Integrated batch‐to‐batch and nonlinear model predictive control for polymorphic transformation in pharmaceutical crystallization

Polymorphism, a phenomenon in which a substance can have more than one crystal form, is a frequently encountered phenomenon in pharmaceutical compounds. Different polymorphs can have very different physical properties such as crystal shape, solubility, hardness, color, melting point, and chemical reactivity, so that it is important to ensure consistent production of the desired polymorph. In this study, an integrated batch‐to‐batch and nonlinear model predictive control (B2B‐NMPC) strategy based on a hybrid model is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The hybrid model comprising of a nominal first‐principles model and a correction factor based on an updated PLS model is used to predict the process variables and final product quality. At each sampling instance during a batch, extended predictive self‐adaptive control (EPSAC) is employed as a NMPC technique to calculate the control action by using the current hybrid model as a predictor. At the end of the batch, the PLS model is updated by utilizing the measurements from the batch and the above procedure is repeated to obtain new control actions for the next batch. In a simulation study using a previously reported model for a polymorphic crystallization with experimentally determined parameters, the proposed B2B‐NMPC control strategy produces better performance, where it satisfies all the state constraints and produces faster and smoother convergence, than the standard batch‐to‐batch strategy. © 2010 American Institute of Chemical Engineers AIChE J, 2011     

Nonlinear model predictive control for the polymorphic transformation of L‐glutamic acid crystals

Polymorphism, a phenomenon where a substance can have more than one crystal forms, has recently become a major interest to the food, speciality chemical, and pharmaceutical industries. The different physical properties for polymorphs such as solubility, morphology, and dissolution rate may jeopardize operability or product quality, resulting in significant effort in controlling crystallization processes to ensure consistent production of the desired polymorph. Here, a nonlinear model predictive control (NMPC) strategy is developed for the polymorphic transformation of L ‐glutamic acid from the metastable α‐form to the stable β‐form crystals. The robustness of the proposed NMPC strategy to parameter perturbations is compared with temperature control (T‐control), concentration control (C‐control), and quadratic matrix control with successive linearization (SL‐QDMC). Simulation studies show that T‐control is the least robust, whereas C‐control performs very robustly but long batch times may be required. SL‐QDMC performs rather poorly even when there is no plant‐model mismatch due to the high process nonlinearity, rendering successive linearization inaccurate. The NMPC strategy shows good overall robustness for two different control objectives, which were both within 7% of their optimal values, while satisfying all constraints on manipulated and state variables within the specified batch time. © 2009 American Institute of Chemical Engineers AIChE J, 2009     

Product quality improvement of batch crystallizers by a batch-to-batch optimization and nonlinear control approach

Batch crystallization is one of the widely used processes for separation and purification in many chemical industries. Dynamic optimization of such a process has recently shown the improvement of final product quality in term of a crystal size distribution (CSD) by determining an optimal operating policy. However, under the presence of unknown or uncertain model parameters, the desired product quality may not be achieved when the calculated optimal control profile is implemented. In this study, a batch-to-batch optimization strategy is proposed for the estimation of uncertain kinetic parameters in the batch crystallization process, choosing the seeded batch crystallizer of potassium sulfate as a case study. The information of the CSD obtained at the end of batch run is employed in such an optimization-based estimation. The updated kinetic parameters are used to modify an optimal operating temperature policy of a crystallizer for a subsequent operation. This optimal temperature policy is then employed as new reference for a temperature controller which is based on a generic model control algorithm to control the crystallizer in a new batch run.     

On‐Line PEMFC Control Using Parameterized Nonlinear Model‐Based Predictive Control

In this work, a fast nonlinear model‐based predictive control (NMPC) strategy is designed and experimentally validated on‐line on a real fuel cell. Regarding NMPC strategies, the most challenging part remains to achieve on‐line implementation, especially when dealing with fast dynamic systems. As previously demonstrated in a recent work, the proposed control strategy is ideally suited to address this problem. Indeed, it is 30 times faster than classical NMPC controllers. This strategy relies on a specific parameterization of the control actions to reduce the computational time and achieve on‐line implementation. Due to its short computational time compared to mechanistic models, an artificial neural network model is designed and experimentally validated. This model is employed as internal model in the NMPC controller to predict the system behavior. To confirm the applicability and the relevance of the proposed NMPC controller varying control scenarios are investigated on a test bench. The built‐in controller is overridden and the NMPC controller is implemented externally and executed on‐line. Experimental results exhibit the outstanding tracking capability and robustness against model‐process mismatch of the proposed strategy. The parameterized NMPC controller turns out to be an excellent candidate for on‐line applications.     

