A positive observer for the chemostat model with biogas measurement

In anaerobic digestion plants, it is often crucial to measure state variables such as the substrate or biomass densities for monitoring the process. But, this task can be very difficult to achieve because the sensors are sometimes unavailable, unreliable or very expensive. For these reasons software sensors can be sought instead, using indirect measurements. In this paper, we design a new observer for the chemostat model with the single measurement of biogas flow rate. This observer is positive and we show its adjustable convergence. Through simulations we also show its robustness under noise measurements. The key point is to construct a non-linear observer using hidden symmetries in the framework of the theory of symmetry preserving nonlinear systems. The effectiveness of the proposed methodology is shown through simulations.