Application of a Robust Interval Observer to an Anaerobic Digestion Process

Alcaraz-González, V.; Steyer, Jean‐Philippe; Harmand, Jérôme; Rapaport, Alain; González‐Álvarez, V.; Pelayo-Ortíz, Carlos

doi:10.1002/apj.5500130308

Cited by 29 publications

(53 citation statements)

References 9 publications

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“…Another variant of stability proof for Proposition 3 can be found in Alcaraz-Gonzlez et al (2005). Consequently, Proposition 3 fixes the conditions under which the distributed parameter system (3) possesses the input-to-state stability property Dashkovskiy et al (2011);Dashkovskiy and Mironchenko (2013), where boundary conditions α, β influence the external disturbance r and the initial conditions as well.…”

Section: Heat Equationmentioning

confidence: 96%

On design of interval observers for parabolic PDEs

et al. 2017

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The problem of state estimation for heat non-homogeneous equations under distributed in space measurements is considered. An interval observer is designed, described by Partial Differential Equations (PDEs), for uncertain distributed parameter systems without application of finite-element approximations. Conditions of boundedness of solutions of interval observer with non-zero boundary conditions and measurement noise are proposed. The results are illustrated by numerical experiments with an academic example.

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Section: Heat Equationmentioning

confidence: 96%

On design of interval observers for parabolic PDEs

et al. 2017

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“…The structures of interval observers can be found in (Gouzé et al, 2000;Alcaraz-González et al, 2004;Rapaport and Dochain, 2005). In (Alcaraz-González et al, 2004), it was shown that, if some conditions are satisfied by the system (24), then the interval observer for this system is stable and robust in spite of the uncertainty in the non-linear part of the system dynamics, inputs and initial conditions.…”

Section: Interval Observermentioning

confidence: 99%

“…In (Alcaraz-González et al, 2004), it was shown that, if some conditions are satisfied by the system (24), then the interval observer for this system is stable and robust in spite of the uncertainty in the non-linear part of the system dynamics, inputs and initial conditions. We havė…”

Section: Interval Observermentioning

confidence: 99%

“…Moreover, in (Rapaport and Dochain, 2005) it was shown that if state measurements are uncertain, the interval observer can still be stable. An application of the interval observer to the wastewater treatment process can be found in (Gouzé et al, 2000;Hadj-Sadok and Gouzé, 2001;Harmand and Rapaport, 2002;Alcaraz-González et al, 2004).…”

Section: Interval Observermentioning

confidence: 99%

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Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator

Łangowski¹,

Brdyś²

2007

International Journal of Applied Mathematics and Computer Science

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This paper describes the design of an interval observer for the estimation of unmeasured quality state variables in drinking water distribution systems. The estimator utilizes a set bounded model of uncertainty to produce robust interval bounds on the estimated state variables of the water quality. The bounds are generated by solving two differential equations. Hence the numerical efficiency is sufficient for on-line monitoring of the water quality. The observer is applied to an exemplary water network and its performance is validated by simulations.

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“…Our approach consist to provide an upper observer of the system and through theory of monotone dynamical systems, we prove global partial stabilization of the upper observer of substrate concentration s about s d and by the way keeping s ≤ s d . Many works are interested by similar problems where issues of : optimal control [12,13], observers [1,2,5,9,10,12,15], simulation [6,14], have been studied. Robust control has been also treated, [4,5,7,8], but without recycle biomass.…”

Section: Introductionmentioning

confidence: 99%

Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model

Serhani

Raïssi

Cartigny

2009

Math. Model. Nat. Phenom.

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Abstract. In this work we deal with the design of the robust feedback control of wastewater treatment system, namely the activated sludge process. This problem is formulated by a nonlinear ordinary differential system. On one hand, we develop a robust analysis when the specific growth function of the bacterium µ is not well known. On the other hand, when also the substrate concentration in the feed stream s in is unknown, we provide an observer of system and propose a design of robust feedback control in term of recycle rate, in order to keep the pollutant concentration lower than an allowed maximum level s d .

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Application of a Robust Interval Observer to an Anaerobic Digestion Process

Cited by 29 publications

References 9 publications

On design of interval observers for parabolic PDEs

On design of interval observers for parabolic PDEs

Monitoring of Chlorine Concentration in Drinking Water Distribution Systems Using an Interval Estimator

Robust Feedback Control Design for a Nonlinear Wastewater Treatment Model

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