Global stabilization of continuous bioreactors
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abstract
This paper studies the problem of designing controllers for enlarging the stability region of continuous stirred microbial bioreactors. A specific application is in anaerobic digestion, where the stability region can be very small if the operating steady state is selected to maximize the methane production rate. A control Lyapunov function approach is followed to construct a globally stabilizing state feedback control law in continuous time. This turns out to be proportional output feedback in the case of anaerobic digestion, where the measurement is the methane production rate. The control law is implemented in discrete time under zero-order hold. Stability analysis of the resulting closed-loop system is performed using the same control Lyapunov function, leading to an upper bound on the sampling period for guaranteed stability over a given region. Numerical simulation results indicate that closed-loop stability under sampled-data control is global, irrespective of the size of the sampling period.