Profile control in distributed parameter systems using lexicographic optimization based MPC

Process equipment that exhibits significant spatial variation of system properties, such as temperature or concentration in a fixed bed reactor, are typically modeled as distributed parameter systems. While some properties of the final product exiting the equipment may depend on the states concerning the endpoint, others may be a function of the history of processing within the equipment. In such instances, control of the spatial property profile may be beneficial. In this work, we explore the idea of profile control using extended MPC and outline the additional challenges that must be addressed in this context. In case that the target profile is unachievable, we present an MPC formulation that uses lexicographic optimization to prioritize the different sections of the profile. Simulation of a simple representative system namely a hypothetical plug flow reactor is used to demonstrate that the lexicographic optimization based MPC provides a systematic approach to profile control and spans between the endpoint control strategy and the whole profile control strategy. The benefits of lexicographic optimization based MPC were also demonstrated on a large-scale distributed parameter system of industrial size, namely the continuous pulp digester.© Elsevie

Hybrid system identification using a structural approach and its model based control: an experimental validation

For implementation of various model based techniques such as in control and fault diagnosis, data-driven identification is key for enabling cheap and rapid development of models of hybrid systems of industrial interest. In the present work, a novel identification method is proposed for a class of hybrid systems which are linear and separable in the discrete variables (that is discrete states and discrete inputs). The method takes cognizance of the fact that the separable structure of the hybrid system constrains the evolution of system dynamics. In particular, the proposed method identifies models corresponding to a certain number of modes, far fewer than the total possible modes of the system. It then generates the models for the remaining modes without any further requirement for input–output data by exploiting the separable structure of the hybrid system. We experimentally validate the method by identifying the model for a three tank benchmark hybrid system followed by model predictive control using the identified model.© Elsevie

Multiple feedback loops are key to a robust dynamic performance of tryptophan regulation in Escherichia coli

Living systems must adapt quickly and stably to uncertain environments. A common theme in cellular regulation is the presence of multiple feedback loops in the network. An example of such a feedback structure is regulation of tryptophan concentration in Escherichia coli. Here, three distinct feedback mechanisms, namely genetic regulation, mRNA attenuation and enzyme inhibition, regulate tryptophan synthesis. A pertinent question is whether such multiple feedback loops are “a case of regulatory overkill, or do these different feedback regulators have distinct functions?” [Freeman (2000) Nature 295, 313–319]. Another moot question is how robustness to uncertainties can be achieved structurally through biological interactions. Correlation between the feedback structure and robustness can be systematically studied by tools commonly employed in feedback theory. An analysis of feedback strategies in the tryptophan system in E. coli reveals that the network complexity arising due to the distributed feedback structure is responsible for the rapid and stable response observed even in the presence of system uncertainties.© Elsevie

Dynamic model of Escherichia coli tryptophan operon shows an optimal structural design

A mathematical model has been developed to study the effect of external tryptophan on the trp operon. The model accounts for the effect of feedback repression by tryptophan through the Hill equation. We demonstrate that the trp operon maintains an intracellular steady-state concentration in a fivefold range irrespective of extracellular conditions. Dynamic behavior of the trp operon corresponding to varying levels of extracellular tryptophan illustrates the adaptive nature of regulation. Depending on the external tryptophan level in the medium, the transient response ranges from a rapid and underdamped to a sluggish and highly overdamped response. To test model fidelity, simulation results are compared with experimental data available in the literature. We further demonstrate the significance of the biological structure of the operon on the overall performance. Our analysis suggests that the tryptophan operon has evolved to a truly optimal design

Mathematical modeling of fission yeast Schizosaccharomyces pombe cell cycle: exploring the role of multiple phosphatases

Cell cycle is the central process that regulates growth and division in all eukaryotes. Based on the environmental condition sensed, the cell lies in a resting phase G0 or proceeds through the cyclic cell division process (G1→S→G₂→M). These series of events and phase transitions are governed mainly by the highly conserved Cyclin dependent kinases (Cdks) and its positive and negative regulators. The cell cycle regulation of fission yeast Schizosaccharomyces pombe is modeled in this study. The study exploits a detailed molecular interaction map compiled based on the published model and experimental data. There are accumulating evidences about the prominent regulatory role of specific phosphatases in cell cycle regulations. The current study emphasizes the possible role of multiple phosphatases that governs the cell cycle regulation in fission yeast S. pombe. The ability of the model to reproduce the reported regulatory profile for the wild-type and various mutants was verified though simulations

Experimental and steady-state analysis of the GAL regulatory system in Kluyveromyces lactis

The galactose uptake mechanism in yeast is a well-studied regulatory network. The regulatory players in the Galactose Regulatory Mechanism (GAL system) are conserved in Saccharomyces cerevisiae and Kluyveromyces lactis, but the molecular mechanisms that occur as a result of the molecular interactions between them are different. The key differences in the GAL system of K. lactis relative to that of S. cerevisiae are: (a) the autoregulation of KlGAL4; (b) the dual role of KlGal1p as a metabolizing enzyme as well as a galactose-sensing protein; (c) the shuttling of KlGal1p between nucleus and cytoplasm; and (d) the nuclear confinement of KlGal80p. A steady-state model was used to elucidate the roles of these molecular mechanisms in the transcriptional response of the GAL system. The steady-state results were validated experimentally using measurements of β-galactosidase to represent the expression for genes having two binding sites. The results showed that the autoregulation of the synthesis of activator KlGal4p is responsible for the leaky expression of GAL genes, even at high glucose concentrations. Furthermore, GAL gene expression in K. lactis shows low expression levels because of the limiting function of the bifunctional protein KlGal1p towards the induction process in order to cope with the need for the metabolism of lactose/galactose. The steady-state model of the GAL system of K. lactis provides an opportunity to compare with the design prevailing in S. cerevisiae. The comparison indicates that the existence of a protein, Gal3p, dedicated to the sensing of galactose in S. cerevisiae as a result of genome duplication has resulted in a system which metabolizes galactose efficiently