Ala Eldin Bouaswaig

Efficient Robust Economic Nonlinear Model Predictive Control of an Industrial Batch Reactor

Abstract In this paper we present a systematic and efficient approach to deal with uncertainty in Nonlinear Model Predictive Control (NMPC). The main idea of the approach is to represent the NMPC setting as a real-time decision problem under uncertainty that is formulated as a multi-stage stochastic problem with recourse, based on a description of the uncertainty by a scenario tree. This formulation explicitly takes into account the fact that new information will be available in the future and thus reduces the conservativeness compared to open-loop worst-case approaches. We show that the proposed multistage NMPC formulation can deal with significant plant-model mismatch as it is usually encountered in the process industry and still satisfies tight constraints for the different values of the uncertain parameters, in contrast to standard NMPC. The use of an economic cost function leads to a superior performance compared to the standard tracking formulation. The potential of the approach is demonstrated for an industrial case study provided by BASF SE in the context of the European Project EMBOCON. The numerical solution of the resulting large optimization problems is implemented using the optimization framework CasADi.

Time Optimal Control of Particle Size Distribution in Emulsion Polymerization

Abstract Emulsion polymers are used in a wide range of applications such as adhesives, inks, paints, coatings, drug delivery systems, gloves, floor polish, films and cosmetics. Because the end-use properties of the polymers strongly depend on the particle size distribution (PSD), modeling and control of the PSD is of high interest and is an active field of research. The aim of this work is to investigate the feasibility and the potential of applying nonlinear model predictive control (NMPC) to the control of the PSD in emulsion polymerization processes. Specifically, time optimal control of the PSD of a semi batch homo-polymerization in a pilot-scale reactor is considered.

Simultaneous Nonlinear Reconciliation and Update of Parameters for Online Use of First-Principles Models: An Industrial Case-Study on Compressors

Abstract Online uses of first-principles models include nonlinear model predictive control, softsensors, real-time optimization, and real-time process monitoring, among others. The industrial implementation of these applications needs accurate adaptive models and reconciled data. The simultaneous reconciliation and update of parameters of a first- principles model can be achieved using an optimization framework that exploits physical and analytical redundancy of information. This paper demonstrates this concept by means of an industrial case-study. The case-study is a multi-stage centrifugal compressor for which a first-principles model was recently developed. The update of the model parameters is necessary to capture slowly progressing mechanical degradation (e.g. due to fouling and erosion). The reconciliation of the data is necessary for reducing downtime of the online model-based applications caused by gross errors. Two industrial cases including sensor failures were analysed. Applying the proposed framework, it was possible to reconcile the measurements for both cases.

Online Performance Monitoring of Industrial Compressors Using Meanline Modelling

This paper proposes a framework for detecting mechanical degradation online and assessing its effect on the performance of industrial compressors. It consists of a model of the machine in undegraded condition and of a degradation adaptive model. The proposed methodology for online degradation detection differentiates itself from those found in the literature as the undegraded model is not linearized and ambient/inlet conditions are explicitly taken into account. The degradation is modelled through adaptive parameters which are estimated and updated online through the solution of a constrained minimization problem within a moving window. It uses available process measurements of flow, pressures, temperatures and composition. The update of the parameters guarantees the model accuracy and it permits the estimation of the effects of mechanical degradation away from the compressor running line.The performance monitoring framework has been successfully applied on an industrial air centrifugal compressor. It was found that after 3250 hours of operation from the previous maintenance the efficiency and the pressure ratio had dropped approximately 5.5% and 2.5% of their respective undegraded values. Furthermore, it was found that the performance deviations from the baseline depend from the position of the operative point in the performance map. In fact, the pressure ratio drop was lower (2%) and efficiency drop was higher (6%) for lower inlet guide vanes opening whereas pressure ratio drop was higher (3%) and efficiency drop was lower (1.6%) for higher inlet guide vane opening.© 2014 ASME

An Inverse Problem Approach to Extract the Growth Kernel in Particulate Processes

Abstract Mathematical models of particulate processes usually include a population balance equation to describe the dynamics of the size distribution. The structure of the population balance equation is the same in all models of particulate processes and the specific physical and chemical interaction of the particles is described by individual kernels. Usually first principles modeling is used to develop the kernels, but in cases in which this is intractable, inverse problem techniques have been proposed in the literature to extract the kernels from experimental data. In this work we introduce an approach that can be used for extracting the growth kernel. This approach is applicable even when the assumption of separable growth rate that has been made in previous approaches does not hold and when coagulation with known dynamics and growth are taking place simultaneously.

Modeling and simulation of the particle size distribution for emulsion polymerization in a tubular reactor

Abstract In this paper, a model for the multiphase process of emulsion polymerization in a tubular reactor is presented. Besides well investigated properties like e.g. conversion., the model predicts the particle size distribution of the polymer particles using a population balance equation. The model consists of a two-dimensional partial differential equation for the particle size distribution and dynamic balance equations for the components that are present in the reactor. It also includes a set of algebraic equations that e.g. describe the monomer distribution among the coexisting phases in the reactor. Numerically, the use of flux limiters is considered for the growth term in the PBE to obtain at least second order accuracy and oscillation-free solutions. Experimental results reported in literature are used to validate the model.

A stochastic approach to improve the particle size distribution prediction of a classical emulsion polymerization model

Abstract Augmenting a deterministic growth model by a stochastic term with a constant dispersion coefficient was suggested in [ 1 ] to overcome the inadequacy of the classical population balance models of emulsion polymerization in predicting the broadening of the particle size distribution which was observed in the experiments. The probability distribution of the resulting stochastic process (Langevin equation) evolves over time based on the Fokker-Planck equation. However, by using a constant dispersion coefficient the distributions tend toward pseudo-Gaussian shaped ones when they evolve over time. This might not be adequate for applications in which not only the mean size and standard deviation of the PSDs but also the shape of PSDs must be captured. To overcome this limitation, in this work it is suggested to consider the dispersion coefficient of the Fokker-Planck equation to be a monotonically increasing function of the particle size. Using this approach, the rate of monomer consumption has to be adapted and the relative magnitude of the deterministic and the stochastic terms has to be monitored.

A new numerical solution scheme for tracking sharp moving fronts

Abstract The numerical solution of a hyperbolic or a convection dominated parabolic partial differential equation is challenging due to the large local gradients that are present in the solution. In this paper, a novel approach that is based on combining the high order weighted essentially non-oscillatory (WENO) scheme with a static moving grid method is presented. The proposed algorithm is tested on two case studies and enhancements in the performance are observed when compared with the conventional WENO scheme on a uniform grid making it a promising alternative when dealing with problems of this nature.