Biomass concentration estimation using the extended Jordan observable form

In this paper, we propose a new observer design for the estimation of the biomass concentration in a bioreactor, using the measurements of the substrate concentration. We consider two cases: in the first, a full knowledge of the specific growth rate is assumed and in the second, only a partial knowledge of the latter is assumed. We show that the bioreactor model is in a special canonical form called the extended Jordan observable canonical (EJOC) form. It is shown, in particular, that an observer design for systems in the EJOC form is fairly simple and straightforward. No particular nonlinear transformation is needed in the design procedure. In addition, the gain of the observer is adaptive since it is a function of the input and the output of the system, and can be tuned in order to obtain a desirable rate of convergence