Positive observers for linear positive systems in a Hilbert lattice space

2020 ◽  
Author(s):  
Abdellaziz Binid ◽  
Mohammed Elarbi Achhab ◽  
Mohamed Laabissi
Keyword(s):  
Plug Flow ◽  
The State ◽  
Observer Design ◽  
Positive Systems ◽  
Reactor Model ◽  
Infinite Dimensional ◽  
Bounded Perturbation ◽  
Lattice Space ◽  
Hilbert Lattice ◽  
Positive Observer

Abstract In this work, we investigate the question of designing a positive observer for a class of infinite dimensional linear positive systems. We present a new observer design based on a classical Luenberger-like observer. The proposed observer is positive. That is, it ensures that the state estimates are nonnegative at any time. The existence of such positive observers is proven by a specific choice of the observer gain and using positive bounded perturbation results. We show in particular that the error of the state estimation converges exponentially to zero. Finally, the main result is applied to an isothermal tubular (bio) reactor model, namely the plug-flow (bio) reactor model. The approach is illustrated by some numerical simulations.

scholarly journals Biofilm carrier migration model describes reactor performance

2017 ◽  
Vol 75 (12) ◽  
pp. 2818-2828 ◽  
Author(s):  
Joshua P. Boltz ◽  
Bruce R. Johnson ◽  
Imre Takács ◽  
Glen T. Daigger ◽  
Eberhard Morgenroth ◽  
...  
Keyword(s):  
Plug Flow ◽  
Biofilm Reactor ◽  
Bulk Liquid ◽  
Reactor Performance ◽  
Reactor Model ◽  
Operational Conditions ◽  
Limit Model ◽  
Biofilm Model ◽  
Reactor Models ◽  
The Impact

The accuracy of a biofilm reactor model depends on the extent to which physical system conditions (particularly bulk-liquid hydrodynamics and their influence on biofilm dynamics) deviate from the ideal conditions upon which the model is based. It follows that an improved capacity to model a biofilm reactor does not necessarily rely on an improved biofilm model, but does rely on an improved mathematical description of the biofilm reactor and its components. Existing biofilm reactor models typically include a one-dimensional biofilm model, a process (biokinetic and stoichiometric) model, and a continuous flow stirred tank reactor (CFSTR) mass balance that [when organizing CFSTRs in series] creates a pseudo two-dimensional (2-D) model of bulk-liquid hydrodynamics approaching plug flow. In such a biofilm reactor model, the user-defined biofilm area is specified for each CFSTR; thereby, Xcarrier does not exit the boundaries of the CFSTR to which they are assigned or exchange boundaries with other CFSTRs in the series. The error introduced by this pseudo 2-D biofilm reactor modeling approach may adversely affect model results and limit model-user capacity to accurately calibrate a model. This paper presents a new sub-model that describes the migration of Xcarrier and associated biofilms, and evaluates the impact that Xcarrier migration and axial dispersion has on simulated system performance. Relevance of the new biofilm reactor model to engineering situations is discussed by applying it to known biofilm reactor types and operational conditions.

scholarly journals Modelling of service reservoirs

2001 ◽  
Vol 3 (3) ◽  
pp. 165-172 ◽  
Author(s):  
Hoi Yeung
Keyword(s):  
Plug Flow ◽  
Flow Characteristics ◽  
Flow Distribution ◽  
Tracer Test ◽  
Computational Fluid Mechanics ◽  
Width Ratio ◽  
Dual Function ◽  
Water Age ◽  
Reactor Model ◽  
Increased Risk

Service reservoirs were built to provide the dual function of balancing supply with demand and provision of adequate head to maintain pressure throughout the distribution network. Changing demographics in the UK and reducing leakage have led to significant increases in water age and hence increased risk of poor water quality. Computational fluid mechanics has been used to study the behaviour of a range of service reservoirs with a rectangular plan form. Detailed analysis of flow distribution and water age suggests that tanks with horizontal inlets are better mixed when compared with vertical top water level inlets. With increasing length to width ratio, the flow characteristics of tanks with vertical inlets increasingly resemble plug flow. A new multi-channel reactor model was developed to model the recirculations in service reservoirs. This simple model can be used to characterise the flow characteristics of service reservoirs from tracer test results.

scholarly journals Observer Design for a Class of Exothermal Plug-Flow Tubular Reactors

2013 ◽  
Vol 2 (4) ◽  
Author(s):  
Nadia Barje ◽  
Mohammed Elarbi Achhab ◽  
Vincent Wertz
Keyword(s):  
Plug Flow ◽  
Observer Design ◽  
Tubular Reactors

Chemical Kinetic Analysis of a Flameless Gas Turbine Combustor

2008 ◽  
Author(s):  
G. Arvind Rao ◽  
Yeshayahou Levy ◽  
Ephraim J. Gutmark
Keyword(s):  
Combustion Chamber ◽  
Kinetic Analysis ◽  
Gas Turbine ◽  
Flame Temperature ◽  
Plug Flow ◽  
Combustion Process ◽  
Chemical Reactor ◽  
Chemical Kinetic ◽  
Combustion Regime ◽  
Reactor Model

Flameless combustion (FC) is one of the most promising techniques of reducing harmful emissions from combustion systems. FC is a combustion phenomenon that takes place at low O2 concentration and high inlet reactant temperature. This unique combination results in a distributed combustion regime with a lower adiabatic flame temperature. The paper focuses on investigating the chemical kinetics of an prototype combustion chamber built at the university of Cincinnati with an aim of establishing flameless regime and demonstrating the applicability of FC to gas turbine engines. A Chemical reactor model (CRM) has been built for emulating the reactions within the combustor. The entire combustion chamber has been divided into appropriate number of Perfectly Stirred Reactors (PSRs) and Plug Flow Reactors (PFRs). The interconnections between these reactors and the residence times of these reactors are based on the PIV studies of the combustor flow field. The CRM model has then been used to predict the combustor emission profile for various equivalence ratios. The results obtained from CRM model show that the emission from the combustor are quite less at low equivalence ratios and have been found to be in reasonable agreement with experimental observations. The chemical kinetic analysis gives an insight on the role of vitiated combustion gases in suppressing the formation of pollutants within the combustion process.

scholarly journals Interval Observer Design for Metzlerian Takagi-Sugeno Systems

2020 ◽  
Author(s):  
Dušan Krokavec ◽  
Anna Filasová
Keyword(s):  
Continuous Time ◽  
Observer Design ◽  
Asymptotic Convergence ◽  
Observer Error ◽  
Analysis And Design ◽  
Interval Observer ◽  
Takagi Sugeno ◽  
Positive Observer ◽  
The Relationship

The generalized interval observer design conditions for continuous-time Metzlerian Takagi-Sugeno systems are presented in the paper. Attention is focused on the analysis and design guaranteeing the asymptotic convergence of the interval observer error and positivity of interval observer state. The relationship between the nonnegativity of the observer gains and the corresponding positive observer state attractiveness is also shown. The method presented extends and generalizes the results that recently appeared in the literature.

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