Second-order sliding mode observer for biomass concentration and growth rate estimation in batch photo-bioreactors

In this work the problem of estimating some variables of interest for monitoring and control of photo-fermentation processes is addressed. The focus is on a batch cultivation of Rhodobacter capsulatus where biohydrogen production rate is represented by a Luedeking–Piret expression. The use of second-order sliding mode algorithms to estimate biomass concentration and bacterial specific growth rate is explored. It is concluded that the proposed observer does not require a kinetic model, thus eliminating a source of uncertainty. Also, it is shown that the error dynamics converges exponentially with short time constant determined by process parameters. Numerical simulations corroborate the convergence properties of the algorithm in the nominal case, as well as its robustness against parametric uncertainty and its performance under noisy measurement.