Modification of the Luedeking and Piret model with a delay time parameter for biotechnological lactic acid production.

OBJECTIVES: To obtain a mathematical model that adequately describes the time lag between biomass generation and lactic acid production of lactic fermentations. METHODS: Seven experimental kinetics from other research works were studied to validate our proposal: four studies of Fungal Submerged Fermentation and three cases of Bacterial Submerged Fermentation, including the data recollected by Luedeking and Piret. RESULTS: We introduce a modification to the Luedeking and Piret model that consist in the introduction of a time delay parameter in the model, this parameter would account for the lag time that exists between the production of biomass and lactic acid. It is possible to determine this time delay in a simple way by approximating the biomass and product formation considering that they behave as a first order plus dead time system. The duration of this phenomenon, which is not described with the classical Luedeking and Piret model, is a function of microorganism physiology (ease of biomass growth), environment (nutrients) and type of inoculum. CONCLUSION: The Luedeking and Piret with delay model applications reveal an increase of the R2 in all cases, evidencing the quality of fit and the simplicity of the method proposed. These model would improve the accuracy of bioprocess scaling up.

State estimation and nonlinear tracking control simulation approach. Application to a bioethanol production system.

Tracking control of specific variables is key to achieve a proper fermentation. This paper analyzes a fed-batch bioethanol production process. For this system, a controller design based on linear algebra is proposed. Moreover, to achieve a reliable control, on-line monitoring of certain variables is needed. In this sense, for unmeasurable variables, state estimators based on Gaussian processes are designed. Cell, ethanol and glycerol concentrations are predicted with only substrates measurement. Simulation results when the controller and estimators are coupled, are shown. Furthermore, the algorithms were tested with parametric uncertainties and disturbances in the control action, and are compared, in all cases, with neural networks estimators (previous work). Bayesian estimators show a performance improvement, which is reflected in a decrease of the total error. Proposed techniques give reliable monitoring and control tools, with a low computational and economic cost, and less mathematical complexity than neural network estimators.

Trajectory tracking controller for unmanned helicopter under environmental disturbances.

This paper develops a trajectory tracking control design algorithm to be applied in unmanned aerial vehicles (UAVs). The strategy is simple but effective and it is based on linear algebra theory. The proposed approach reforms the column space of a system of linear equations at each sampling time to ensure the tracking objective when environmental disturbances appear. This new formulation ensures a uniform signal without affecting the error convergence to zero (demonstration available), which is one of the main contributions of this work. A statistical method is used to tune the system control minimizing a pre-defined cost function. In addition, the convergence to zero of the tracking errors is demonstrated in this work. Finally, the controller's effectiveness is tested through several simulations in realistic test scenarios in the presence of disturbances.

Tracking control of concentration profiles in a fed-batch bioreactor using a linear algebra methodology.

Based on a linear algebra approach, this paper aims at developing a novel control law able to track reference profiles that were previously-determined in the literature. A main advantage of the proposed strategy is that the control actions are obtained by solving a system of linear equations. The optimal controller parameters are selected through Monte Carlo Randomized Algorithm in order to minimize a proposed cost index. The controller performance is evaluated through several tests, and compared with other controller reported in the literature. Finally, a Monte Carlo Randomized Algorithm is conducted to assess the performance of the proposed controller.