Optimal control of batch processes using particle swam optimisation with stacked neural network models

An optimal control strategy for batch processes using particle swam optimisation (PSO) and stacked neural networks is presented in this paper. Stacked neural network models are developed form historical process operation data. Stacked neural networks are used to improve model generalisation capability, as well as provide model prediction confidence bounds. In order to improve the reliability of the calculated optimal control policy, an additional term is introduced in the optimisation objective function to penalize wide model prediction confidence bounds. The optimisation problem is solved using PSO, which can cope with multiple local minima and could generally find the global minimum. Application to a simulated fed-batch process demonstrates that the proposed technique is very effective.     

Scale-up of binder agglomeration processes

This review article describes scale-up of batch and continuous granulation processes where liquid binder is added to fine powder in order to form a granular product. The technical goal of scale-up is to maintain similarity of critical product attributes as the production scale and/or throughput of a manufacturing process is increased. This paper provides a framework for scaling-up that considers critical process transformations in relation to the desired product attributes. A similar approach can be taken in developing process control strategies. In any agglomeration process, transformations can be used to describe how raw materials (typically fine powders and liquid binders) are converted into a granular product. Often the critical product attributes are characterized on the scale of individual granules (e.g., size, shape, porosity, mechanical strength, etc.). On the other hand, industrial scale-up requires predictive relations for the sizing, design and operation of process equipment. Considering scale-up on the basis of transformations is one way to link the macro-scale equipment decisions with micro-scale product attributes. This approach can be applied to the scale-up of batch and/or continuous granulation processes as well as transitioning from small batch prototypes to continuous production circuits.     

Modelling of granulation by a two-stage auto-layering mechanism in continuous industrial drums

A mechanistic model for the granulation of particulate materials with a wide size distribution in a large-scale continuous drum is presented. It takes cognizance of the effect of relevant process variables: feed size distribution, moisture content, binders such as lime, residence time distribution, feed rate, etc. The model is based on the auto-layering mechanism of granule growth and incorporates a piecewise linear model for granulation kinetics. Laboratory scale tests on a batch drum are used to provide kinetic parameters. The size-dependent residence time distribution of agglomerating mass in the continuous drum is represented by a combination of mixed and plug flow regimes operating in parallel. The model is customized for a continuous drum in an iron ore fines sintering plant. The predicted granule size distributions are in good agreement with the plant data under widely varying operating conditions. The modelling framework provides scope for modifying the individual modules for drum residence time distribution or the granulation mechanism and growth kinetics.     

Steady states in granulation of pharmaceutical powders with application to scale-up

Theoretical and experimental evidence is given to show that steady states can be reached during agglomerate growth and break-up in high-shear granulation of fine powders. An earlier theoretical model [G.I. Tardos, I.M. Khan and P.R. Mort, Critical parameters and limiting conditions in binder granulation of fine powders, Powder Technology, 94, 245-258 (1997).], based on simple energy-dissipation considerations hinted at the existence of these states at the point where growth is counterbalanced by breakage. Further theoretical evidence is obtained from molecular dynamic simulations of wet and dry particles situated in a constant shear field [I. Talu, G.I. Tardos and M.I. Khan, Computer simulation of wet granulation, Powder Technology, 110, 59-75 (2000).], where the size distribution of initially identical particles, shifts in time to reach a dynamic steady state. Under the conditions of this steady state, the number of breaking agglomerates approximately equals the number of forming ones to yield a time independent final-size distribution.Experimental evidence to support the theoretical findings is obtained during the present research by measuring particle size distributions at line at crucial points during granulation of a typical pharmaceutical powder in a high-shear mixer. In order to reach a steady state, binder addition has to be slow enough and wet massing has to be long enough so that neither has an influence on the final properties of the granules. We show experimentally that if binder is spread properly and homogeneously in the powder and continuous shearing of the wet mass ensures homogeneous, equal growth of the granules, the steady state will only be a function of the total amount of fluid added provided that the shear forces in the machine are maintained constant.These findings are important in that they show that under carefully controlled conditions of binder addition and shear in the mixer, the granulation process is robust and controllable and can, in principle, be scaled up with ease once the powder ingredients and the total amount of binder are fixed.     

