22 research outputs found

    Further results on stabilization of periodic trajectories for a chemostat with two species,

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    Abstract We discuss an important class of problems involving the tracking of prescribed trajectories in the chemostat model. We provide new tracking results for chemostats with two species and one limiting substrate, based on Lyapunov function methods. In particular, we use a linear feedback control of the dilution rate and an appropriate time-varying substrate input concentration to produce a locally exponentially stable oscillatory behavior. This means that all trajectories for the nutrient and corresponding species concentrations in the closed loop chemostat that stay near the oscillatory reference trajectory are attracted to the reference trajectory exponentially fast. We also obtain a globally stable oscillatory reference trajectory for the species concentrations, using a nonlinear feedback control depending on the dilution rate and the substrate input concentration. This guarantees that all trajectories for the closed loop chemostat dynamics are attracted to the reference trajectory. Finally, we construct an explicit Lyapunov function for the corresponding global error dynamics. We demonstrate the efficacy of our method in a simulation

    Productivity analysis and non-linear gain scheduling approach for multi-species bioprocesses with product inhibition

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    International audienceBioprocesses with product inhibition are known to allow species coexistence. In this work, we first study the productivity of the different possible equilibria, depending on the operating conditions, and show that single species offers the best performances. Then, we propose a control strategy to stabilize the dynamics about the desired equilibria, in presence of instability. Based on output feedback linearization, we propose a family of controllers and a gain-scheduling approach to adapt the controller. Finally, we illustrate our approach on numerical simulations, showing that the attraction basin of the closed-loop system is improved by considering the gain-scheduling approach

    Global stabilisation of continuous bioreactors: tools for analysis and design of feeding laws

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    [EN] This work revisits the dynamic behaviour of stirred continuous reactors in which a single bioreaction with unknown kinetics occurs. Conditions on the feeding strategy to avoid washing out the biomass and falling in batch operation are obtained. These conditions derive in a closed positively invariant region including the desired operating point. It is stated that no closed orbits may exist in this region and, furthermore, that no fixed point exists but on one of its borders. Therefore, global stability is achieved by finding a feeding law that fulfils the aforementioned invariant conditions and gives a single equilibrium for a first-order dynamics. These results are useful to determine the stability properties of different control laws and, more importantly, to design new ones. The main advantages of the proposed approach are its simplicity and that, differing from previous results, input saturation does not affect stability results. The potentiality of the developed tools is illustrated by means of classical and novel feeding laws. (C) 2017 Elsevier Ltd. All rights reserved.Financed by I216-2016 (UNLP), PICT2014-2394 (ANPCyT) and PIP112-2015-01-00837 (CONICET), Argentina; and by DPI2014-55276-C5-1-R MINECO/AEI/FEDER, UE. The material in this paper was not presented at any conference.De Battista, H.; Jamilis, M.; Garelli, F.; Picó, J. (2018). Global stabilisation of continuous bioreactors: tools for analysis and design of feeding laws. Automatica. 89:340-348. https://doi.org/10.1016/j.automatica.2017.12.041S3403488

    Output Feedback Linearization of Turbidostats After Time Scaling

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    "© 2019 IEEE. Personal use of this material is permitted. Permissíon from IEEE must be obtained for all other uses, in any current or future media, including reprinting/republishing this material for advertisíng or promotional purposes, creating new collective works, for resale or redistribution to servers or lists, or reuse of any copyrighted component of this work in other works."[EN] Turbidostats are a class of bioreactors gaining interest due to the recent availability of microscale and small-scale devices for characterization and scalingup of the biotechnological systems relevant in the biotech and pharma industries. The goal is to keep cell density constant in continuous operation. Thus, the control law, i.e., the substrate feeding strategy, must guarantee global or semiglobal convergence to an equilibrium point. However, their control is difficult due to the uncertain, time varying, and nonlinear nature of the processes involved. In this brief, we propose an adaptive control law that globally stabilizes the desired biomass setpoint. Furthermore, in a certain region of the state space, the controller linearizes the dynamic behavior after some time scaling. By this way, the orbits of the closedloop system are imposed by the designer. The intrinsic integral action of the gain adaptation rejects the parameter uncertainties. Moreover, the controller implementation only assumes the biomass concentration to be measured. Both the simulated and experimental results show the performance of the controller.This work was supported in part by the National University of La Plata under Grant 11-I127, in part by ANPCyT under Grant PICT2014 2394, in part by CONICET under Grant PIP112 2015 0837, and in part by MINECO/AEI/FEDER, UE under Grant DPI2014-55276-C5-1-R and Grant DPI2017-82896-C2-1-R. The work of F. N. Santos-Navarro was supported by ai2-UPV.De Battista, H.; Picó-Marco, E.; Santos-Navarro, FN.; Picó, J. (2019). Output Feedback Linearization of Turbidostats After Time Scaling. IEEE Transactions on Control Systems Technology. 27(4):1668-1676. https://doi.org/10.1109/TCST.2018.2834882S1668167627

