E. Aguilar-Garnica, V. Alcaraz-González, and V. González-Álvarez (Mexico)
Asymptotic observer, bioengineering distributed parameter systems, orthogonal collocation, stability, fluidized bed bioreactor.
: In this paper we present the design of an asymptotic observer and its implementation in a fermentation process, carried out in a fluidized bed bioreactor, which is described by a distributed parameter model. The application of the observer on this system results in an homogenous linear system that is solved by means of the orthogonal collocation method. The estimation error dynamics for the species in the bulk phase is further analyzed, and a general expression for the state matrix of this dynamics is developed for N internal collocation points. It is demonstrated, by means of the analysis of this matrix, that the selection of the parameters and of the Jacobi polynomials used in the orthogonal collocation method, as well as of N, influence drastically the stability of the estimation error dynamics for the species in the bulk phase and therefore in the transport dynamics of the reduced model.
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