Modeling and simulation of motor/turbine processes in utility plant

To achieve safe operation and to improve economics it is imperative to monitor and analyze demand and supply of utilities and to meet utility needs in time. The main objective of motor/turbine processes is to manipulate optimal balances on steam and electricity in utility plants. The optimal operation of motor/turbine processes is by far the most important to improve economics in the utility plant. In order to analyze motor/turbine processes, steady state models for steam generation equipment and steam distribution devices as well as turbine generators are developed and analyzed in this work. In addition, heuristics concerning various operational situations are incorporated in the models. The motor/turbine optimal operation system is based on utility models and operational knowledgebase, and provides optimal operating conditions when the amount of steam demand from various steam headers is changed frequently. The optimal operation system also produces optimal selection of driving devices for utility pumps to reduce operating cost.     

Comparison between two types of Artificial Neural Networks used for validation of pharmaceutical processes

Two types of Artificial Neural Networks (ANNs), a Multi-Layer Perceptron (MLP) and a Generalized Regression Neural Network (GRNN), have been used for the validation of a fluid bed granulation process. The training capacity and the accuracy of these two types of networks were compared. The variations of the ratio of binder solution to feed material, product bed temperature, atomizing air pressure, binder spray rate, air velocity and batch size were taken as input variables for training the MLP and GRNN. The properties of size, size distribution, flow rate, angle of repose and Hausner's ratio of granules produced, were measured and used as output variables. Qualitatively, the two networks gave comparable results, as both pointed out the importance of the binder spray rate and the atomizing air pressure to the granulation process. However, the averaged absolute error of the MLP was higher than the averaged absolute error of the GRNN. Furthermore, the correlation coefficients between the experimentally determined and the calculated output values, the corresponding prediction accuracy for the different granule properties as well as the overall prediction accuracy using GRNN were better than using MLP. In conclusion, the comparison of two different networks (MLP, a so-called feed-forward back-propagation network and GRNN, a so-called Bayesian Neural Network) showed the higher capacity of the latter for validation of such granulation processes.     

SELECTION OF MULTICOMPONENT BATCH DISTILLATION SEQUENCES

As in continuous distillation systems, the design of batch distillation begins with the selection of a sequence of separations. This paper considers the usual case where the column processes multicom-ponent mixtures with the recycle of intermediate cuts. It is proved that this cyclic operation does converge to a “steady state” balance. This permits to model batch distillation with recycle as a function of the steady state variables, i.e. without the need of successive simulations to obtain the steady state. Furthermore, we use simplified analytical models which permit a quick approximation to the optimal design of a given sequence, thus aiding the designer in the screening of alternative separation sequences, to preselect one, or a small set of good sequences.     

Binder addition methods and binder distribution in high shear and fluidised bed granulation

Fluidised beds and high shear mixers are both important in industrial granulation. The binder addition method (pouring, melt-in, spraying) affects the growth and properties of granules and is therefore of vital importance to the fundamental understanding of this detailed process. Non-uniformity of binder distribution is well known in high shear melt granulation, however, there is limited literature surrounding binder distribution in fluidised bed granulation. It was therefore the aim of the paper to compare the binder distribution using alternative addition methods in both high shear mixer and fluidised bed.In this work two binder addition methods, ‘wet’ and ‘dry’, in a fluidised bed and high hear mixer were used to successfully produce granules with a typical pharmaceutical size, 150-300 μm. The granules were analysed for final binder distribution in different size classes using Patent V blue dye and ultra-violet spectrometry.All binder addition methods supported previous work showing non-uniformity of binder distribution throughout the size classes. High shear mixer results show great similarity in binder content whichever binder addition method was chosen. This is likely to be due to the same mechanisms occurring due to the impeller forces in the process, mean while the fluidised bed results show little similarity. The binder distribution by mass is also investigated and shows that although most studies show a relative higher binder content in the larger size classes that actually the majority of binder can instead be found around the mean size of the batch.     

