Model description:
The behavior of phytoplankton cells in a continuous reactor is usually described by the Droop model. Cell growth is limited by a nutrient with concentration $S$. The biomass has a concentration $N$ and $Q$ represents the cell quota of assimilated nutrient, expressed as the amount of intracellular nutrient per biomass unit. The dilution rate $D$ corresponds to the flow rate of renewal medium over the volume of the reactor, and $D$ is the input of the system.
We denote $D = D_0 + u$, and the system fits
$$\sum_D \begin{cases} \dot{x}_i = f(x) + ug(x)\\ y=h(x_1) \end{cases}$$
with
$f(x)=\begin{pmatrix} a_2\left(1-\dfrac{1}{x_2}\right)x_1 - D_0x_1\\ a_3\dfrac{x_3}{a_1+x_3} - a_2(x_2 - 1)\\ D_0(1-x_3)-\dfrac{x_1x_3}{a_1+x_3} \end{pmatrix}$
$g(x)=\begin{pmatrix} -x_1\\ 0\\ 1-x_3 \end{pmatrix}$, and $h(x_1)=x_1$, where
$ x_1 = (\rho_m N/S_i);\\ x_2 = (Q/K_Q);\\ x_3 = (S/S_i);\\ a_1 = (K_{\rho}/S_i);\\ a_2 = \mu_m;\\ a_3 = (\rho_m/K_Q). $
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Publication details:
| Title | Nonlinear observers for a class of biological systems: application to validation of a phytoplanktonic growth model |
| Publication Type | Journal Article |
| Year of Publication | 1998 |
| Authors | Bernard, O., Sallet G., and Sciandra A. |
| Journal | IEEE Transactions on Automatic Control |
| Volume | 43 |
| Start Page | 1056 |
| Issue | 8 |
| Pagination | 1056-1065 |
| Date Published | 08/1998 |
| ISSN | 0018-9286 |
| Accession Number | 6002262 |
| Keywords | biocybernetics, living systems, nonlinear systems, observability, observers, physiological models |
| Abstract | The authors construct nonlinear observers in order to discuss the validity of biological models. They consider a class of systems including many classical models used in biological modeling. They formulate the nonlinear observers corresponding to these systems and prove the conditions necessary for their exponential convergence. They apply these observers on the well-known Droop model which describes the growth of a population of phytoplanktonic cells. The validity of this model is discussed based on the performance of the observers working on experimental data |
| DOI | 10.1109/9.704977 |