Two state estimators for the barium sulfate precipitation in a semi-batch reactor

Mangold, Michael; Bück, Andreas; Schenkendorf, René; Steyer, Christiane; Voigt, Andreas; Sundmacher, Kai

doi:10.1016/j.ces.2008.05.039

Cited by 18 publications

(23 citation statements)

References 33 publications

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“…Additionally, more general graph-based concepts were developed [24,25]. However, the application of these concepts to population balance models is scarce and mostly relies on a prior discretization step that transforms the infinite dimensional system to a high-dimensional system of ODEs (e.g., [26]). Recently, a new concept was presented that allows statements on the observability of ensemble systems [27].…”

Section: Observability Of Multicellular Systems Dynamicsmentioning

confidence: 99%

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A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

Dürr

Waldherr

2018

Processes

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Multicellular systems play an important role in many biotechnological processes. Typically, these exhibit cell-to-cell variability, which has to be monitored closely for process control and optimization. However, some properties may not be measurable due to technical and financial restrictions. To improve the monitoring, model-based online estimators can be designed for their reconstruction. The multicellular dynamics is accounted for in the framework of population balance models (PBMs). These models are based on single cell kinetics, and each cellular state translates directly into an additional dimension of the obtained partial differential equations. As multicellular dynamics often require detailed single cell models and feature a high number of cellular components, the resulting population balance equations are often high-dimensional. Therefore, established state estimation concepts for PBMs based on discrete grids are not recommended due to the large computational effort. In this contribution a novel approach is proposed, which is based on the approximation of the underlying number density functions as the weighted sum of Gaussian distributions. Thus, the distribution is described by the characteristic properties of the individual Gaussians, like the mean and covariance. Thereby, the complex infinite dimensional estimation problem can be reduced to a finite dimension. The characteristic properties are estimated in a recursive approach. The method is evaluated for two academic benchmark examples, and the results indicate its potential for model-based online reconstruction for multicellular systems.

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Section: Observability Of Multicellular Systems Dynamicsmentioning

confidence: 99%

“…Furthermore, the system could also be tested for structural observability [24,26] posing a necessary condition on local observability. It has to be mentioned that these conditions are only valid for individual state vectorsẋ (i) , but not for the whole system, i.e., all GMDs i = 1, .…”

Section: Observability Of Multicellular Systems Dynamicsmentioning

confidence: 99%

A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

Dürr

Waldherr

2018

Processes

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“…In the last years, the ProMoT/Diana system has proven useful for various challenging modeling tasks, e.g., in the area of chemical engineering systems [13,14], energy systems [15], and biological systems [16,17]. ProMoT and Dia-na are free open-source software.…”

Section: Introductionmentioning

confidence: 99%

Development and Nonlinear Analysis of Dynamic Plant Models in ProMoT /Diana

Mangold

Khlopov

Danker

et al. 2014

Chemie Ingenieur Technik

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In the process design of chemical production plants, dynamic simulation plays an important role. This paper gives a short introduction to the process modeling tool ProMoT and the simulation tool Diana. Both are open‐source programs intended for the dynamic analysis of chemical engineering and biological systems. They support the implementation and analysis of large nonlinear differential algebraic systems. An overview is given on the functionality of ProMoT and Diana. The use of the tools is illustrated by their application to an innovative fluidized bed crystallization process.

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“…Note that in a number of other applications for which similar ODE observers were applied, the PDE represents a gradient or range in the product quality, and not the reactor conditions. For instance Mangold et al proposed an observer for particle size in precipitation reactions, Edouard et al estimated the particle‐size distribution in emulsion polymerization using a high gain observer and Zhang et al used a high gain observer to estimate the zeroth moment of the crystal size distribution, which is then controlled using the reactor temperature. Using the method of moments approximates the PDE to a very small number of ODEs, but is out of the scope of this work.…”

Section: Introductionmentioning

confidence: 99%

A 2‐D observer to estimate the reaction rate in a stopped flow fixed bed reactor for gas phase olefin polymerization

et al. 2014

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A two-dimensional high gain observer has been constructed to estimate the reaction rate parameters in a laboratory scale stopped flow fixed bed reactor for gas phase ethylene polymerization. The observer is based on the heat balances of a validated model of the reactor and the measured variable is the outlet temperature of the fixed bed. To create an observable system of equations, the polymerization rate is considered in two parts, an activation energy term and a lumped parameter. The effective radial conductivity in the fixed bed and the heat-transfer coefficient at the wall are considered separately. The polymerization rate is calculated from the observer results and is in good agreement with the measured data and calculated values.

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Two state estimators for the barium sulfate precipitation in a semi-batch reactor

Cited by 18 publications

References 33 publications

A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

A Novel Framework for Parameter and State Estimation of Multicellular Systems Using Gaussian Mixture Approximations

Development and Nonlinear Analysis of Dynamic Plant Models in ProMoT /Diana

A 2‐D observer to estimate the reaction rate in a stopped flow fixed bed reactor for gas phase olefin polymerization

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