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Journal of Applied Mathematics
Volume 2003 (2003), Issue 5, Pages 243-276

On controllability, parametrization, and output tracking of a linearized bioreactor model

Department of Mathematics and Statistics, University of Kuopio, P.O. Box 1627, Kuopio FIN-70211, Finland

Received 12 April 2002; Revised 30 October 2002

Copyright © 2003 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


The paper deals with a distributed parameter system related to the so-called fixed-bed bioreactor. The original nonlinear partial differential system is linearized around the steady state. We find that the linearized system is not exactly controllable but it is approximatively controllable when certain algebraic equations hold. We apply frequency-domain methods (transfer function analysis) to consider a related output tracking problem. The input-output system can be formulated as a translation invariant pseudodifferential equation. A simulation shows that the calculation scheme is stable. An idea to use frequency-domain methods and certain pseudodifferential operators for parametrization of control systems of more general systems is pointed out.