Relaxation Methods for Mixed-Integer Optimal Control of Partial Differential Equations

We consider integer-restricted optimal control of systems governed by abstract semilinear evolution equations. This includes the problem of optimal control design for certain distributed parameter systems endowed with multiple actuators, where the task is to minimize costs associated with the dynamics of the system by choosing, for each instant in time, one of the actuators together with ordinary controls. We consider relaxation techniques that are already used successfully for mixed-integer optimal control of ordinary differential equations. Our analysis yields sufficient conditions such that the optimal value and the optimal state of the relaxed problem can be approximated with arbitrary precision by a control satisfying the integer restrictions. The results are obtained by semigroup theory methods. The approach is constructive and gives rise to a numerical method. We supplement the analysis with numerical experiments

Need for a next generation of chromatography models: academic demands for thermodynamic consistency and industrial requirements in everyday project work

Process chromatography modelling for process development, design, and optimization as well as process control has been under development for decades. Still, the discussion of scientific potential and industrial applications needs is open to innovation. The discussion of next-generation modelling approaches starting from Langmuirian to steric mass action and multilayer or thermodynamic consistent real and ideal adsorption theory or colloidal particle adsorption approaches is continued

Advanced control strategies for bioprocess chromatography: Challenges and opportunities for intensified processes and next generation products

Recent advances in process analytical technologies and modelling techniques present opportunities to improve industrial chromatography control strategies to enhance process robustness, increase productivity and move towards real-time release testing. This paper provides a critical overview of batch and continuous industrial chromatography control systems for therapeutic protein purification. Firstly, the limitations of conventional industrial fractionation control strategies using in-line UV spectroscopy and on-line HPLC are outlined. Following this, an evaluation of monitoring and control techniques showing promise within research, process development and manufacturing is provided. These novel control strategies combine rapid in-line data capture (e.g. NIR, MALS and variable pathlength UV) with enhanced process understanding obtained from mechanistic and empirical modelling techniques. Finally, a summary of the future states of industrial chromatography control systems is proposed, including strategies to control buffer formulation, product fractionation, column switching and column fouling. The implementation of these control systems improves process capabilities to fulfil product quality criteria as processes are scaled, transferred and operated, thus fast tracking the delivery of new medicines to market

OPTIMAL CONTROL OF ION EXCHANGE PROCESS FOR CHROMATE REMOVAL AND PROTEIN A CHROMATOGRAPHY FOR ANTIBODY EXTRACTION

Ion exchange resins are widely used in the extraction of hazardous chemicals as well as the recovery of precious molecules. Therefore, an early breakthrough from the resin system can lead to toxic compounds affecting the drinking water quality or inefficient use of costly resins. Hence, accurate modeling of the ion exchange process and control strategy can enable decisions that assist in avoiding leakage when facing fluctuations in the inlet contaminant concentrations. In this work, the ion exchange process is modeled via the method of moments where the system uncertainties are captured via stochastic modeling using Ito processes. The flow rate is controlled to optimize the resin performance by maximizing its dynamic removal efficiency. The process runs more efficiently with a well-controlled varying flow rate rather than a constant flow, a standard industrial practice. The optimal control reveals that introducing the feed at a high flow rate followed by a decreasing flow can achieve significant removal of the target molecules and increase the efficiency of the purification process. This work has wide applicability ranging from chromate removal from water to extracting antibodies with a costly affinity chromatography resin

Towards continuous biomanufacturing a computational approach for the intensification of monoclonal antibody production

