Robust asymptotic super twisting sliding mode observer for non-linear uncertain biochemical systems

The problem of state estimation (reconstruction of the state vector) for a given class of biochemical systems under uncertain system dynamics has been addressed in this paper. In detail, the bioreactor at a water resource recovery facility represents the considered biochemical systems. The biochemical processes taking place in the bioreactor have been modelled using an activated sludge model. Based on this model, an appropriate utility model has been derived for estimation purposes. The internal dynamics of the model have been burdened with unstructured and parametric uncertainty due to the unknown reaction kinetics functions. Taking this uncertainty into account, an analysis of the observability and detectability of the utility model has been carried out. The utility model and the available set of inputs and measured outputs have been used to design a new robust non-linear observer that allows the estimation of state variables in the presence of uncertainty. In the synthesis of the observer, the asymptotic observer methodology has been combined with a second-order sliding mode observer, a so-called super twisting algorithm. The developed observer generates not only robust and stable estimates of the state variables but also enables the reconstruction of unknown kinetic functions. The stability of the designed observer has been proven using the Lyapunov stability theory. The observer has been implemented in the Matlab/Simulink environment. The comprehensive simulation studies carried out show the high efficiency of the estimation process using the developed state observer.