Super twisting observers (STOs) are particularly useful in situations where the process model is uncertain or in the presence of non measurable perturbations. Despite their increasing popularity, the selection of design parameters is delicate and is usually performed in an ad-hoc fashion. In this study, a robust design procedure is developed based on assumptions related to the boundedness of the uncertainties, and a computational procedure based on semi-definite programming is proposed and tested in simulation. Specifically, this procedure is applied to the design of STOs to monitor the internal substrate quota in cultures of micro-algae in photo-bioreactors, which is a key variable in the Droop model and cannot be measured on-line. Using the measurements of the concentrations of biomass and substrate in the culture medium, a state estimation scheme based on two STOs, one for the cell growth rate and the other for the substrate uptake rate, is therefore developed.