流化床造粒影响因素及层式成长模型的研究

将流态化技术应用于粉体物料的造粒过程,在我国还是一项亟待研究开发的课题。本文对流化床造粒进行了实验研究,着重探讨了流化气速,粘合剂种类、浓度、流率,原料初始粒度,喷嘴位置等因素对颗粒成长速率及机理的影响。在此基础上,建立了粒子层式成长模型,并与实验数据进行了比较。     

Optimal operation policies in batch reactors

Optimal operation policies in batch reactors are obtained using dynamic optimisation technique. Two different types of optimisation problems, namely, maximum conversion and minimum time problems are formulated and solved and optimal operation policies in terms of reactor temperature or coolant flow rate are obtained. A path constraint on the reactor temperature is imposed for safe reactor operation and an endpoint constraint on undesired waste production (by-product) is imposed to minimise environmental impact.Two different types of models are considered within the optimisation framework. The shortcut model allows determination of optimal reactor temperature profile to be used for detailed design of the reactor. The detailed model allows optimising operating conditions for an already designed batch reactors.     

Kinetics and mechanisms of growth in batch and continuous fluidized bed granulation

Aspects of the development of a model for prediction of product size distributions from fluidized bed granulation by agglomeration are described. Experimental work includes small scale continuous and batch granulation and analysis of the distribution of sprayed binder. A simple method of measuring one of the parameters in the numerical model is presented.     

Batch-to-batch optimal control of a batch polymerisation process based on stacked neural network models

A neural network based batch-to-batch optimal control strategy is proposed in this paper. In order to overcome the difficulty in developing mechanistic models for batch processes, stacked neural network models are developed from process operational data. Stacked neural networks have enhanced model generalisation capability and can also provide model prediction confidence bounds. However, the optimal control policy calculated based on a neural network model may not be optimal when applied to the true process due to model plant mismatches and the presence of unknown disturbances. Due to the repetitive nature of batch processes, it is possible to improve the operation of the next batch using the information of the current and previous batch runs. A batch-to-batch optimal control strategy based on the linearisation of stacked neural network model is proposed in this paper. Applications to a simulated batch polymerisation reactor demonstrate that the proposed method can improve process performance from batch to batch in the presence of model plant mismatches and unknown disturbances.     

OPTIMAL DESIGN AND OPERATION OF BATCH PROCESSES

The economical design of continuous chemical processes to produce commodity products has reached an advanced state of development. Modern computer tools are used routinely to simulate and optimize these processes. This is not the case, however, for the manufacture of speciality products which must be made in batch operations. The continuing shift towards the production of higher value-added specialty products by the CPI has stimulated efforts aimed at developing good computer assisted design strategies for batch processes.

This paper discusses the formulation of the problem for the optimal design and operation of batch processes. The batch problem differs from the continuous one in a number of important ways. First, batch plants do not operate at steady state. There are important trade-offs between the processing time and the severity (intensity) of processing in single units. Cycle time and performance trade-offs also exist among the various units in the process. Second, batch plants produce multiple products in many cases. There is often a competition for shared resources (labor, utilities, and equipment) among the various products. This paper presents a hierarchical solution approach for the design and optimization of a batch process. The approach is demonstrated by solving an example problem which illustrates the fundamental economic trade-offs.     

Predictive control of particle size distribution in particulate processes

In this work, we focus on the development and application of predictive-based strategies for control of particle size distribution (PSD) in continuous and batch particulate processes described by population balance models (PBMs). The control algorithms are designed on the basis of reduced-order models, utilize measurements of principle moments of the PSD, and are tailored to address different control objectives for the continuous and batch processes. For continuous particulate processes, we develop a hybrid predictive control strategy to stabilize a continuous crystallizer at an open-loop unstable steady-state. The hybrid predictive control strategy employs logic-based switching between model predictive control (MPC) and a fall-back bounded controller with a well-defined stability region. The strategy is shown to provide a safety net for the implementation of MPC algorithms with guaranteed stability closed-loop region. For batch particulate processes, the control objective is to achieve a final PSD with desired characteristics subject to both manipulated input and product quality constraints. An optimization-based predictive control strategy that incorporates these constraints explicitly in the controller design is formulated and applied to a seeded batch crystallizer. The strategy is shown to be able to reduce the total volume of the fines by 13.4% compared to a linear cooling strategy, and is shown to be robust with respect to modeling errors.     