Current industrial trends encourage the development of sustainable, environmentally friendly processes with reduced energy and raw material consumption. Meanwhile, the increasing market demand as well as the tight regulations in product quality, necessitate efficient operating procedures that guarantee products of high purity. In this direction, process intensification via continuous operation paves the way for the development of novel, eco-friendly processes, characterized by higher productivity compared to batch (Nicoud, 2014). The shift towards continuous operation could advance the market of high value biologics, such as monoclonal antibodies (mAbs), as it would lead to shorter production times, decreased costs, as well as significantly less energy consumption (Konstantinov and Cooney, 2015, Xenopoulos, 2015). In particular, mAb production comprises two main steps: the culturing of the cells (upstream) and the purification of the targeted product (downstream). Both processes are highly complex and their performance depends on various parameters. In particular, the efficiency of the upstream depends highly on cell growth and the longevity of the culture, while product quality can be jeopardized in case the culture is not terminated timely. Similarly, downstream processing, whose main step is the chromatographic separation, relies highly on the setup configuration, as well as on the composition of the upstream mixture. Therefore, it is necessary to understand and optimize both processes prior to their integration. In this direction, the design of intelligent computational tools becomes eminent. Such tools can form a solid basis for the: (i) execution of cost-free comparisons of various operating strategies, (ii) design of optimal operation profiles and (iii) development of advanced, intelligent control systems that can maintain the process under optimal operation, rejecting disturbances. In this context, this work focuses on the development of advanced computational tools for the improvement of the performance of: (a) chromatographic separation processes and (b) cell culture systems, following the systematic PAROC framework and software platform (Pistikopoulos et al., 2015). In particular we develop model-based controllers for single- and multi-column chromatographic setups based on the operating principles of an industrially relevant separation process. The presented strategies are immunized against variations in the feed stream and can successfully compensate for time delays caused due to the column residence time. Issues regarding the points of integration in multi-column systems are also discussed. Moreover, we design and test in silico model-based control strategies for a cell culture system, aiming to increase the culture productivity and drive the system towards continuous operation. Challenges and potential solutions for the seamless integration of the examined bioprocess are also investigated at the end of this thesis.Open Acces

Systematic approaches for modelling and optimisation of chromatographic processes.

Chromatography is an increasingly important separation technique in the fine chemical, pharmaceutical and biotechnological industries. The development of accurate, reliable mathematical models for chromatography is necessary for an efficient optimisation of the process. The past decade has seen a tremendous advance in the mathematical modelling and optimisation of the chromatographic processes, with the increase in computational power that is now available. The purposes of this work are to (1) compare chromatographic models, (2) examine the choice of chromatographic models employed and (3) compare different chromatography configurations applied to the same process. With the variety of chromatography models available, there is a need to decide which model is best suited to a given process and the means by which the model parameters can be determined. A novel approach is proposed in this thesis for the model parameter and model selection for chromatographic processes to address both these issues and is illustrated using three case studies. This work highlights the differences in using simulated, theoretical data (which most modelling work commonly illustrated with) and experimental data, particularly data of complex bio-mixtures. Model selection is conducted using a recent graphical interpretation method, discussing the advantages and disadvantages of this method. Over the years, the operation of the chromatographic process in these industries has undergone some changes and it is no longer limited to batch processing. Whilst the single column is still popular in preparative chromatography, multi-column processes are now becoming increasingly popular in industrial-scale chromatography to produce large amounts of highly purified products. In light of the diversity of operational policies now available to chromatography, the second half of this thesis addresses examines the differences between the single column and the multicolumn chromatographic processes. Preliminary work is done on developing a detailed model of the simulated moving bed (SMB) chromatographic process, presenting both a dynamic model and two cyclic steady state (CSS) models. A theoretical case study is then optimised for the operation of the SMB process. The simulated moving bed (SMB) process and its recent variation, the Varicol process, are particularly well known. Such processes are continuous and are able to produce large quantities of high purified products. The decision of choosing either a single column or multi-column process for a separation is not a clear cut one. As the configurations and process operations in these processes are vastly different, an economic comparison between the optimised process alternatives is thus necessary to properly assess the strengths and weaknesses of each system, particularly from an industrial point of view. In column chromatography, a single column, as well as a single column with recycle and peak shaving operations, are considered, whilst for the multi-column alternative, the SMB process and its variations (Varicol, Powerfeed etc.) are examined