Model based robust control approach for batch crystallization product design

Data-driven set-point learning control with ESO and RBFNN for nonlinear batch processes subject to nonrepetitive uncertainties

This paper proposes an extended state observer (ESO) based data-driven set-point learning control (DDSPLC) scheme for a class of nonlinear batch processes with a priori P-type feedback control structure subject to nonrepetitive uncertainties, by only using the process input and output data available in practice. Firstly, the unknown process dynamics is equivalently transformed into an iterative dynamic linearization data model (IDLDM) with a residual term. A radial basis function neural network is adopted to estimate the pseudo partial derivative information related to IDLDM, and meanwhile, a data-driven iterative ESO is constructed to estimate the unknown residual term along the batch direction. Then, an adaptive set-point learning control law is designed to merely regulate the set-point command of the closed-loop control structure for realizing batch optimization. Robust convergence of the output tracking error along the batch direction is rigorously analyzed by using the contraction mapping approach and mathematical induction. Finally, two illustrative examples from the literature are used to validate the effectiveness and advantage of the proposed design.

Model-Based Evaluation of a Data-Driven Control Strategy: Application to Ibuprofen Crystallization

This work presents a methodology that relies on the application of the radial basis functions network (RBF)-based feedback control algorithms to a pharmaceutical crystallization process. Within the scope of the model-based evaluation of the proposed strategy, firstly strategies for the data treatment, data structure and the training methods reflecting the possible scenarios in the industry (Moving Window, Growing Window and Golden Batch strategies) were introduced. This was followed by the incorporation of such RBF strategies within a soft sensor application and a nonlinear predictive data-driven control application. The performance of the RBF control strategies was tested for the undisturbed cases as well as in the presence of disturbances in the process. The promising results from both RBF soft sensor control and the RBF predictive control demonstrated great potential of these techniques for the control of the crystallization process. In particular, both Moving Window and Golden Batch strategies performed the best results for an RBF soft sensor, and the Growing Window outperformed the remaining methodologies for predictive control.

Application of PAT-Based Feedback Control Approaches in Pharmaceutical Crystallization

Crystallization is one of the important unit operations for the separation and purification of solid products in the chemical, pharmaceutical, and pesticide industries, especially for realizing high-end, high-value solid products. The precise control of the solution crystallization process determines the polymorph, crystal shape, size, and size distribution of the crystal product, which is of great significance to improve product quality and production efficiency. In order to develop the crystallization process in a scientific method that is based on process parameters and data, process analysis technology (PAT) has become an important enabling platform. In this paper, we review the development of PAT in the field of crystallization in recent years. Based on the current research status of drug crystallization process control, the monitoring methods and control strategies of feedback control in the crystallization process were systematically summarized. The focus is on the application of model-free feedback control strategies based on the solution and solid information collected by various online monitoring equipment in product engineering, including improving particle size distribution, achieving polymorphic control, and improving purity. In this paper, the challenges of feedback control strategy in the crystallization process are also discussed, and the development trend of the feedback control strategy has been prospected.

Continuous Generation of Millimeter-Sized Glycine Crystals in Non-Seeded Millifluidic Slug Flow

Millimeter-sized α-glycine crystals were generated from continuous non-seeded cooling crystallization in slug flow. The crystallization process is composed of three steps in sequence: slug formation, crash-cooling nucleation, and growth. Stable uniform slugs of three different aspect ratios (slug length/tubing inner diameter) were formed, by adjusting the flow rates of both the solution and air streams. Besides supersaturation, the slug aspect ratio can also affect primary nucleation outcome. Stable slug flow can accommodate a relative supersaturation (C/C*) of up to 1.5 without secondary nucleation. Large glycine crystals can grow to millimeter size within 10 min, inside millimeter-sized slugs without reducing the slug quality.

Robust Process Design in Pharmaceutical Manufacturing under Batch-to-Batch Variation

Model-based concepts have been proven to be beneficial in pharmaceutical manufacturing, thus contributing to low costs and high quality standards. However, model parameters are derived from imperfect, noisy measurement data, which result in uncertain parameter estimates and sub-optimal process design concepts. In the last two decades, various methods have been proposed for dealing with parameter uncertainties in model-based process design. Most concepts for robustification, however, ignore the batch-to-batch variations that are common in pharmaceutical manufacturing processes. In this work, a probability-box robust process design concept is proposed. Batch-to-batch variations were considered to be imprecise parameter uncertainties, and modeled as probability-boxes accordingly. The point estimate method was combined with the back-off approach for efficient uncertainty propagation and robust process design. The novel robustification concept was applied to a freeze-drying process. Optimal shelf temperature and chamber pressure profiles are presented for the robust process design under batch-to-batch variation.