    Output Feedback Linearization of Turbidostats After Time Scaling

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    Turbidostats are a class of bioreactors gaining interest due to the recent availability of microscale and small-scale devices for characterization and scalingup of the biotechnological systems relevant in the biotech and pharma industries. The goal is to keep cell density constant in continuous operation. Thus, the control law, i.e., the substrate feeding strategy, must guarantee global or semiglobal convergence to an equilibrium point. However, their control is difficult due to the uncertain, time varying, and nonlinear nature of the processes involved. In this brief, we propose an adaptive control law that globally stabilizes the desired biomass setpoint. Furthermore, in a certain region of the state space, the controller linearizes the dynamic behavior after some time scaling. By this way, the orbits of the closed-loop system are imposed by the designer. The intrinsic integral action of the gain adaptation rejects the parameter uncertainties. Moreover, the controller implementation only assumes the biomass concentration to be measured. Both the simulated and experimental results show the performance of the controller.Instituto de Investigaciones en Electrónica, Control y Procesamiento de Señale

    Instrumentation and control of anaerobic digestion processes: a review and some research challenges

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    The final publication is available at Springer via http://dx.doi.org/10.1007/s11157-015-9382-6[EN] To enhance energy production from methane or resource recovery from digestate, anaerobic digestion processes require advanced instrumentation and control tools. Over the years, research on these topics has evolved and followed the main fields of application of anaerobic digestion processes: from municipal sewage sludge to liquid mainly industrial then municipal organic fraction of solid waste and agricultural residues. Time constants of the processes have also changed with respect to the treated waste from minutes or hours to weeks or months. Since fast closed loop control is needed for short time constant processes, human operator is now included in the loop when taking decisions to optimize anaerobic digestion plants dealing with complex solid waste over a long retention time. Control objectives have also moved from the regulation of key variables measured online to the prediction of overall process perfor- mance based on global off-line measurements to optimize the feeding of the processes. Additionally, the need for more accurate prediction of methane production and organic matter biodegradation has impacted the complexity of instrumentation and should include a more detailed characterization of the waste (e.g., biochemical fractions like proteins, lipids and carbohydrates)andtheirbioaccessibility andbiodegradability characteristics. However, even if in the literature several methodologies have been developed to determine biodegradability based on organic matter characterization, only a few papers deal with bioaccessibility assessment. In this review, we emphasize the high potential of some promising techniques, such as spectral analysis, and we discuss issues that could appear in the near future concerning control of AD processes.The authors acknowledge the financial support of INRA (the French National Institute for Agricultural Research), the French National Research Agency (ANR) for the "Phycover" project (project ANR-14-CE04-0011) and ADEME for Inter-laboratory assay financial support.Jimenez, J.; Latrille, E.; Harmand, J.; Robles Martínez, Á.; Ferrer Polo, J.; Gaida, D.; Wolf, C.... (2015). Instrumentation and control of anaerobic digestion processes: a review and some research challenges. Reviews in Environmental Science and Biotechnology. 14(4):615-648. doi:10.1007/s11157-015-9382-6S615648144Aceves-Lara CA, Latrille E, Steyer JP (2010) Optimal control of hydrogen production in a continuous anaerobic fermentation bioreactor. 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    Analysis and Control of Bacterial Populations in Synthetic Biology