Model based control of a liquid swelling constrained batch reactor subject to recipe uncertainties

This work presents the application of nonlinear model predictive control (NMPC) to a simulated industrial batch reactor subject to safety constraint due to reactor level swelling, which can occur with relatively fast dynamics. Uncertainties in the implementation of recipes in batch process operation are of significant industrial relevance. The paper describes a novel control-relevant formulation of the excessive liquid rise problem for a two-phase batch reactor subject to recipe uncertainties. The control simulations are carried out using a dedicated NMPC and optimization software toolbox OptCon which implements efficient numerical algorithms. The open-loop optimal control problem is computed using the multiple-shooting technique and the arising nonlinear programming problem is solved using a sequential quadratic programming (SQP) algorithm tailored for large-scale problems, based on the freeware optimization environment HQP. The fast response of the NMPC controller is guaranteed by the initial value embedding and real-time iteration technologies. It is concluded that the OptCon implementation allows small sampling times and the controller is able to maintain safe and optimal operation conditions, with good control performance despite significant uncertainties in the implementation of the batch recipe.     

Handling multi‐rate and missing data in variable duration economic model predictive control of batch processes

In the present work, we consider the problem of variable duration economic model predictive control of batch processes subject to multi‐rate and missing data. To this end, we first generalize a recently developed subspace‐based model identification approach for batch processes to handle multi‐rate and missing data by utilizing the incremental singular value decomposition technique. Exploiting the fact that the proposed identification approach is capable of handling inconsistent batch lengths, the resulting dynamic model is integrated into a tiered EMPC formulation that optimizes process economics (including batch duration). Simulation case studies involving application to the energy intensive electric arc furnace process demonstrate the efficacy of the proposed approach compared to a traditional trajectory tracking approach subject to limited availability of process measurements, missing data, measurement noise, and constraints. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2705–2718, 2017     

Robust batch‐to‐batch optimization in the presence of model‐plant mismatch and input uncertainty

In model‐based optimization in the presence of model‐plant mismatch, the set of model parameter estimates which satisfy an identification objective may not result in an accurate prediction of the gradients of the cost‐function and constraints. To ensure convergence to the optimum, the predicted gradients can be forced to match the measured gradients by adapting the model parameters. Since updating all available parameters is impractical due to estimability problems and overfitting, there is a motivation for adapting a subset of parameters for updating the predicted outputs and gradients. This article presents an approach to select a subset of parameters based on the sensitivities of the model outputs and of the cost function and constraint gradients. Furthermore, robustness to uncertainties in initial batch conditions is introduced using a robust formulation based on polynomial chaos expansions. The improvements in convergence to the process optimum and robustness are illustrated using a fed‐batch bioprocess. © 2017 American Institute of Chemical Engineers AIChE J, 63: 2660–2670, 2017     

一种基于状态估计的间歇过程模型实时更新预测控制策略简

Nonlinear model predictive control （NMPC） is an appealing control technique for improving the per- formance of batch processes, but its implementation in industry is not always possible due to its heavy on-line computation. To facilitate the implementation of NMPC in batch processes, we propose a real-time updated model predictive control method based on state estimation. The method includes two strategies： a multiple model building strategy and a real-time model updated strategy. The multiple model building strategy is to produce a series of sim- plified models to reduce the on-line computational complexity of NMPC. The real-time model updated strategy is to update the simplified models to keep the accuracy of the models describing dynamic process behavior. The method is validated with a typical batch reactor. Simulation studies show that the new method is efficient and robust with respect to model mismatch and changes in process parameters.     

