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On controllability, parametrization, and output tracking of a linearized bioreactor model. (English) Zbl 1029.93038
The controllability, parametrization, and output tracking properties of the fixed-bed bioreactor around the steady state are analyzed. The original system of nonlinear partial differential equations is linearized, and the properties of the linearized system are discussed. It is found that the linearized model is not exactly controllable. Also, it is shown how the frequency space factorizations can be applied to get a state space parametrization. Next, the related output tracking problem is considered. At first the total transfer function of the infinite-dimensional system (using the integrated state- and frequency-domain method) is obtained. Then the system is parametrized using translation invariant pseudodifferential operators. Finally, the stabilizing compensator which (asymptotically) tracks the given reference output is designed. The simulations show exponentially stable feedback dynamics.

MSC:
93C20 Control/observation systems governed by partial differential equations
93C95 Application models in control theory
93C80 Frequency-response methods in control theory
93B05 Controllability
35K57 Reaction-diffusion equations
93B18 Linearizations
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