# Control of specific growth rate in fed-batch bioreactors

Fed-batch processes, extensively used in the biotechnological industry, present a large number of obstacles to control engineers. The control designer must deal with complex dynamic behavior of microorganisms, strong modeling approximations, external disturbances, nonlinear and even inherently unstable dynamics, scarce on-line measurements of most representative variables, etc.

From a biological standpoint, the ideal control of a biotechnological process would achieve microorganisms to reach a (possibly time-varying) metabolic state at which their physiological behavior is appropriate for the desired goals: e.g. production of a given metabolite. To that end, control of fermentation processes makes use of available measured or estimated variables that somehow can be related to the cell metabolic state as a function of nutrients supply. In this respect, cell growth underlies many key cellular and developmental processes. Thus, the desired microorganism metabolic states are usually strongly related to growth rate, as key representative of the underlying metabolic processes. Consecuently, its control is the underlying main problem in many cases.

In this research line, we develop specific growth rate control strategies based on the minimal model paradigm, requiring only biomass and volume measurement along with some bounds on the reaction rate. The controller has the structure of a partial state feed-back with adjustable gain. An integral-proportional control algorithm is designed to adjust this gain. First, a nonlinear integral action that makes invariant a goal manifold defined by a reference model dynamics is developed. Then, a proportional output error feed-back is incorporated to the control law with the aim of fastening convergence.

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