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2 Archives of Control Sciences

2 1999

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Parameter and state variable estimation of nonlinear distributed parameter bioreactors

Boubaker O., Babary J.

Archives of Control Sciences

1999

Vol. 9, no. 3/4

93-110

Due to a lack of on-line reliable sensors, the measurement of biological variables such as biomass concentration and its specific growth rate, is not possible; this fact can be a difficulty, mainly when considering state feedback control problems. The aim of this paper consists of designing an estimator of biological variables and parameters in the case of a nonlinear distributed parameter bioreactor. By applying an orthogonal collocation method, the distributed parameter model is transformed into a lumped parameter model. Then, a joint estimator of time-varying parameters and state variables is designed by using asymptotic stability properties. Simulation runs show the feasibility and the robustness of the estimator designed for this nonlinear process.

Linearising control via FEM scheme of a distributed parameter bioreactor

Nihtila M., Tervo J., Kaipio J. P., Babary J. P.

Archives of Control Sciences

1999

Vol. 9, no. 3/4

135-156

Control of a distributed parameter bioreactor model is studied via linearisations and numerical approximations. Galerkin's finite element method (FEM) is applied to approximate the original nonlinear partial differential equation (PDE) model by an ordinary differential equation (ODE) system. Then linearising control which tracks a given reference is applied in the ODE system. Controllability of the original PDE system and the approximate ODE model are studied via physical considerations and linearisation pointing out a difference in the controllability properties of the two models. Some simulation results based on the FEM approximation by using realistic model parameter values illustrate feasibility of the joint FEM approximation and linearising control technique.