Nonlinear MPC for fed-batch multiple stages sugar crystallization

This paper addresses the issue of developing feasible advanced control strategies for the operation of industrial fed-batch multi-stage sugar crystallization processes. The operation of such processes poses very challenging problems mainly those inherent to its batch nature and also those due to the difficulties in measuring key process variables. Inadequate control policies lead to out-of-spec batches, with consequent losses resulting from the need of product recycling.In order to address these problems, a modification of the general Nonlinear Model Predictive Control (NMPC) is proposed in this paper, where the NMPC is executed only when the tracking error is outside a pre-specified bound α. Once the error converges towards the α-strip, the NMPC is switched off and the control action is kept constant. In order to further reduce the complexity of the control system, the proposed modification, termed Error Tolerant MPC (ETMPC), is provided with a Recurrent Neural Network (RNN) predictive model. The ETMPC + RNN control scheme was extensively tested on a crystallizer dynamic simulator, tuned with data from two industrial units, and compared with the classical NMPC and PI strategy. The results demonstrate that both NMPC and ETMPC controllers lead to improved end point process specifications, when compared with the PI controller. The explicit introduction of the error tolerance in the optimization relaxes the computational burden and can complement several other suggestions in the literature for feasible industrial real time control.     

Flow Synthesis of a Thiazolidine Drug Intermediate in Capillary Microreactors

Microreactor technology can help to reduce the time to market new drugs. It was applied to produce (Z)‐5‐benzylidenethiazolidine‐2,4‐dione, a heterocyclic intermediate in the synthesis of various drugs. Ethanol was the optimum solvent and piperidine the best catalyst in the batch process. The continuous/microreactor process exhibited a much better performance than the batch process. The productivity, which was strongly influenced by solvent and temperature, reached a maximum at 160 °C using methanol as solvent. A kinetic/thermodynamic study indicated that the reaction followed the second‐order model and allowed estimating its main thermodynamic parameters. A product recovery protocol was finally proposed. The microreactor proved an efficient alternative to the batch reactor in scaling up the production of active pharmaceutical ingredients.     

Monetizing shale gas to polymers under mixed uncertainty: Stochastic modeling and likelihood analysis

A novel framework based on stochastic modeling methods and likelihood analysis to address large‐scale monetization processes of converting shale gas to polymers under the mixed uncertainties of feedstock compositions, estimated ultimate recovery, and economic parameters is presented. A new stochastic data processing strategy is developed to quantify the feedstock variability through generating the appropriate number of scenarios. This strategy includes the Kriging‐based surrogate model, sample average approximation, and the integrated decline‐stimulate analysis curve. The feedstock variability is then propagated through performing a detailed techno‐economic modeling method on distributed‐centralized conversion network systems. Uncertain economic parameters are incorporated into the stochastic model to estimate the maximum likelihood of performance objectives. The proposed strategy and models are illustrated in four case studies with different plant locations and pathway designs. The results highlight the benefits of the hybrid pathway as it is more amenable to reducing the economic risk of the projects. © 2018 American Institute of Chemical Engineers AIChE J, 64: 2017–2036, 2018     

Optimal operation of batch enantiomer crystallization: From ternary diagrams to predictive control

In this work, the modeling and control of batch crystallization for racemic compound forming systems is addressed in a systematic fashion. Specifically, a batch crystallization process is considered for which the initial solution has been pre‐enriched in the desired enantiomer to enable crystallization of only the preferred enantiomer. A method for determining desired operating conditions (composition of the initial pre‐enriched solution and temperature to which the mixture must be cooled for maximum yield) for the batch crystallizer based on a ternary diagram for the enantiomer mixture in a solvent is described. Subsequently, it is shown that the information obtained from the ternary diagram, such as the maximum yield attainable from the process due to thermodynamics, can be used to formulate constraints for an optimization‐based control method to achieve desired product characteristics such as a desired yield. The proposed method is demonstrated for the batch crystallization of mandelic acid in a crystallizer with a fines trap that is seeded with crystals of the desired enantiomer. The process is controlled with an optimization‐based controller to minimize the ratio of the mass of crystals obtained from nuclei to the mass obtained from seeds while maintaining the desired enantioseparation. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1618–1637, 2018     

Mathematical modelling and experimental validation of a novel periodic flow crystallization using MSMPR crystallizers

