A positive observer for the chemostat model with biogas measurement. (February 2023) - Didi, Ibtissem; Rapaport, Alain; Dib, Hacen; Cherki, Brahim
Abstract: 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. Highlights: Definition and design of an invariant observer for the chemostat model with the biogas as the measured output. Positivity of the observer with an asymptotic convergence. Design of the observer based on the symmetries of the dynamical system. Numerical simulations results showing the effectiveness of the proposed observer.