Self-optimal stabilization of a class of positive compartmental systems via variable-structure control: Bioreactors
In this paper a class of positive compartmental systems is stabilized via variable-structure feedback in sense that the control signal is self-adjusted to reach the optimal set-point (unknown). The goal is to design a self-optimizing control scheme for the substrate stabilization in bioreactors with inhibition kinetics. Open-loop analysis for the bioreactor suggests that the optimal behavior, respect to maximal biomass production, occurs in an unstable region (structurally unstable). The controller is designed based on sliding modes techniques, such that the sliding regime on the optimal manifold is achieved. The self-optimizing comprises an uncertainty estimator which computes the unknown terms for increasing the robustness issues of the sliding-mode scheme. By exploiting the inhibitory effect of substrate concentration under the biomass growth, the controller proposed achieve the practical stabilization around to the optimal substrate concentration (unknown) and, consequently, the growth-rate achieves its maximum. Numerical experiments for a microbial growth process in continuous and fed-batch operating modes illustrate the performance and execution of the control scheme.