The challenges of insufficient residence time for crystal growing and transfer line blockage in conventional continuous mixed‐suspension mixed‐product removal (MSMPR) operations are still not well addressed. Periodic flow crystallization is a novel method whereby controlled periodic disruptions are applied to the inlet and outlet flows of an MSMPR crystallizer to increase its residence time. A dynamic model of residence time distribution in an MSMPR crystallizer was first developed to demonstrate the periodic flow operation. Besides, process models of periodic flow crystallizations were developed with an aim to provide a better understanding and improve the performance of the periodic flow operation, wherein the crystallization mechanisms and kinetics of the glycine‐water system were estimated from batch cooling crystallization experiments. Experiments of periodic flow crystallizations were also conducted in single‐/three‐stage MSMPR crystallizers to validate the process models and demonstrate the advantages of using periodic flow operation in MSMPR stages. © 2016 American Institute of Chemical Engineers AIChE J, 63: 1313–1327, 2017     

Integrated solvent and process design for continuous crystallization and solvent recycling using PC‐SAFT

Solvent usage is a major source of environmental waste in pharmaceutical industry. The current paradigm shift toward continuous manufacturing in pharmaceutical industry has renewed the interest in continuous crystallization, which offers the prospect of easy solvent recycling. However, the selection of solvents for an integrated crystallization processes is nontrivial due to the likely trade‐off between optimal solvent properties for crystallization and solvent separation and recycling. A systematic approach for the simultaneous optimization of process conditions and solvent selection for continuous crystallization including solvent recycling is presented. A unified perturbed‐chain statistical associating fluid theory model framework is applied to predict thermodynamic properties related to solubility and vapor‐liquid equilibrium, which is integrated with a process model. A continuous mapping procedure is adopted to solve the optimization problem effectively. A case study based on continuous antisolvent crystallization of paracetamol with solvent separation via flash demonstrates the approach. © 2017 American Institute of Chemical Engineers AIChE J, 64: 1205–1216, 2018     

Data‐driven adaptive nested robust optimization: General modeling framework and efficient computational algorithm for decision making under uncertainty

A novel data‐driven adaptive robust optimization framework that leverages big data in process industries is proposed. A Bayesian nonparametric model—the Dirichlet process mixture model—is adopted and combined with a variational inference algorithm to extract the information embedded within uncertainty data. Further a data‐driven approach for defining uncertainty set is proposed. This machine‐learning model is seamlessly integrated with adaptive robust optimization approach through a novel four‐level optimization framework. This framework explicitly accounts for the correlation, asymmetry and multimode of uncertainty data, so it generates less conservative solutions. Additionally, the proposed framework is robust not only to parameter variations, but also to anomalous measurements. Because the resulting multilevel optimization problem cannot be solved directly by any off‐the‐shelf solvers, an efficient column‐and‐constraint generation algorithm is proposed to address the computational challenge. Two industrial applications on batch process scheduling and on process network planning are presented to demonstrate the advantages of the proposed modeling framework and effectiveness of the solution algorithm. © 2017 American Institute of Chemical Engineers AIChE J, 63: 3790–3817, 2017     

Dynamic nonlinear batch process fault detection and identification based on two‐directional dynamic kernel slow feature analysis

The batch process generally covers high nonlinearity and two‐directional dynamics: time‐wise dynamics, which correspond to inherently time‐varying dynamics resulting from the slowly varying underlying driving forces within each batch duration; and batch‐wise dynamics, which are associated with different operating modes among different batches. However, most existing dynamic nonlinear monitoring methods cannot extract the slowly varying underlying driving forces of the nonlinear batch process and rarely tackle the batch‐wise dynamic characteristics among batch runs. In order to address these issues, a new monitoring scheme based on two‐directional dynamic kernel slow feature analysis (TDKSFA) is developed by combining kernel SFA with a global modelling strategy. In the TDKSFA method, kernel SFA is integrated with the ARMAX time series model to mine the nonlinear and time‐wise dynamic properties within a batch run due to its capability of extracting the slowly varying underlying driving forces. Furthermore, the global modelling strategy is presented to handle the batch‐wise dynamics among batches by calculating the total average kernel matrix of all training batches. After the slow features are extracted, Hotelling's T² and SPE statistics are built to detect faults. To solve the issue of fault variable nonlinear identification, a novel nonlinear contribution plot inspired by the pseudo‐sample variable projection trajectories in the TDKSFA model is further proposed to identify fault variables. Finally, the feasibility and effectiveness of the TDKSFA‐based fault diagnosis strategy is demonstrated through a numerical system and the penicillin fermentation process.     

