Jeremy G. VanAntwerp

A tutorial on linear and bilinear matrix inequalities

Abstract This is a tutorial on the mathematical theory and process control applications of linear matrix inequalities (LMIs) and bilinear matrix inequalities (BMIs). Many convex inequalities common in process control applications are shown to be LMIs. Proofs are included to familiarize the reader with the mathematics of LMIs and BMIs. LMIs and BMIs are applied to several important process control applications including control structure selection, robust controller analysis and design, and optimal design of experiments. Software for solving LMI and BMI problems is reviewed.

Fast model predictive control of sheet and film processes

Sheet and film processes are prevalent in the chemical and pulp and paper industries, and include paper coating, polymer film extrusion, and papermaking. A model predictive control algorithm is developed which is based on an off-line singular value decomposition of the plant. The input constraints are approximated by an ellipsoid whose size is optimized online to reduce conservatism. The controller has a structure proven to be robust to model inaccuracies and is computationally efficient enough for real-time implementation on large scale sheet and film processes (e.g., manipulated variable settings computed for 200 actuators in less than ten CPU seconds). The algorithm is applied to a paper machine model constructed from industrial data.

Cross-directional control of sheet and film processes

Sheet and film processes include polymer film extrusion, coating processes of many types, paper manufacturing, sheet metal rolling, and plate glass manufacture. Identification, estimation, monitoring, and control of sheet and film processes are of substantial industrial interest since effective control means reduced usage of raw materials, increased production rates, improved product quality, elimination of product rejects, and reduced energy consumption. This paper reviews recent developments in sheet and film process control with particular attention to the effectiveness of existing techniques at addressing the critical aspects of sheet and film processes.

Robust cross-directional control of large scale sheet and film processes

Abstract Sheet and film processes, which include papermaking, polymer film extrusion, and adhesive coating, are of substantial industrial importance. The processes are poorly conditioned and truly large scale, with up to hundreds of manipulated variables and thousands of sensor locations. The uncertainties in sheet and film process models require that they be explicitly taken into account during the control design procedure. Numerically efficient algorithms are developed that provide robust optimal controllers for a wide variety of uncertainty descriptions. The robust optimality of the controllers can be relaxed to provide low order controllers suitable for real time implementation. Robust controllers are designed for a simulated paper machine, based on a realistic description of the interactions across the machine, and the level of model inaccuracies.

Globally optimal robust process control

Abstract A computational approach is developed for designing a globally optimal controller which is robust to time-varying nonlinear perturbations in the plant. This controller design problem is formulated as an optimization with bilinear matrix inequality (BMI) constraints, and is solved to optimality by a branch and bound algorithm. The algorithm is applied to a reactive ion etcher, and provides superior performance while providing robustness to nonlinear plant/model mismatch. The algorithm is also applied to a well known benchmark problem.

Robust cross-directional control of large scale paper machines

Paper machines pose a challenging multivariable control problem. The processes are poorly conditioned and truly large scale, in that the number of inputs and outputs can range from 100-1000. Their large scale nature makes it important to account for inaccuracies in the process models. A control algorithm is developed that addresses model inaccuracies in a numerically efficient and effective manner.

Globally optimal robust control of large scale sheet and film processes

Improved multivariable control of sheet and film processes can mean significant reductions in material and energy consumption, greater production rates for existing equipment, improved product quality, elimination of product rejects, and reduced energy consumption. One of the main weaknesses of modern sheet and film process control approaches is their inability to explicitly account for model inaccuracies. Here we develop a novel computational approach for designing controllers for large scale sheet and film processes that addresses model inaccuracy in a globally optimal manner. This approach is computationally feasible for industrial sheet and film processes (up to 500 inputs and outputs).

Elastic net with Monte Carlo sampling for data-based modeling in biopharmaceutical manufacturing facilities

Abstract Biopharmaceutical manufacturing involves multiple process steps that can be challenging to model. Oftentimes, operating conditions are studied in bench-scale experiments and then fixed to specific values during full-scale operations. This procedure limits the opportunity to tune process variables to correct for the effects of disturbances. Generating process models has the potential to increase the flexibility and controllability of the biomanufacturing processes. This article proposes a statistical modeling methodology to predict the outputs of biopharmaceutical operations. This methodology addresses two important challenging characteristics typical of data collected in the biopharmaceutical industry: limited data availability and data heterogeneity. Motivated by the final aim of control, regularization methods, specifically the elastic net, are combined with sampling techniques similar to the bootstrap to develop mathematical models that use only a small number of input variables. This methodology is evaluated on an antibody manufacturing dataset.

Model predictive control of large scale processes

Abstract Model predictive control is a receding horizon control policy in which a linear or quadratic program with linear constraints is solved on-line at each sampling instance. An algorithm is developed that allows quick computation of sub-optimal control moves. The linear constraint set is approximated by an ellipsoid and a change of variables is performed so that a solution may be computed efficiently via bisection. The ellipsoid is rescaled on-line to reduce conservatism. This allows the implementation of model predictive control algorithms to large scale processes using simple control hardware.

Identification and Control of Polymerization Reactors

This chapter considers the identification and control of free-radical polymerization reactors. A discussion of the modeling and simulation of such reactors is followed by an optimal control study that demonstrates the potential of optimal control of the molecular-weight distribution based on mechanistic models. Achieving this potential in a batch reactor requires an accurate estimation of the free-radical polymerization kinetic parameters. The remainder of the chapter describes an experimental investigation of the free-radical polymerization of methyl methacrylate, in which modern sensing techniques are used to estimate kinetic parameters. The monomer conversion is measured using inline ATR-FTIR spectroscopy and robust chemometrics, and the molecular-weight distribution is measured by gas-permeation chromatography. The resulting parameter estimates and confidence intervals are used to discuss the importance of various reactions in the free-radical polymerization reaction mechanism. Discrepancies between theory and experiments are discussed.