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1. Evaluation of a Combined MHE-NMPC Approach to Handle Plant-Model Mismatch in a Rotary Tablet Press

   https://doi.org/10.3390/pr9091612  

   Huang, Yan-Shu; Sheriff, M Ziyan; Bachawala, Sunidhi; Gonzalez, Marcial; Nagy, Zoltan K; Reklaitis, Gintaras V (September 2021, Processes)

   The transition from batch to continuous processes in the pharmaceutical industry has been driven by the potential improvement in process controllability, product quality homogeneity, and reduction of material inventory. A quality-by-control (QbC) approach has been implemented in a variety of pharmaceutical product manufacturing modalities to increase product quality through a three-level hierarchical control structure. In the implementation of the QbC approach it is common practice to simplify control algorithms by utilizing linearized models with constant model parameters. Nonlinear model predictive control (NMPC) can effectively deliver control functionality for highly sensitive variations and nonlinear multiple-input-multiple-output (MIMO) systems, which is essential for the highly regulated pharmaceutical manufacturing industry. This work focuses on developing and implementing NMPC in continuous manufacturing of solid dosage forms. To mitigate control degradation caused by plant-model mismatch, careful monitoring and continuous improvement strategies are studied. When moving horizon estimation (MHE) is integrated with NMPC, historical data in the past time window together with real-time data from the sensor network enable state estimation and accurate tracking of the highly sensitive model parameters. The adaptive model used in the NMPC strategy can compensate for process uncertainties, further reducing plant-model mismatch effects. The nonlinear mechanistic model used in both MHE and NMPC can predict the essential but complex powder properties and provide physical interpretation of abnormal events. The adaptive NMPC implementation and its real-time control performance analysis and practical applicability are demonstrated through a series of illustrative examples that highlight the effectiveness of the proposed approach for different scenarios of plant-model mismatch, while also incorporating glidant effects. 

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2. Process analysis of end-to-end continuous pharmaceutical manufacturing using PharmaPy

   https://doi.org/10.69997/sct.154363  

   Shahab, Mohammad; Matsunami, Kensaku; Nagy, Zoltan; Reklaitis, Gintaras (July 2025, PSE Press)

   As pharmaceutical manufacturing is transitioning from traditional batch to continuous manufacturing (CM), there is a lack of tools for CM design and development, which can integrate drug substance and drug product unit operations for overall evaluation. Recently, a Python-based PharmaPy framework was proposed to advance the design, simulation, and analysis of continuous pharmaceutical processes. However, the initial library of models only addressed upstream drug substance processing. In this work, new capabilities, including drug product unit operations such as feeder, blender, and tablet press, have been added to the PharmaPy framework, enabling end-to-end study and optimizing the effects of material properties and process conditions on solid oral dosage products. The platform supports computational efficiency and model accuracy by allowing the development of different mechanistic and semi-mechanistic models. Sensitivity analysis is performed on the integrated end-to-end simulator to identify critical input variables influencing product quality and control strategies. The analysis lowers the complexity of the model by ranking significant input variables. Finally, feasibility studies are conducted on extracted influential input variables to characterize the process design space and achieve desirable output. The enhanced PharmaPy package can now support decision-making from early research and development stages through manufacturing. 

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3. Making context explicit in equation construction and interpretation: Symbolic blending

   https://doi.org/10.1103/PhysRevPhysEducRes.19.020149  

   Schermerhorn, Benjamin P; Thompson, John R (October 2023, Physical Review Physics Education Research)

   Much of physics involves the construction and interpretation of equations. Research on physics students’ understanding and application of mathematics has employed Sherin’s symbolic forms or Fauconnier and Turner’s conceptual blending as analytical frameworks. However, previous symbolic forms analyses have commonly treated students’ in-context understanding as their conceptual schema, which was designed to represent the acontextual, mathematical justification of the symbol template (structure of the expression). Furthermore, most conceptual blending analyses in this area have not included a generic space to specify the underlying structure of a math-physics blend. We describe a conceptual blending model for equation construction and interpretation, which we call symbolic blending, that incorporates the components of symbolic forms with the conceptual schema as the generic space that structures the blend of a symbol template space with a contextual input space. This combination complements symbolic forms analysis with contextual meaning and provides an underlying structure for the analysis of student understanding of equations as a conceptual blend. We present this model in the context of student construction of non-Cartesian differential length vectors. We illustrate the affordances of such a model within this context and expand this approach to other contexts within our research. The model further allows us to reinterpret and extend literature that has used either symbolic forms or conceptual blending. 

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4. Technoeconomic and Sustainability Analysis of Batch and Continuous Crystallization for Pharmaceutical Manufacturing

   https://doi.org/10.69997/sct.107722  

   Rhim, Jungsoo; Nagy, Zoltan K (July 2024, Syst. Control Trans.)

   Continuous manufacturing in pharmaceutical industries has shown great promise to achieve process intensification. To better understand and justify such changes to the current status quo, a technoeconomic analysis of a continuous production must be conducted to serve as a predictive decision-making tool for manufacturers. This paper uses PharmaPy, a custom-made Python-based library developed for pharmaceutical flowsheet analysis, to simulate an annual production cycle for a given active pharmaceutical ingredient (API) of varying production volumes for a batch crystallization system and a continuous mixed suspension, mixed product removal (MSMPR) crystallizer. After each system is optimized, the generalized cost drivers, categorized as capital expenses (CAPEX) or operational expenses (OPEX), are compared. Then, a technoeconomic and sustainability cost analysis is done with the process mass intensity (PMI) as a green metric. The results indicate that while the batch system does have an overall lower cost and better PMI metric at smaller manufacturing scales in comparison with the continuous system, the latter system showed more potential for scaling-up for larger production volumes. 

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5. A phase field model for dynamic simulations of reactive blending of polymers

   https://doi.org/10.1039/d1sm01686e  

   Tikekar, Mukul D.; Delaney, Kris T.; Villet, Michael C.; Tree, Douglas R.; Fredrickson, Glenn H. (January 2022, Soft Matter)

   A facile way to generate compatibilized blends of immiscible polymers is through reactive blending of end-functionalized homopolymers. The reaction may be reversible or irreversible depending on the end-groups and is affected by the immiscibility and transport of the reactant homopolymers and the compatibilizing copolymer product. Here we describe a phase-field framework to model the combined dynamics of reaction kinetics, diffusion, and multi-component thermodynamics on the evolution of the microstructure and reaction rate in reactive blending. A density functional with no fitting parameters, which is obtained by adapting a framework of Uneyama and Doi and qualitatively agrees with self-consistent field theory, is used in a diffusive dynamics model. For a symmetric mixture of equal-length reactive polymers mixed in equal proportions, we find that depending on the Flory χ parameter, the microstructure of an irreversibly reacting blend progresses through a rich evolution of morphologies, including from two-phase coexistence to a homogeneous mixture, or a two-phase to three-phase coexistence transitioning to a homogeneous blend or a lamellar copolymer. The emergence of a three-phase region at high χ leads to a previously unreported reaction rate scaling. For a reversible reaction, we find that the equilibrium composition is a function of both the equilibrium constant for the reaction and the χ parameter. We demonstrate that phase-field models are an effective way to understand the complex interplay of thermodynamic and kinetic effects in a reacting polymer blend. 

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