Performance evaluation of batch and unsteady state fed‐batch reactor operations for the production of a marine microbial surfactant

BACKGROUND: Biosurfactants are microbially derived surface‐active and amphipathic molecules produced by various microorganisms. These versatile biomolecules can find potential applications in food, cosmetics, petroleum recovery and biopharmaceutical industries. However, their commercial use is impeded by low yields and productivities in fermentation processes. Thus, an attempt was made to enhance product yield and process productivity by designing a fed‐batch mode reactor strategy. RESULTS: Biosurfactant (BS) production by a marine bacterium was performed in batch and fed‐batch modes of reactor operation in a 3.7 L fermenter. BS concentration of 4.61 ± 0.07 g L^?1 was achieved in batch mode after 22 h with minimum power input of 33.87 × 10³ W, resulting in maximum mixing efficiency. The volumetric oxygen flow rate (K_La) of the marine culture was about 0.08 s^?1. BS production was growth‐associated, as evident from fitting growth kinetics data into the Luedeking‐Piret model. An unsteady state fed batch (USFB) strategy was employed to enhance BS production. Glucose feeding was done at different flow rates ranging from 3.7 mL min^?1 (USFB‐I) to 10 mL min^?1 (USFB‐II). USFB‐I strategy resulted in a maximum biosurfactant yield of 6.2 g l^?1 with an increment of 35% of batch data. The kinetic parameters of USFB‐I were better than those from batch and USFB‐II. CONCLUSION: Comparative performance evaluation of batch and semi‐continuous reactor operations was accomplished. USFB‐I operation improved biosurfactant production by about 35% over batch mode. USFB‐I strategy was more kinetically favorable than batch and USFB‐II. © 2012 Society of Chemical Industry     

Reaction engineering with enzymes: A relatively uncharted territory

This article discusses the history of enzyme kinetics developed by Michaelis and Menten, and recent work extending kinetics for enzyme‐catalyzed reactions in organic solvents. Based on kinetic studies of the transesterification of vinyl methacrylate with 2‐hydroxyethyl acrylate catalyzed by Candida antarctica lipase B, a new model is proposed that resembles the kinetic model of controlled/living polymerizations governed by dynamic equilibrium of active and dormant species. Experimental data indicates that by judicious selection of reaction conditions steady‐state conditions can be achieved and very clean products with quantitative conversion can be produced. © 2016 American Institute of Chemical Engineers AIChE J, 63: 266–272, 2017     

间歇结晶过程的分批优化

It is the fact that several process parameters are either unknown or uncertain. Therefore, an optimal control, profile calculated with developed process models with respect to such process parameters may not give an optimal performance when implemented to real processes. This study proposes a batch-to-batch optimization strategy for the estimation of uncertain kinetic.par.ameters in a batch crystallization process of potassium sulfate production. The knowledge of a crystal size distribution of the product at the end of batch operation is used in the proposed methodology. The updated kinetic parameters are applied for determining an optimal operating temperature policy for the next batch run.     

Quantitative design of seed load for solution cooling crystallization based on kinetic analysis

Seed load of crystallization has a direct effect on the product qualities. To further reveal the effects of seed load on crystallization kinetics and improve the product size distribution, the aqueous solution of potassium nitrate (KNO₃–H₂O) is employed as a model system and the relevant kinetic experiments are conducted in a batch cooling crystallizer. The crystal nucleation and growth rate parameters are firstly estimated with the concentration and transmittance data using a mathematical model reported in our lab, and then the backward calculations with the help of the model parameters are successfully performed. It is found that the nucleation capacity decreases and growth capacity increases with increasing seed load, and the size distribution of crystal products tends to be more uniform. However, with the increasing of seed load, the linear growth rate of single crystal and the mean size of products both reduce accordingly. Based on the calculational and experimental results, a quantitative design scheme concerning seed load is proposed by further kinetic analyses, and the corresponding verification experiments are carried out. The results show that under the guidance of the proposed scheme, the size distribution of crystal products is more concentrated and the mean size of final particles can also escape from reducing obviously.