A perspective on Quality-by-Control (QbC) in pharmaceutical continuous manufacturing

The Quality-by-Design (QbD) guidance issued by the US Food and Drug Administration (FDA) has catalyzed the modernization of pharmaceutical manufacturing practices including the adoption of continuous manufacturing. Active process control was highlighted recently as a means to improve the QbD implementation. This advance has since been evolving into the concept of Quality-by-Control (QbC). In this study, the concept of QbC is discussed, including a definition of QbC, a review of the recent developments towards the QbC, and a perspective on the challenges of QbC implementation in continuous manufacturing. The QbC concept is demonstrated using a rotary tablet press, integrated into a pilot scale continuous direct compaction process. The results conclusively showed that active process control, based on product and process knowledge and advanced model-based techniques, including data reconciliation, model predictive control (MPC), and risk analysis, is indispensable to comprehensive QbC implementation, and ensures robustness and efficiency.

Constructing regions of attainable sizes and achieving target size distribution in a batch cooling sonocrystallization process

The application of ultrasound to a crystallization process has several interesting benefits. The temperature of the crystallizer increases during ultrasonication and this makes it difficult for the temperature controller of the crystallizer to track a set temperature trajectory precisely. It is thus necessary to model this temperature rise and the temperature-trajectory tracking ability of the crystallizer controller to perform model-based dynamic optimization for a given cooling sonocrystallization set-up. In our previous study, we reported a mathematical model based on population balance framework for a batch cooling sonocrystallization of l-asparagine monohydrate (LAM). Here we extend the previous model by including energy balance equations and a Generic Model Control algorithm to simulate the temperature controller of the crystallizer that tracks a cooling profile during crystallization. The improved model yields very good closed-loop prediction and is conveniently used for studies related to particle engineering by optimization. First, the model is used to determine the regions of attainable particle sizes for LAM batch cooling sonocrystallization process by solving appropriate dynamic optimization problems. Then the model is used to determine optimal operating conditions for achieving a target crystal size distribution. The experimental evidence clearly demonstrates the efficiency of the particle engineering approach by optimization.

Improved design of constrained model predictive tracking control for batch processes against unknown uncertainties

In this paper, an improved constrained tracking control design is proposed for batch processes under uncertainties. A new process model that facilitates process state and tracking error augmentation with further additional tuning is first proposed. Then a subsequent controller design is formulated using robust stable constrained MPC optimization. Unlike conventional robust model predictive control (MPC), the proposed method enables the controller design to bear more degrees of tuning so that improved tracking control can be acquired, which is very important since uncertainties exist inevitably in practice and cause model/plant mismatches. An injection molding process is introduced to illustrate the effectiveness of the proposed MPC approach in comparison with conventional robust MPC.

Particle engineering by optimization for the unseeded batch cooling crystallization of l-asparagine monohydrate

A model-based optimization approach is proposed to obtain temperature profiles to achieve the target CSD in a batch cooling crystallization process.

Introducing uncertainty analysis of nucleation and crystal growth models in Process Analytical Technology (PAT) system design of crystallization processes

This paper presents the application of uncertainty and sensitivity analysis as part of a systematic model-based process monitoring and control (PAT) system design framework for crystallization processes. For the uncertainty analysis, the Monte Carlo procedure is used to propagate input uncertainty, while for sensitivity analysis, global methods including the standardized regression coefficients (SRC) and Morris screening are used to identify the most significant parameters. The potassium dihydrogen phosphate (KDP) crystallization process is used as a case study, both in open-loop and closed-loop operation. In the uncertainty analysis, the impact on the predicted output of uncertain parameters related to the nucleation and the crystal growth model has been investigated for both a one- and two-dimensional crystal size distribution (CSD). The open-loop results show that the input uncertainties lead to significant uncertainties on the CSD, with appearance of a secondary peak due to secondary nucleation for both cases. The sensitivity analysis indicated that the most important parameters affecting the CSDs are nucleation order and growth order constants. In the proposed PAT system design (closed-loop), the target CSD variability was successfully reduced compared to the open-loop case, also when considering uncertainty in nucleation and crystal growth model parameters. The latter forms a strong indication of the robustness of the proposed PAT system design in achieving the target CSD and encourages its transfer to full-scale implementation.

Advances and New Directions in Crystallization Control

The academic literature on and industrial practice of control of solution crystallization processes have seen major advances in the past 15 years that have been enabled by progress in in-situ real-time sensor technologies and driven primarily by needs in the pharmaceutical industry for improved and more consistent quality of drug crystals. These advances include the accurate measurement of solution concentrations and crystal characteristics as well as the first-principles modeling and robust model-based and model-free feedback control of crystal size and polymorphic identity. Research opportunities are described in model-free controller design, new crystallizer designs with enhanced control of crystal size distribution, strategies for the robust control of crystal shape, and interconnected crystallization systems for multicomponent crystallization.