Stable fuzzy control and observer via LMIs in a fermentation process

Márquez-Vera, Marco Antonio; Ramos-Velasco, Luis Enrique; Balderrama-Hernández, B.D.

doi:10.1016/j.jocs.2018.06.002

Cited by 11 publications

(11 citation statements)

References 27 publications

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“…In this case, the transfer state matrices are defined as i ∈ R 3×3 , and the observer gains are the matrices i ∈ R 3×1 . To confirm linear matrix inequalities, a change in variables is done to have the necessary properties [14], the common matrix is positive definite and symmetric. The matrix found to stability holds was: ).…”

Section: Resultsmentioning

confidence: 99%

“…In Table 3, the estimated errors are presented. In the intermediate concentration estimation, the error must be improved if the relative error criterion is taken into consideration, and also the ITAE (28) because the final error seems to be large [14]. Both criteria are shown in a relative way, dividing by the maxima values to have a better idea about the observer performance because different concentration magnitudes were obtained.…”

Section: Resultsmentioning

confidence: 99%

“…This work shows a relatively simple implementation against a more complicated design, for example, the use of super-twisting [12] or sliding mode observers [13]. To guarantee stability, an LMI approach was used to propose the matrices used for the observers [14]. A comparison between this approach and a fuzzy sliding mode observes is shown to have a better idea about the observer performance [13].…”

Section: Introductionmentioning

confidence: 99%

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Interval Type-2 Fuzzy Observers Applied in Biodegradation

Márquez-Vera

Rodríguez-Romero

Márquez-Vera

et al. 2021

IJRCS

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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.

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Section: Resultsmentioning

confidence: 99%

Section: Resultsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Interval Type-2 Fuzzy Observers Applied in Biodegradation

Márquez-Vera

Rodríguez-Romero

Márquez-Vera

et al. 2021

IJRCS

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“…In practice, many engineering systems are subject to hard-limitations in their inputs due to physical constraints, such as power systems (Soliman and Yousef, 2015), DC-DC converters (Moreno-Valenzuela and Guzman-Guemez, 2016), fermentation processes (Márquez-Vera et al, 2018), and aircraft systems (Wu et al, 2000). These systems require some additional conditions in the design phase, that is, taking into account control constraints while ensuring stability under a certain level of performance.…”

Section: Introductionmentioning

confidence: 99%

Constrained stochastic control of positive Takagi-Sugeno fuzzy systems with Markov jumps and its application to a DC-DC boost converter

Aatabe

Guezar

Bouzahir

et al. 2020

Transactions of the Institute of Measurement and Control

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This paper presents a stabilization control for positive, Takagi-Sugeno fuzzy systems subject to Markov jump parameters. In the continuous-time formulation, the approach guarantees mean-square stability with constraints on the control—the main condition hinges upon linear matrix inequalities. The proposed method’s usefulness is illustrated by a practical-oriented example, which was designed to control the output voltage of a DC-DC boost converter subject to both voltage and load variations driven by a Markov chain.

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“…The observer–controller methods for T–S fuzzy systems can be categorised as two cases according to the property of premise variables. The first case refers to known premise variables (KPVs) as in [14–16]; the second case refers to the unknown premise variables (UPVs), for this situation, the membership functions also depend on the estimated premise variables [17]. Since the UPV case is a more general situation in real engineering applications, it has drawn much more attention in recent years: stability conditions of the observer–controller are derived separately based on the Lipschitz hypothesis in [18].…”

Section: Introductionmentioning

confidence: 99%