An approach to the selection of optimal sensor locations in distributed parameter systems

Wouwer, Alain Vande; Point, Nicolas; Porteman, S.; Remy, M.

doi:10.1016/s0959-1524(99)00048-7

Cited by 121 publications

(46 citation statements)

References 12 publications

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“…In particular efficient oxygen estimation schemes need be developed to enable the reduction of the number of sensors [30]. These issues may be properly addressed in the framework of reduced order models (ROM), i.e.…”

Section: State Estimation Of Process Variablesmentioning

confidence: 99%

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On-line estimation in a distributed parameter bioreactor: Application to the gluconic acid production

García¹,

Vilas²,

Balsa‐Canto³

et al. 2011

Computers & Chemical Engineering

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This work presents a methodology which exploits the underlying biochemical structure of bioprocesses to estimate concentrations in aerobic fermenters from oxygen measurements. Although a number of estimators have been proposed over the years in the literature, the methodology proposed in this work is able to operate in transient conditions while does not require the knowledge of the growth kinetics. In addition, it can be also applied to fermenters where the spatial distribution of the concentrations is relevant. In this case, we propose a systematic approach to optimally locate the sensors based on the use of reduced order models. This method allows the reconstruction of the oxygen concentrations from a limited number of sensors. Finally, the methodology proposed will be illustrated on a horizontal tubular reactor for the production of gluconic acid by free-growth of Aspergillus niger.

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Section: State Estimation Of Process Variablesmentioning

confidence: 99%

“…In addition, the estimations of the non-measurable variables should be combined with measurements of the remaining variables covering the whole spatial domain. This requires having access to a large number of on-line sensors which may be too expensive or physically impossible to be implemented in the desired process [12,30,1].…”

Section: Introductionmentioning

confidence: 99%

On-line estimation in a distributed parameter bioreactor: Application to the gluconic acid production

García¹,

Vilas²,

Balsa‐Canto³

et al. 2011

Computers & Chemical Engineering

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show abstract

“…Moreover, complete measurements of the field x m are not usually available due to the large number of sensors required, which calls for efficient field reconstruction schemes from a reduced number of sensors 6 . These questions will be properly addressed next in the framework of reduced order modelling (ROM) of dissipative systems 7,12 .…”

Section: Observer Implementationmentioning

confidence: 99%

“…In this class of systems, the mass and energy balances result into a nonlinear set of partial differential equations whose solution usually involves the integration of a large set of ordinary differential equations 5 . In addition the observer must be supplied with on-line state measurements covering the whole spatial domain which are usually unavailable due to the limited number of sensors 4,6,7 .…”

Section: Introductionmentioning

confidence: 99%

Exponential observers for distributed tubular (bio)reactors

García¹,

Vilas²,

Banga³

et al. 2008

AIChE Journal

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In this work, the dissipative nature of spatially distributed process systems is exploited to develop efficient exponential state observers based on a low dimensional dynamic representation of the original set of partial differential equations. The approach we suggest combines standard observer design techniques for reactors where the reaction rates are unknown with efficient model reduction methodologies based on projection of the original concentration and temperature fields on low dimensional subspaces capturing the slow dynamics of the process. The global exponential stability of the resulting observer is derived combining classical Lyapunov analysis with a transformation that allows us to obtain a diffusion system from a diffusionconvection system. In addition aspects related to the location of sensors and their influence on the ability to reconstruct the necessary fields to feed the observer will also be considered.

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“…Nahor et al (2003) minimised the ratio of the largest to the smaller eigenvalue of the FIM to compute optimal temperature sensor positions for food processes. To the best of our knowledge, these techniques have not been applied yet to systems described by partial differential equations, in spite of their resolute advantages (Uciński, 1999, Löhner and Camelli, 2005, Waterhouse et al, 2009, Vande, 2000, Venkateswarlu and Kumar, 2006, Punithakumar et al, 2006, Peng, 2005, Cotae et al, 2008, Balsa-Canto et al, 2008. Christofides and Antoniades (2000, 2001 presented new approaches to calculate the optimal actuator/sensor locations of uncertain transportreaction systems under control.…”

Section: Introductionmentioning

confidence: 99%

Optimal measurement locations for parameter estimation of non linear distributed parameter systems

Alaña

2010

Braz. J. Chem. Eng.

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-A sensor placement approach for the purpose of accurately estimating unknown parameters of a distributed parameter system is discussed. The idea is to convert the sensor location problem to a classical experimental design. The technique consists of analysing the extrema values of the sensitivity coefficients derived from the system and their corresponding spatial positions. This information is used to formulate an efficient computational optimum experiment design on discrete domains. The scheme studied is verified by a numerical example regarding the chemical reaction in a tubular reactor for two possible scenarios; stable and unstable operation conditions. The resulting approach is easy to implement and good estimates for the parameters of the system are obtained. This study shows that the measurement location plays an essential role in the parameter estimation procedure.

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An approach to the selection of optimal sensor locations in distributed parameter systems

Cited by 121 publications

References 12 publications

On-line estimation in a distributed parameter bioreactor: Application to the gluconic acid production

On-line estimation in a distributed parameter bioreactor: Application to the gluconic acid production

Exponential observers for distributed tubular (bio)reactors

Optimal measurement locations for parameter estimation of non linear distributed parameter systems

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