Hybrid Control of a Bioreactor with Quantized Measurements: Extended Version

We consider the problem of global stabilization of an unstable bioreactor model (e.g. for anaerobic digestion), when the measurements are discrete and in finite number ("quantized"), with control of the dilution rate. The model is a differential system with two variables, and the output is the biomass growth. The measurements define regions in the state space, and they can be perfect or uncertain (i.e. without or with overlaps). We show that, under appropriate assumptions, a quantized control may lead to global stabilization: trajectories have to follow some transitions between the regions, until the final region where they converge toward the reference equilibrium. On the boundary between regions, the solutions are defined as a Filippov differential inclusion. If the assumptions are not fulfilled, sliding modes may appear, and the transition graphs are not deterministic

Optimization of the separation of two species in a chemostat

International audienceIn this work, we study a two species chemostat model with one limiting substrate, and our aim is to optimize the selection of the species of interest. More precisely, the objective is to find an optimal feeding strategy in order to reach in minimal time a target where the concentration of the first species is significantly larger than the concentration of the other one. Thanks to Pontryagin maximum principle, we introduce a singular feeding strategy which allows to reach the target, and we prove that the feedback control provided by this strategy is optimal whenever initial conditions are chosen in the invariant attractive manifold of the system. The optimal synthesis of the problem in presence of more than one singular arc and for initial conditions outside this set is also investigated

Optimization of strain selection in evolutionary continuous culture

International audienceIn this work, we study a minimal time control problem for a perfectly mixed continuous culture with n ≥ 2 species and one limiting resource. The model that we consider includes a mutation factor for the microorganisms. Our aim is to provide optimal feedback control laws to optimize the selection of the species of interest. Thanks to Pontryagin's Principle, we derive optimality conditions on optimal controls and introduce a sub-optimal control law based on a most rapid approach to a singular arc that depends on the initial condition. Using adaptive dynamics theory, we also study a simplified version of this model which allows to introduce a near optimal strategy

Estimation of neutral lipid and carbohydrate quotas in microalgae using adaptive interval observers

International audienceUnder stress conditions, microalgae are known to accumulate large amounts of neutral lipids and carbohydrates, which can be used for biofuel production. However, on-line measurement of microalgal biochemical composition is a difficult task which makes the microalgal process rather difficult to manage. In this paper, we propose a so called adaptive interval observer for the on-line estimation of neutral lipid and carbohydrate quotas in microalgae. The observer is based on a change of coordinates that involves a time-varying gain. We introduce dynamics for the gain, whose trajectory converges toward a predefined optimal value (which maximizes the convergence rate of the observer). The observer performance is illustrated with experimental data of Isochrysis sp. cultures under nitrogen limitations and day-night cycle. The proposed observer design appears to be a suitable robust estimation technique

Minimal time problem for a fed-batch bioreactor with a non admissible singular arc

International audienceIn this paper, we consider an optimal control problem for a system describing a fed-batch bioreactor with one species and one substrate. Our aim is to find an optimal feedback control in order to steer the system to a given target in minimal time. The growth function is of Haldane type implying the existence of a singular arc. Unlike many studies on the minimal time problem governed by an affine system w.r.t. the control with one input, we assume that the singular arc is non-necessary controllable. This brings interesting issues in terms of optimal synthesis. Thanks to the Pontryagin Maximum Principle, we provide the optimal synthesis of the problem, It turns out that singular extremal trajectories are no longer optimal on a subset of the singular arc

Adaptive control for optimizing microalgae production

International audienceIn this paper, we propose a nonlinear adaptive controller for light-limited microalgae culture. This controller regulates the light absorption factor, defined by the ratio between the incident light and the light at the bottom of the reactor. Then, we propose a set-point for the light absorption factor which allows to optimize biomass productivity under constant illumination. Finally, we show by numerical simulation that the adaptive controller can be used to obtain near optimal productivity under day-night cycles

Driving microalgal production in raceway systems to near optimal productivities.

International audienceIn this paper, we propose a simple operational criterion for raceway systems that when integrated in a strategy of closed-loop control allows to attain microalgal productivities very near to the maximal productivities. The strategy developed was tested numerically by using a mathematical model of microalgae growth in raceways. The model takes into account the dynamics of environmental variables such temperature and light intensity and their influence on microalgae growth

Optimizing microalgal production in raceway systems

International audienceThe industrial exploitation of microalgae is characterized by the production of high-value compounds. Optimization of the performance of microalgae culture systems is essential to render the process economically viable. For raceway systems, the optimization based on optimal control theory is rather challenging, because the process is by essence periodically forced and, as a consequence, optimization must be carried out in a periodic framework. In this article, we propose a simple operational criterion for raceway systems that when integrated in a strategy of closed-loop control allows attaining biomass productivities very near to the theoretical maximal productivities. The strategy developed was tested numerically using a mathematical model of microalgae growth in raceways. The model takes into account the temporal variation of the environmental variables temperature and light intensity and their influence on microalgae growth