1188 IEEE TRANSACTIONS ON CONTROL SYSTEMS TECHNOLOGY, VOL. 20, NO. 5, SEPTEMBER 2012 Nonlinear Model-Based Control of a Semi-Industrial Batch Crystallizer Using a Population Balance Modeling Framework Ali Mesbah, Zoltan K. Nagy, Adrie E. M. Huesman, Herman J. M. Kramer, and Paul M. J. Van den Hof, Fellow, IEEE Abstract—This paper presents an output feedback nonlinear model-based control approach for optimal operation of industrial batch crystallizers. A full population balance model is utilized as the cornerstone of the control approach. The modeling framework allows us to describe the dynamics of a wide range of industrial batch crystallizers. In addition, it facilitates the use of performance objectives expressed in terms of crystal size distribution. The core component of the control approach is an optimal control problem, which is solved by the direct multiple shooting strategy. To ensure the effectiveness of the optimal operating policies in the presence of model imperfections and process uncertainties, the model predictions are adapted on the basis of online measurements using a moving horizon state estimator. The nonlinear model-based control approach is applied to a semi-industrial crystallizer. The simulation results suggest that the feasibility of real-time control of the crystallizer is largely dependent on the discretization coarse- ness of the population balance model. The control performance can be greatly deteriorated due to inadequate discretization of the population balance equation. This results from structural model imperfection, which is effectively compensated for by using the online measurements to confer an integrating action to the dy- namic optimizer. The real-time feasibility of the output feedback control approach is experimentally corroborated for fed-batch evaporative crystallization of ammonium sulphate. It is observed that the use of the control approach leads to a substantial increase, i.e., up to 15%, in the batch crystal content as the product quality is sustained. Index Terms—Batch crystallization, direct multiple shooting strategy, dynamic optimization, moving horizon estimation, popu- lation balance equation (PBE), real-time control. I. INTRODUCTION B ATCH crystallization is prevalent in the specialty chem- ical, food, and pharmaceutical industries to separate and to purify high value-added chemical substances. Crystalliza- Manuscript received September 23, 2010; revised February 16, 2011; ac- cepted June 01, 2011. Manuscript received in final form June 24, 2011. Date of publication August 15, 2011; date of current version June 28, 2012. Recom- mended by Associate Editor J. H. Lee. This work was carried out within the EUREKA/IS-project E! 3458/IS043074, called crystallizer based processing: fundamental research into modelling (CryPTO). This work was supported by SenterNovem. A. Mesbah is with the Delft Center for Systems and Control, Delft University of Technology, 2628 CD Delft, The Netherlands, and also with the Process and Energy Laboratory, Delft University of Technology Leeghwaterstraat 44, 2628 CA Delft, The Netherlands (e-mail: ali.mesbah@tudelft.nl). A. E. M. Huesman and P. M. J. Van den Hof are with the Delft Center for Sys- tems and Control, Delft University of Technology, 2628 CD Delft, The Nether- lands. H. J. M. Kramer is with the Process and Energy Laboratory, Delft University of Technology, 2628 CA Delft, The Netherlands. Z. K. Nagy is with the Chemical Engineering Department, Loughborough University, LE11 3TU, U.K. Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TCST.2011.2160945 tion processes are governed by several physico-chemical phe- nomena such as nucleation, crystal growth, and agglomeration, which arise from the co-presence of a continuous phase and a dispersed phase. These kinetic phenomena result in distributed nature of the physical and chemical properties of the manu- factured crystals. One of the key characteristics of crystals is their size distribution, providing the critical link between var- ious product quality attributes and the process operating condi- tions [23]. Despite their extensive use, optimal operation of batch crys- tallizers is particularly challenging. The difficulties primarily re- sult from the complexity of process models, uncertainties of the crystallization kinetics, sensor limitations in reliably measuring the process variables, and the inherent process uncertainties that may impair the effectiveness of advanced control strategies [3]. In addition, the optimal operation of batch crystallizers is often hampered by the lack of process actuation. Numerous strategies have been proposed for advanced con- trol of batch crystallizers. These strategies can be broadly cat- egorized into the model-based control approach [6], [16], [25], [26], [34], [37], [45], [47] and the direct design approach [12], [36], [53]. In the former approach, a process model is used to op- timally exploit the degrees of freedom of the process to achieve the desired product properties in accordance with a performance objective. A desirable product typically consists in crystals with a large mean size and a narrow size distribution [42]. In re- cent years, the advent of process analytical technology has led to the emergence of the direct design approach. This approach aims to control the crystallization within the metastable zone bounded by the solubility curve and the metastable limit. In the direct design approach, a supersaturation profile is determined experimentally with the aid of different process analytical tech- niques. Subsequently, the setpoint profile is tracked in the phase diagram by means of a supersaturation controller, which re- lies on in-situ measurements of process variables. Although the direct design approach circumvents the need for derivation of first-principles models and accurate determination of crystal- lization kinetics, it only ensures near-optimal operation of the process. It is self-evident that the cornerstone of any model-based con- trol approach is its dynamic process model, describing the rela- tion between the relevant inputs and outputs of the system. The population balance equation provides a natural framework for mathematical modeling of the evolution of crystal size distri- bution (CSD) in crystallization processes [17]. The prime diffi- culty in the synthesis of feedback model-based controllers arises from the distributed nature of the population balance modeling 1063-6536/$26.00 © 2011 IEEE