In order to improve the behavior of any bioprocess, it is required to know some of its key biochemical variables, such as the reaction rates and the influent feeding rates. However, these variables are hard to measure, challenging to describe mathematically, or can be the source of unknown disturbances. Moreover, even though many unknown input observers were designed for their estimation, their convergence cannot be modified. In this work, an extended generalized super-twisting algorithm is designed to simultaneously estimate reaction rates and influent feeding rates in finite time. For this task, a change of variables is used, valid if the dilution rate is strictly positive. The proposed algorithm is applied on an alcoholic fermentation process, and simulated results show a good performance from the design observer.