Simplified Interval Observer Scheme: A New Approach for Fault Diagnosis in Instruments

Martínez-Sibaja, Albino; Astorga‐Zaragoza, C.M.; Alvarado-Lassman, Alejandro; Posada-Gómez, Rubén; Aguila-Rodríguez, Gerardo; Rodríguez-Jarquín, José Pastor; Medina, Manuel Adam

doi:10.3390/s110100612

Cited by 16 publications

(11 citation statements)

References 8 publications

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“…The proposed method is evaluated via numerical simulations by using a fourth-order mathematical model which has been previously described and validated by Martínez-Sibaja et al (2011). This model represents an upflow anaerobic sludge blanket bioreactor (UASB).…”

Section: Application: An Anaerobic Bioreactormentioning

confidence: 99%

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Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

López‐Estrada

Ponsart

Astorga‐Zaragoza

et al. 2015

International Journal of Applied Mathematics and Computer Science

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This paper addresses the design of a state estimation and sensor fault detection, isolation and fault estimation observer for descriptor-linear parameter varying (D-LPV) systems. In contrast to where the scheduling functions depend on some measurable time varying state, the proposed method considers the scheduling function depending on an unmeasurable state vector. In order to isolate, detect and estimate sensor faults, an augmented system is constructed by considering faults to be auxiliary state vectors. An unknown input LPV observer is designed to estimate simultaneously system states and faults. Sufficient conditions to guarantee stability and robustness against the uncertainty provided by the unmeasurable scheduling functions and the influence of disturbances are synthesized via a linear matrix inequality (LMI) formulation by considering H∞ and Lyapunov approaches. The performances of the proposed method are illustrated through the application to an anaerobic bioreactor model.

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Section: Application: An Anaerobic Bioreactormentioning

confidence: 99%

“…The inputs variables are: u 1 (t) = D(t), the dilution rate, and u 2 (t) = s i 1 (t), the concentration of COD in the yield affluent. From the model given by Martínez-Sibaja et al (2011), the following nonlinear descriptor system is deduced:ẋ…”

Section: Application: An Anaerobic Bioreactormentioning

confidence: 99%

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

López‐Estrada

Ponsart

Astorga‐Zaragoza

et al. 2015

International Journal of Applied Mathematics and Computer Science

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“…Next a simplified ADM1 mathematical model used in [18] is considered, given by the mass balance equations:…”

Section: Model Of Anaerobic Bioprocess and Control Goalmentioning

confidence: 99%

“…Much more, by controlling S 1 it is possible to guarantee a desired methane production [3,16]. As control input we chose, like in [18], the dilution rate D u = . Since in model (1) the relative degree (i.e.…”

Section: Ch Qmentioning

confidence: 99%

“…1) under more realistic conditions: the concentration S 1,in is not measurable, that is in model (5) The control objective is the same as in the previous case. Under these conditions, we propose a robust-adaptive controller derived from (18), which uses a linearizing control law coupled with the interval observer (10) used for the reconstruction of unmeasured states, and with the parameter estimator (17) for the unknown kinetics of the process. This estimator also utilizes the information provided by the interval observer (10).…”

Section: A Robust-adaptive Control Strategymentioning

confidence: 99%

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Adaptive and robust-adaptive control schemes for an anaerobic bioprocess with biogas production

Petre

Selişteanu

2013

2013 17th International Conference on System Theory, Control and Computing (ICSTCC)

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This paper presents the design of adaptive and robust-adaptive control strategies for an anaerobic bioprocess with biogas production. The design schemes are developed under the realistic assumption that both bacterial growth rates and influent flow rates are time-varying and uncertain, but some lower and upper bounds of these uncertainties are known. The proposed control structures are achieved by combining a linearizing control law with a state asymptotic observer or an interval observer, and with a parameter estimator used for online estimation of unknown kinetics of the process. Numerical simulations are performed to test the proposed algorithms.

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State estimation of system with bounded uncertain parameters: Interval multimodel approach

Ichalal

Marx

Maquin

et al. 2018

Adaptive Control & Signal

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The objective of this study is the analysis of dynamic systems represented by a multimodel expression with variable parameters. Changes in these parameters are unknown but bounded. Since it is not possible to estimate these parameters over time, the simulation of such systems requires the consideration of all possible values taken by these parameters. More precisely, the goal is to determine, at any moment, the smallest set containing all the possible values of the state vector simultaneously compatible with the state equations and with a priori known bounds of the uncertain parameters. This set will be characterized by two trajectories corresponding to the lower and upper limits of the state at every moment.This characterization can be realized by a direct simulation of the system, given the bounds of its parameters. It can also be implemented with a Luenberger-type observer, fed with the system measurements. KEYWORDSbounded uncertainties, interval observers, multimodel technique, uncertain systems INTRODUCTIONAs widely known, one of the main difficulties in system simulation, control, or estimation is dealing with uncertainties. These uncertainties may affect the input or output signals of the system (eg, unknown input, disturbance, measurement noises, etc) as well as the system model itself (eg, nonmodeled dynamics, unknown parameter, etc). The uncertainties may also be of different natures: total lack of information (unknown value of a parameter) or partial knowledge (upper and lower bounds, statistical properties, etc). This paper deals with systems with uncertain parameters.Even a low magnitude change in some parameters may have a significant impact on the system behavior and, namely, on the system state trajectory. Uncertain parameters can be considered from two main points of view: the stochastic and the deterministic ones. In the first approach, the uncertain parameters are assumed to be the results of random process realizations. It then needs to choose the probability density functions and their parameters describing the system's uncertain parameters. In the deterministic approach, no statistical models of the parameters are assumed to be available, and only the upper and lower bounds of the parameter values are known. This approach, also known as the interval approach, is adopted in this paper.The search for trajectories, which are solutions of differential inclusions, 1 were the starting point of the large amount of works on stability, stabilization, and state estimation. In the latter topic, our communication follows the pioneering work of Gouzé et al, 2 which proposed the synthesis of the interval-type observer to reconstruct the system state 480 ;32:480-493. ICHALAL ET AL. 481from measurements of inputs and outputs. Since then, many results were published on designing observers adapted to nonlinear systems with uncertain but bounded parameters. [3][4][5][6] The model-based state estimation techniques in the context of bounded uncertainties can be classified into two categories. The first one is ba...

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Simplified Interval Observer Scheme: A New Approach for Fault Diagnosis in Instruments

Cited by 16 publications

References 8 publications

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

Robust sensor fault estimation for descriptor-LPV systems with unmeasurable gain scheduling functions: Application to an anaerobic bioreactor

Adaptive and robust-adaptive control schemes for an anaerobic bioprocess with biogas production

State estimation of system with bounded uncertain parameters: Interval multimodel approach

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