Self-optimising control for a class of continuous bioreactor via variable-structure feedback

A self-optimising controller is designed for stabilisation of a class of bioreactor exploiting sliding-mode techniques. The stability analysis for the class of bioreactor, in open-loop configuration, suggests that the optimal behaviour, respect to maximal biomass production, occurs in an unstable region (structurally unstable). In this contribution, a variable-structure controller is designed, exploiting the inhibitory effect of substrate concentration under the biomass growth rate, such that the closed-loop system reaches the optimal manifold where the effect induced by the growth rate gradient is compensated (favouring the maximum growth rate). The self-optimising comprises an uncertainty estimator which computes the unknown terms for increasing the robustness issues of the sliding-mode scheme. Numerical experiments illustrate the performance and execution of the control strategy considering different parameter values for biomass growth rate. The robustness and fragility of the proposed controller are also discussed with respect to the modelling uncertainty and small changes in the controller gains, respectively.