The optimal control of polymerisation reactors

Two separate but related problems are treated in this paper: (i) the optimal control policy for continuous stirred tank polymerization reactors; (ii) the optimal control program for batch polymerization reactors. The first problem concerns determining the temperature and initiator control policy which brings the reactor to the desired steady state while minimizing some objective functional (e.g. start-up time, cost of control action, etc.). The second problem is concerned with finding the best temperature and initiator program so that the product from the batch reactor has the best possible molecular weight distribution. Both free radical polymerization and linear condensation polymerization examples are considered with molecular weight distribution moments being used to characterize the polymer. Kinetic parameters typical of styrene are used for the free radical case, and realistic parameters are chosen for the condensation examples. The techniques used can be immediately carried over to other polymerization systems, and hopefully generalizations about the character of the optimal policies for such new systems can be made by considering the policies found for the systems studied. The results of the study demonstrate some of the potential gains possible through supervisory computer control of polymerization reactors.     

Drop penetration time in heterogeneous powder beds

Wet granulation is a technique in which enlarged particles or ‘granules’ are produced from the coalescence of fine particles, with the intention of improving the powder properties. High shear granulators are often used to carry out the granulation process where the powder mass is agitated in a vessel by mechanical means while liquid is sprayed from above onto the powder bed surface. When the binder droplets impact the powder surface, the drop penetration time of the droplet into the powder is important for uniform binder dispersion and the prediction of the formation of granule nuclei from the nucleation map, which depends on the dimensionless spray flux. Previous studies on the drop penetration time were carried out on predominantly hydrophilic powder beds. Although this gives a good prediction of the nucleation behaviour in granulation, it does not reflect the condition where hydrophobic drugs are used in the formulation without surfactants. This paper aims to look at the effects of powder bed hydrophobicity on the drop penetration time.Single drop nucleation experiments using a syringe and a small powder bed were carried out on varying ratios of salicylic acid and lactose powders to study the kinetic of drop penetration. As expected, the drop penetration time increased as the proportion of hydrophobic component increased in the powder mixture. However, long drop penetration times were observed for low degrees of drug loading, showing that hydrophobicity strongly influences the drop penetration time. The wettability of the powder mixture also has a pronounced affect on the granule properties in which the hydrophobicity of the powder mixture is proportional to the granule strength and inversely proportional to the granule size. These findings have important implications in terms of the design of the granulation process where conditions of minimum spray flux or efficient mechanical forces are recommended to produce a more uniform granulation batch.     

High shear granulation of dolomite – II: Effect of amount of binder liquid on process kinetics

This paper, the second of a series, analyzes the effect of binder amount on the kinetics of wet granulation process. Granulation experiments were conducted in batch, lab-scale high shear mixer with formulation system that was initially studied in first part of a series. First, we identify the effect of binder content on the net granulation behaviour during early stage of the process. Single entity property (its size) was accounted only within this research. The results indicate that binder content strongly promotes growth of dolomite entities. Secondly, 1-D discretized population balance equation (PBE) and Equi-Partition of Kinetic Energy (EKE) theory were used to simulate the net granulation process. Tested “coalescence-only” models provide good prediction of real dolomite granule size distributions (GSDs) during early stage of the process for each binder content value. By using modelling procedure granule growth rates were quantified. Ultimate goal of relating the coalescence rates of dolomite entities with binder amount variable is provided. This will result in a better perspective of the meso-scale of the dolomite granulation process.     

熔铸余热锅炉汽包水位的控制

针对熔铸余热锅炉汽包水位的特点,开发了基于汽包水位、蒸汽流量（微分）的双冲量控制方案。生产运行表明,该控制方案成功实现了使汽包水位平稳、波动小、给水稳定等目标。