In this study, two dynamic models of beer fermentation are proposed, and their parameters are estimated using experimental data collected during several batch experiments initiated with different sugar concentrations. Biomass, sugar, ethanol, and vicinal diketone concentrations are measured off-line with an analytical system while two on-line immersed probes deliver temperature, ethanol concentration, and carbon dioxide exhaust rate measurements. Before proceeding to the estimation of the unknown model parameters, a structural identifiability analysis is carried out to investigate the measurement configuration and the kinetic model structure. The model predictive capability is investigated in cross-validation, in view of opening up new perspectives for monitoring and control purposes. For instance, the dynamic model could be used as a predictor in receding-horizon observers and controllers.

In this study, the parameters of a dynamic model of cultures of the microalgae Scenedesmus obliquus are estimated from datasets collected in batch photobioreactors operated with various initial conditions and light illumination conditions. Measurements of biomass, nitrogen quota, bulk substrate concentration, as well as chlorophyll concentration are achieved, which allow the determination of parameters with satisfactory confidence intervals and model cross-validation against independent data. The dynamic model is then used as a predictor in a nonlinear model predictive control strategy where the dilution rate and the incident light intensity are simultaneously manipulated in order to optimize the cumulated algal biomass production.

This paper investigates the application of adaptive slope-seeking strategies to dual-input single output dynamic processes. While the classical objective of extremum seeking control is to drive a process performance index to its optimum, this paper also considers slope seeking, which allows driving the performance index to a desired level (which is thus sub-optimal). Moreover, the consideration of more than one input signal allows minimizing the input energy thanks to the degrees of freedom offered by the additional inputs. The actual process is assumed to be locally approachable by a Hammerstein model, combining a nonlinear static map with a linear dynamic model. The proposed strategy is based on the interplay of three components: (i) a recursive estimation algorithm providing the model parameters and the performance index gradient, (ii) a slope generator using the static map parameter estimates to convert the performance index setpoint into slope setpoints, and (iii) an adaptive controller driving the process to the desired setpoint. The performance of the slope strategy is assessed in simulation in an application example related to lipid productivity optimization in continuous cultures of micro-algae by acting on both the incident light intensity and the dilution rate. It is also validated in experimental studies where biomass production in a continuous photo-bioreactor is targeted.