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A three-dimensional finite element model for the control of certain nonlinear bioreactors. (English) Zbl 0982.76065
Summary: This paper deals with the dynamics of nonlinear distributed parameter fixed-bed bioreactors described by two nonlinear partial differential (evolution) equations. The true spatially three-dimensional situation is considered instead of usual one-dimensional approximation. This enables one to take into account the effects of flow profile and the true location of measurement transducer. The (output) evolution of the corresponding open-loop control system is simulated. Furthermore, we are able to examine the associated closed-loop system with respect to the relevant output function. Especially, the asymptotic output tracking is found to be successful by applying the usual process based on a feedback linearization.

MSC:
76M10 Finite element methods applied to problems in fluid mechanics
76Z05 Physiological flows
93C20 Control/observation systems governed by partial differential equations
92C10 Biomechanics
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