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    Synthetic Biology is a new field of research that aims at engineering new functionalities in living beings. Analogously to electronic circuits, more advanced functionalities can be realised by putting together smaller functional modules that perform elementary tasks; however, the interaction of these basic pieces is somewhat complex and fragile. Therefore, to increase the robustness and reliability of the whole system, typical tools from Control Theory, such as feedback loops, can be employed. In the first part of this thesis we propose feedback control strategies to balance the gene expression of a bistable genetic circuit, known as genetic toggle switch, in an unstable region far away from its stable equilibria - a problem analogous to the stabilization of the inverted pendulum in mechanics. The effectiveness of the proposed control strategies is validated via realistic agent-based simulations of a bacterial population endowed with the genetic toggle switch. Later in the thesis we move towards the growth control of bacterial cells in bioreactors, introducing a novel open-source and versatile design of a turbidostat to host in vivo control experiments. In the last part, we want to control bioreactors to guarantee the coexistence of multiple species in the same environment. We analyse the dynamics of a simple one-chamber bioreactor, proposing control strategies to achieve the control goal. However, simple bioreactors have several drawback when the concentrations of multiple species are regulated at the same time; for these reason, we propose a novel layout for a bioreactor, with two growth chambers and a mixing one, to be used in multicellular in vivo control experiments

    Advanced numerical treatment of chemotaxis driven PDEs in mathematical biology

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    From the first formulation of chemotaxis-driven partial differential equations (PDEs) by Keller and Segel in the 1970's up to the present, much effort has been expended in modelling complex chemotaxis re- lated processes. The shear complexity of such resulting PDEs crucially limits the postulation of analytical results. In this context the sup- port by numerical tools are of utmost interest and, thus, render the implementation of a numerically well elaborated solver an undoubt- edly important task. In this work I present different iteration strategies (linear/nonlinear, decoupled/monolithic) for chemotaxis-driven PDEs. The discretiza- tion follows the method of lines, where I employ finite elements to resolve the spatial discretization. I extensively study the numerical efficiency of the iteration strategies by applying them on particular chemotaxis models. Moreover, I demonstrate the need of numerical stabilization of chemotaxis-driven PDEs and apply a exible scalar algebraic ux correction. This methodology preserves the positivity of the fully discretized scheme under mild conditions and renders the numerical solution non-oscillatory at a low level of additional compu- tational costs. This work provides a first detailed study of accurate, efficient and exible finite element schemes for chemotaxis-driven PDEs and the implemented numerical framework provides a valuable basis for fu- ture applications of the solvers to more complex models

    Towards the implementation of distributed systems in synthetic biology

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    The design and construction of engineered biological systems has made great strides over the last few decades and a growing part of this is the application of mathematical and computational techniques to problems in synthetic biology. The use of distributed systems, in which an overall function is divided across multiple populations of cells, has the potential to increase the complexity of the systems we can build and overcome metabolic limitations. However, constructing biological distributed systems comes with its own set of challenges. In this thesis I present new tools for the design and control of distributed systems in synthetic biology. The first part of this thesis focuses on biological computers. I develop novel design algorithms for distributed digital and analogue computers composed of spatial patterns of communicating bacterial colonies. I prove mathematically that we can program arbitrary digital functions and develop an algorithm for the automated design of optimal spatial circuits. Furthermore, I show that bacterial neural networks can be built using our system and develop efficient design tools to do so. I verify these results using computational simulations. This work shows that we can build distributed biological computers using communicating bacterial colonies and different design tools can be used to program digital and analogue functions. The second part of this thesis utilises a technique from artificial intelligence, reinforcement learning, in first the control and then the understanding of biological systems. First, I show the potential utility of reinforcement learning to control and optimise interacting communities of microbes that produce a biomolecule. Second, I apply reinforcement learning to the design of optimal characterisation experiments within synthetic biology. This work shows that methods utilising reinforcement learning show promise for complex distributed bioprocessing in industry and the design of optimal experiments throughout biology
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