Minimizing the Euclidean Condition Number

This paper considers the problem of determining the row and/or column scaling of a matrix A that minimizes the condition number of the scaled matrix. This problem has been studied by many authors. For the cases of the ∞-norm and the 1-norm, the scaling problem was completely solved in the 1960s. It is the Euclidean norm case that has widespread application in robust control analyses. For example, it is used for integral controllability tests based on steady-state information, for the selection of sensors and actuators based on dynamic information, and for studying the sensitivity of stability to uncertainty in control systems. Minimizing the scaled Euclidean condition number has been an open question—researchers proposed approaches to solving the problem numerically, but none of the proposed numerical approaches guaranteed convergence to the true minimum. This paper provides a convex optimization procedure to determine the scalings that minimize the Euclidean condition number. This optimization can be solved in polynomial-time with off-the-shelf software

Stability and Performance Analysis of Systems Under Constraints

All real world control systems must deal with actuator and state constraints. Standard conic sector bounded nonlinearity stability theory provides methods for analyzing the stability and performance of systems under constraints, but it is well-known that these conditions can be very conservative. A method is developed to reduce conservatism in the analysis of constraints by representing them as nonlinear real parametric uncertainty

Control of Molecular Purity, Crystal Structure, and Particle Size Distribution in Pharmaceutical Crystallization

An overview is provided on advances in the design and operation of pharmaceutical crystallizations to control polymorphic identity, shape, and size distribution. A systematic methodology is described for the selective crystallization of metastable and stable polymorphic and solvatamorphic forms based on the feedback control of solution concentration measured in process using Attenuated total reflection-Fourier transform infrared (ATR-FTIR) spectroscopy calibrated using chemometrics methods. The methodology enables the design and operation of seeded batch crystallizers to manufacture large crystals of uniform size by suppressing secondary nucleation. A modification of the methodology is able to achieve a target size distribution in semi-batch crystallization by employing continual seeds manufactured by a spatially localized zone of highly intense mixing such as occurs in a dual-impinging jet crystallizer. The methodology has been evaluated in theoretical, simulation, and experimental studies for a large variety of pharmaceutical compounds. The maximum supersaturation to allow during the crystallizer operations is determined by employing in-situ laser backscattering (focused beam reflectance measurement, FBRM) during a semi-automated initial experiment design, and FBRM is also employed to confirm that secondary nucleation is suppressed during pharmaceutical production runs. A methodology is proposed for the manipulation of crystal shape, by employing in-situ fines dissolution. The presentation ends with a discussion of directions towards control of multiple properties of the crystal product

Robust Loopshaping for Process Control

Strong trends in chemical engineering and plant operation have made the control of processes increasingly difficult and have driven the process industry's demand for improved control techniques. Improved control leads to savings in resources, smaller downtimes, improved safety, and reduced pollution. Though the need for improved process control is clear, advanced control methodologies have had only limited acceptance and application in industrial practice. The reason for this gap between control theory and practice is that existing control methodologies do not adequately address all of the following control system requirements and problems associated with control design: * The controller must be insensitive to plant/model mismatch, and perform well under unmeasured or poorly modeled disturbances. * The controlled system must perform well under state or actuator constraints. * The controlled system must be safe, reliable, and easy to maintain. * Controllers are commonly required to be decentralized. * Actuators and sensors must be selected before the controller can be designed. * Inputs and outputs must be paired before the design of a decentralized controller. A framework is presented to address these control requirements/problems in a general, unified manner. The approach will be demonstrated on adhesive coating processes and distillation columns

Avery Final Report: Identification and Cross-Directional Control of Coating Processes

Coating refers to the covering of a solid with a uniform layer of liquid. Of special industrial interest is the cross-directional control of coating processes, where the cross-direction refers to the direction perpendicular to the substrate movement. The objective of the controller is to maintain a uniform coating under unmeasured process disturbances. Assumptions that are relevant to coating processes found in industry are used to develop a model for control design. We show how to identify the model from input-output data. This model is used to derive a model predictive controller to maintain flat profiles of coating across the substrate by varying the liquid flows along the cross direction. The model predictive controller computes the control action which minimizes the predicted deviation in cross-directional uniformity. The predictor combines the estimate obtained from the model with the measurement of the cross-directional uniformity to obtain a prediction for the next time step. A filter is used to obtain robustness to model error and insensitivity to measurement noise. The tuning of the noise filter and different methods for handling actuator constraints are studied in detail. The three different constraint-handling methods studied are: the weighting of actuator movements in the objective function, explicitly adding constraints to the control algorithm, i.e. constrained model predictive control, and scaling infeasible control actions calculated from an unconstrained control law to be feasible. Actuator constraints, measurement noise, model uncertainty, and the plant condition number are investigated to determine which of these limit the achievable closed loop performance. From knowledge of how these limitations affect the performance we find how the plant could be modified to improve the process uniformity. Also, because identification of model parameters is time-consuming and costly, we study how accurate the identification must be to achieve a given level of performance. The theory developed throughout the paper is rigorously verified though simulations and experiments on a pilot plant. The effect of interactions on the closed loop performance is shown to be negligible for this pilot plant. The measurement noise and the actuator constraints are shown to have the largest effect on closed loop performance

