An Extended Adaptive Generalized Second-Order Algorithm for Simultaneous Estimation of Reaction Rates and an Input Disturbance in Bioprocesses

Currently, monitoring and controlling a bioreactor is crucial for the improvement of any bioprocess behavior. Hence, it is necessary to know the system dynamics, such as reaction rates, which are challenging to describe mathematically. Although many observers were designed for its estimation, these algorithms are not robust under an external disturbance in the dilution rate, which can interfere with monitoring reaction rates and unmeasurable states, or designing control laws. Using sliding mode observers is an option to deal with this problem. However, its application depends on knowing the upper bounds of the unknown dynamics, which, if they are poorly selected, can increase the effect of chattering phenomena and degrade the performance of any proposed observer or control algorithms. In this work, an extended adaptive generalized second-order algorithm is designed and analyzed to estimate reaction rates and scalar external disturbances in bioprocesses. Furthermore, a criterion is developed to tune the adaptive law's gains. The application of this algorithm depends on a change of variables, which is valid under the persistent excitation condition. The designed algorithm is studied in a simulated continuous bioproduction of beta-carotene, which shows that the proposed algorithm performs well in estimating the desired dynamics.