Online monitoring of fermentation processes is a necessary task to determine concentrations of key biochemical compounds, diagnose faults in process operations, and implement feedback controllers. However, obtaining the signals of all-important variables in a real process is a task that may be difficult and expensive due to the lack of adequate sensors, or simply because some variables cannot be directly measured. From the above, a model-based approach such as state observers may be a viable alternative to solve the estimation problem. This work shows a comparative analysis of the real-time performance of a family of sliding-mode observers for reconstructing key variables in a batch bioreactor for fermentative ethanol production. These observers were selected for their robust performance under model uncertainties and finite-time estimation convergence. The selected sliding-mode observers were the first-order sliding mode observer, the proportional sliding mode observer, and the high-order sliding mode observer. For estimation purposes, a power law kinetic model for ethanol production by Saccharomyces cerevisiae was performed. A hybrid methodology allows the kinetic parameters to be adjusted, and an approach based on inference diagrams allows the observability of the model to be determined. The experimental results reported here show that the observers under analysis were robust to modeling errors and measurement noise. Moreover, the proportional sliding-mode observer was the algorithm that exhibited the best performance.

We provide conditions for stable equilibrium in Cournot duopoly models with tax evasion and time delay. We prove that our conditions actually imply asymptotically stable equilibrium and delay independence. Conditions include the same marginal cost and equal probability for evading taxes. We give examples of cost and inverse demand functions satisfying the proposed conditions. Some economic interpretations of our results are also included.

La creciente demanda de Gas Licuado de Petróleo (GLP) requiere procesos de envasado más eficientes y seguros. Este artículo presenta el desarrollo de un sistema de automatización industrial para un carrusel de llenado de cilindros de GLP de 30 Kg, inspirado en la planta "Gas Bienestar" en Tepeji, Hidalgo, México. El sistema fue diseñado para eliminar cuellos de botella operativos y reducir la exposición del personal a riesgos asociados con el manejo manual del gas. La propuesta de solución se basa en un Controlador de Automatización Programable (PAC) Emerson PACSystems RX3i, cuya lógica de control se desarrolló en el software Proficy Machine Edition. La supervisión y operación en tiempo real se realiza a través de una Interfaz Hombre-Máquina (HMI) diseñada en Cimplicity Workbench. El artículo detalla el diseño del sistema, incluyendo los diagramas de tubería e instrumentación (DTI), la selección de instrumentos de campo (sensores de nivel, masa, caudal y presión) y la secuencia de control automatizada. Los resultados demuestran que la propuesta establece las bases para un proceso continuo, robusto y seguro, mejorando la productividad y reduciendo la intervención humana.