Latent Variable Method Demonstrator -- Software for Understanding Multivariate Data Analytics Algorithms

The ever-increasing quantity of multivariate process data is driving a need for skilled engineers to analyze, interpret, and build models from such data. Multivariate data analytics relies heavily on linear algebra, optimization, and statistics and can be challenging for students to understand given that most curricula do not have strong coverage in the latter three topics. This article describes interactive software - the Latent Variable Demonstrator (LAVADE) - for teaching, learning, and understanding latent variable methods. In this software, users can interactively compare latent variable methods such as Partial Least Squares (PLS), and Principal Component Regression (PCR) with other regression methods such as Least Absolute Shrinkage and Selection Operator (lasso), Ridge Regression (RR), and Elastic Net (EN). LAVADE helps to build intuition on choosing appropriate methods, hyperparameter tuning, and model coefficient interpretation, fostering a conceptual understanding of the algorithms' differences. The software contains a data generation method and three chemical process datasets, allowing for comparing results of datasets with different levels of complexity. LAVADE is released as open-source software so that others can apply and advance the tool for use in teaching or research.Comment: 18 pages, 14 figures, code available: https://github.com/JoachimSchaeffer/LAVADE, preprint submitted to Computers & Chemical Engineerin

Robust Control Structure Selection

Screening tools for control structure selection in the presence of model/plant mismatch are developed in the context of the Structured Singular Value (μ) theory. The developed screening tools are designed to aid engineers in the elimination of undesirable control structure candidates for which a robustly performing controller does not exist. Through application on a multicomponent distillation column, it is demonstrated that the developed screening tools can be effective in choosing an appropriate control structure while previously existing methods such as the Condition Number Criterion can lead to erroneous results

Digital transformation in bio manufacturing

This presentation describes ways to leverage and implement digitalization technologies in biopharmaceutical manufacturing. An accelerated process development workflow is described that employs micro-scale technologies, modular unit operations with integrated process control and monitoring systems, systems integration, and full plant automation. The presentation describes how to best develop and transfer knowledge between steps in the workflow via first-principles models, data analytics, and machine learning. Case studies are described that illustrate the application of each of the above methods, including where process equipment was designed digitally by using first-principles models first, then the process equipment was constructed and implemented experimentally, with the experimental results confirming model predictions

Modeling and Analysis of Drug-Eluting Stents With Biodegradable PLGA Coating: Consequences on Intravascular Drug Delivery

Increasing interests have been raised toward the potential applications of biodegradable poly(lactic-co-glycolic acid) (PLGA) coatings for drug-eluting stents in order to improve the drug delivery and reduce adverse outcomes in stented arteries in patients. This article presents a mathematical model to describe the integrated processes of drug release in a stent with PLGA coating and subsequent drug delivery, distribution, and drug pharmacokinetics in the arterial wall. The integrated model takes into account the PLGA degradation and erosion, anisotropic drug diffusion in the arterial wall, and reversible drug binding. The model simulations first compare the drug delivery from a biodegradable PLGA coating with that from a biodurable coating, including the drug release profiles in the coating, average arterial drug levels, and arterial drug distribution. Using the model for the PLGA stent coating, the simulations further investigate drug internalization, interstitial fluid flow in the arterial wall, and stent embedment for their impact on drug delivery. Simulation results show that these three factors, while imposing little change in the drug release profiles, can greatly change the average drug concentrations in the arterial wall. In particular, each of the factors leads to significant and yet distinguished alterations in the arterial drug distribution that can potentially influence the treatment outcomes. The detailed integrated model provides insights into the design and evaluation of biodegradable PLGA-coated drug-eluting stents for improved intravascular drug delivery.National Institutes of Health (U.S.) (NIBIB 5RO1EB005181