A fixed-time convergent observer for biomass in a batch process

This paper presents an observer to estimate the biomass in a batch bioprocess, the δ-endotoxins production of bacillus thuringiensis. The proposed observer is based on a class of second order sliding mode algorithms, allowing a fixed-time estimation of the biomass. This last feature is specially important for the case of a batch process since the whole process is completed in a given time period. In addition, a simple scaling in the measured output variables is preformed in order to reduce numerical issues due to near to singularity states in the observability conditions. Simulations show the feasibility of the proposed observer. Convergence proofs are also presented.