On dynamical behaviour of two-dimensional biological reactors

Fuzzy servo controller for CSTB with substrate inhibition kinetics

“…From Eqs. (1) and (2), three equilibrium points are possible [1]; the first two for x 2 are obtained from the roots of the expression…”

“…Obtaining higher yields requires operating the processes near their maximum productivity. However, these high yields are not easy to achieve, especially for CSTB with non-monotonic growth kinetics (i.e., by substrate inhibition) where bifurcation and multiple equilibrium points are exhibited [1]. The maximum productivity for CSTB with substrate inhibition is found at the limit of bifurcation conditions, where even small uncertainties in parameter values can drive the system to an undesired oscillatory regime.…”

Neural Network-Based State Estimation for a Closed-Loop Control Strategy Applied to a Fed-Batch Bioreactor

“…With a similar procedure to that used for deriving (15) and after adding two integrators (k 1 U 1, +1 and k 2 U 2, +1 ), the error dynamics can be expressed as…”

“…Therefore, K and k 1 are chosen in order to ensure the stability of the linear system represented in the left-hand side of (15). To achieve this condition, the roots of such polynomial ( ) must lie inside the unit circle.…”

“…Additionally, nonmodeled external perturbations can disturb the process. In general, model uncertainties and external perturbations can cause severe risks in bioreactors, such as leading to undesirable operating conditions [14][15][16]. For instance, inadequate modeling of the inhibitory effect of a substrate can lead to a structural instability in the dynamical behavior of a bioprocess [15].…”