Interval Type-2 Fuzzy Observers Applied in Biodegradation

(1) * Marco Antonio Márquez-Vera Mail (Polytechnic University of Pachuca, Mexico)
(2) Andrea Rodríguez-Romero Mail (Polytechnic University of Pachuca, Mexico)
(3) Carlos Antonio Márquez-Vera Mail (Universidad Veracruzana, Mexico)
(4) Karla Refugio Ramos-Téllez Mail (Polytechnic University of Pachuca, Mexico)
*corresponding author


There exist processes difficult to control because of the lack of inline sensors, as occurs in biotechnology engineering. Commonly the sensor is expensive, damaged, or even they do not exist.  It is important to build an observer to have an approximation of the process output to have a closed-loop control. The biotechnological processes are nonlinear, thus in this work is proposed a fuzzy observer to endure nonlinearities. To improve the results reported in the literature, type-2 fuzzy logic was used to justify the membership functions used. The observer's gains were computed via LMIs to guarantee the observer's stability.  To facilitate the fuzzy inference computation, interval type-2 fuzzy sets were implemented. The results obtained with the interval type-2 fuzzy observer were compared with a similar technique that uses a fuzzy sliding mode observer; this new approach gives better results obtaining an error 60% lower than the obtained with the other technique. They were designed three observers that work ensemble via a fuzzy relation. The best approximation was to estimate the intermediate concentration. It is important to know this variable because this sub-product was also toxic. It was concluding that by using the oxygen concentration and the liquid volume inside the reactor, the other concentrations were estimated. Finally, this result helps to design a fuzzy controller by using the estimated state. Using this approach, the estimation errors for the phenol and biomass concentrations were 49.26% and 21.27% lower than by using sliding modes.


Fuzzy logic; Observers design; Fuzzy observers; Biodegradation



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