A sliding mode observer for estimating substrate consumption rate in a fermentation process

In a fermentation system, the biomass balance and the substrate mass balance are coupled by a nonlinear growth rate condition. In order to control this nonlinear process, many researchers assume that both substrate and biomass concentration are measurable. In practice, only online measurement of substrate concentration is readily available. Estimating the biomass concentration can be done but it is often an expensive procedure. This paper will consider the development of a software sensor or observer using sliding mode techniques to estimate substrate consumption rate, which comprises a combination of the substrate concentration, biomass concentration, specific growth rate and yield production coefficient. This observer parameterisation simplifies the nonlinear differential equations of the fermentation process. It is shown that the sliding mode exhibited by the observer error dynamics is exponentially stable, and uncertainty effects are considered. The constructive observer parameterisation ensures the sliding mode is reached in finite time. Nonlinear simulation results support the theoretical developments and demonstrate the robustness of the observer in the presence of both parameter uncertainties and external disturbances.