. Mhaskar, P.D. Christofides, Predictive control of particle size distribution in particulate processes, Chem. Eng. Sci. 61 (2006) 268–281. [9] M.W. Hermanto, M. Chiu, X. Woo, R.D. Braatz, Robust optimal control of polymorphic transformation in batch crystallization, AIChE J. 53 (2007) 2643–2650. [10] W. Paengjuntuek, P. Kittisupakorn, A. Arpornwichanop, On-line dynamic optimization integrated with generic model control of a batch crystallizer, J. Ind. Eng. Chem. 14 (2008) 442–448. [11] Z.K. Nagy, J.W. Chew, M. Fujiwara, R.D. Braatz, Comparative performance of concentration and temperature controlled batch crystallizations, J. Process Control 18 (2008) 399–407. [12] P. Georgieva, S.F. De Azevedo, Application of feed forward neural networks in modeling and control of a fed-batch crystallization process, Trans. Eng. Comput. Tech. 12 (2006). [13] M.A. Hussain, Review of the application of neural networks in chemical process control-simulation and online implementation, Artif. Intel. Eng. 13 (1999) 55–68. [14] F.S. Mjalli, S. Al-Asheh, H.E. Alfadala, Use of artificial neural network blackbox modeling for the prediction of wastewater treatment plants performance, J. Environ. Manage. 83 (2007) 329–338. [15] Z.K. Nagy, Model based control of a yeast fermentation bioreactor using optimally designed artificial neural networks, Chem. Eng. J. 127 (2007) 95–109. [16] A. Arpornwichanop, N. Shomchoam, Control of fed-batch bioreactors by a hybrid on-line optimal control strategy and neural network estimator, Neurocomputing 72 (2009) 2297–2302. [17] Z.K. Nagy, M Fujiwara, R.D. Braatz, Modeling and control of combined cooling and antisolvent crystallization processes, J. Process Control 18 (2008) 856–864. [18] H.B. Matthews, Model identification and control of batch crystallization for an industrial chemical system, PhD Thesis, University of Wisconsin at Madison, 1997. [19] A. Arpornwichanop, N. Shomchoam, Studies on optimal control approach in a fed-batch fermentation, Korean J. Chem. Eng. 24 (2007) 11–15.
4.7681 108 9.6841 109
strategy was implemented to find an optimal temperature profile with the aim to minimize a total volume of nucleated fine particles (mn3) and to maximize a total volume of the crystals growing from seeds (ms3) at the end of the operation. The neural network model of batch crystallizer was developed to predict the future process response in terms of the solution concentration and the moment variables that represent a crystal product quality and then employed as a predictor in the optimal control algorithm. It was found that the neural network shows a good state predictor and the optimal control with the neural network model provides a superior control performance compared to a conventional control methodologies.
Acknowledgment Support from The Thailand Research Fund and Commission on Higher Education (MRG5280109), Thammasat University and the Special Task Force for Activating Research (STAR), Chulalongkorn University Centenary Academic Development Project is gratefully acknowledged. References [1] P.A. Larsen, D.B. Patience, J.B. Rawlings, Industrial crystallization process and control, IEEE Control Syst. Mag. (2006) 70–80. [2] C.B.B. Costa, A.C. Da Costa, R.M. Filho, Mathematical modeling and optimal control strategy development for an adipic acid crystallization process, Chem. Eng. Proc ess. 44 (2005) 737–753. [3] H. Hojjati, S. Rohani, Cooling and seeding effect on supersaturation and final crystal size distribution of ammonium sulphate in a batch crystallizer, Chem. Eng. Process. 44 (2005) 949–957. [4] J.D. Ward, D.A. Mellichamp, M.F. Doherty, Choosing an operating policy for seeded batch crystallization, AIChE J. 52 (2006) 2046–2054.
Woranee Paengjuntuek received the B.Eng. degree (first class honours) in chemical engineering from Khon Kaen University (Thailand) in 2004 and the D.Eng. degree in chemical engineering from Chulalongkorn University (Thailand) in 2008. Since 2008, she has been a lecturer at the department of chemical engineering, faculty of engineering, Thammasat University. Her research fields of interest include process control and optimization and their applications in chemical processes and crystallization.
Linda Thanasinthana received B.Eng and M.Eng degrees in chemical engineering from Chulalongkorn University (Thailand) in 2006 and 2008, respectively. Her past research focused on the control of batch crystallization, optimal control and neural network. She is presently a consulting engineer at Invensys Process System, Thailand.
Amornchai Arpornwichanop received B.Eng. and D. Eng. degrees in chemical engineering from Chulalongkorn University (Thailand) in 1997 and 2003, respectively. Since 2003, he has been with the department of chemical engineering, faculty of engineering, Chulalongkorn University. His current research interests include modeling and optimization, optimal control and model predictive control, neural network. Presently, his research projects mainly focus on systems such as reactive distillation, solid oxide fuel cell, crystallizer, membrane reactor and batch and fedbatch biochemical reactor.