Abstract
Nonlinear feedback control design is demonstrated in this study for a continuous mixed-culture biological reactor model exhibiting competition and external inhibition. The model considered describes the growth of two species in a continuous stirred tank, for which one species is sensitive to an external inhibitor, and for which both species compete for the same rate-limiting substrate. It is shown that choosing the dilution rate and the inhibitor addition rate as manipulated variables admits a global linearization transformation which can be used to construct a multivariable feedback controller. The transformed state variables are found to be the cell density of the substrate insensitive species, the log ratio of cell densities, and the net difference in specific growth rates. An extended Kalman filter is used to estimate the unmeasured states when only a single measurement of the total cell mass is available. Simulated performance of the closed-loop system appears to be satisfactory for a wide region of the phase space.
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