Saturated PI control of continuous bioreactors with Haldane kinetics

On the estimation problem of a class of continuous bioreactors with unknown input

“…In particular, continuous bioreactors with nonisotonic growth rate due to quadratic inhibition mechanism exhibit a complex nonlinear behavior, including multiplicity, bifurcation with respect to dilution rate, and presence of a stable or unstable undesired washout steady-state [1,2]. The understanding of the effect of the nonisotony property of the reaction kinetics plays a central role in the design of globally stabilizing saturated controllers for bioreactors [2,3].…”

“…The understanding of the effect of the nonisotony property of the reaction kinetics plays a central role in the design of globally stabilizing saturated controllers for bioreactors [2,3]. In the global nonlinear stochastic behavior of reactors with monostability (or bistability) due to isotonic (or nonisotonic) kinetics, the isotony (or nonisotony) property manifests itself as monomodality (or bimodality) of the state probability density function [4][5][6], or equivalently the existence of one (or two) probable state(s).…”

Nonlinear PI controllers with output transformations

“…Parameterized control systems with changing operating points have long been studied in the categories of "gain scheduling" 7 or "extended linearization". 8,9 Linear and nonlinear PI controllers with constant or gain-scheduled parameters have been used for various processes, for example, fuel cell processes, 10 bio processes, 11 batch processes, 12 and real-time optimization. 13 There have been several types of nonlinear PI controllers that do not use explicit gain scheduling parameters.…”

The buffered chemostat with non-monotonic response functions

“…It imposes also to ensure that initial condition belongs to the attracting basin of the desired equilibrium. A common technique to overcome theses difficulties and allow an initial stage with a small concentration of biomass, is to control the input flow rate Q with a stabilizing feedback [6,36] (it consists in finding a feedback law that reduces the flow rate when the state belongs to the attracting basin of the wash-out equilibrium). But this solution requires an upstream storage and an actuator.…”

“…Such inhibition can be modeled by non-monotonic response functions [1,3] and lead to instability in the chemostat [2,46,24]. Several control strategies of the input flow have been proposed in the literature to globally stabilize such systems [6,14,34,36] but the ability of a spatial structure to passively stabilize such dynamics has not been yet studied (in [38] a general structure of networks of chemostats is considered but with monotonic growth rates, while in [44] non-monotonic functions are considered but for the serial gradostat only).…”