State estimation of a stratified storage tank

Kreuzinger, Tobias; Bitzer, Matthias; Marquardt, Wolfgang

doi:10.1016/j.conengprac.2007.04.013

Cited by 32 publications

(9 citation statements)

References 16 publications

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“…[11] However UKF has been barely applied to solve chemical engineering problems especially for nonlinear distributed parameter systems. [12] One of the successful applications has been the state estimation of a lumped parameter CSTR system by Romanenko and Castro. [13] Another one is for the stratified domestic hot water storage tank described by nonlinear PDEs.…”

Section: Introductionmentioning

confidence: 99%

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State estimation of a solid‐state polymerization reactor for PET based on improved SR‐UKF

Liu

2009

Asia-Pacific J Chem Eng

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A state estimator for the continuous solid-state polymerization (SSP) reactor of polyethylene terephthalate (PET) is designed in this study. Because of its invalidity in the application to some of the practical examples such as SSP processes, the square-root unscented Kalman filter (SR-UKF) algorithm is improved for the state estimation of arbitrary nonlinear systems with linear measurements. Discussions are given on how to avoid the filter invalidation and accumulating additional error. Orthogonal collocation method has been used to spatially discretize the reactor model described by nonlinear partial differential equations. The reactant concentrations on chosen collocation points are reconstructed from the outlet measurements corrupted with a large noise. Furthermore, the error performance of the developed ISR-UKF is investigated under the influence of various initial parameters, inaccurate measurement noise parameters and model mismatch. Simulation results show that this technique can produce fast convergence and good approximations for the state estimation of SSP reactor. 

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Section: Introductionmentioning

confidence: 99%

“…[13] Another one is for the stratified domestic hot water storage tank described by nonlinear PDEs. [12] The estimation used both a distributed parameter observer and the standard UKF posterior to the model discretization.…”

Section: Introductionmentioning

confidence: 99%

State estimation of a solid‐state polymerization reactor for PET based on improved SR‐UKF

Liu

2009

Asia-Pacific J Chem Eng

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“…Then, traditional state estimation and/or control methods from finite-dimensional system theory can be exploited for the resulting early lumped systems. The widely-utilized early lumping methods are reported as: modal analysis (Galerkin's method) [47,48], finite difference [49], proper orthogonal decomposition (POD) [50,51], finite element method (FEM) [52], FEM Galerkin cubic b-splines method [53], etc. In contrast, late lumping means that one conducts observer, filter, and/or controller design steps on the original infinite-dimensional space and applies spatial approximation later for simulation purposes, where the backstepping method [54,55], the adjoint-based approach [56], and the Crank-Nicolson method [57] are widely used.…”

Section: Introductionmentioning

confidence: 99%

Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems

Xie

Dubljević

2019

Processes

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As the optimal linear filter and estimator, the Kalman filter has been extensively utilized for state estimation and prediction in the realm of lumped parameter systems. However, the dynamics of complex industrial systems often vary in both spatial and temporal domains, which take the forms of partial differential equations (PDEs) and/or delay equations. State estimation for these systems is quite challenging due to the mathematical complexity. This work addresses discrete-time Kalman filter design and realization for linear distributed parameter systems. In particular, the structural- and energy-preserving Crank–Nicolson framework is applied for model time discretization without spatial approximation or model order reduction. In order to ensure the time instance consistency in Kalman filter design, a new discrete model configuration is derived. To verify the feasibility of the proposed design, two widely-used PDEs models are considered, i.e., a pipeline hydraulic model and a 1D boundary damped wave equation.

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“…In Alonso et al the most appropriate sensor type and locations are chosen through a guided search algorithm that minimizes orthonormality distortion, using a low dimensional representation of the original distributed system. As the system observability also depends on the inputs, Kreuzinger et al indicate that simulation is the best way to investigate the system dynamics to deduce reasonable sensor locations and appropriate simplifications. They implemented their results together with an unscented Kalman filter or a Luenberger structure observer to monitor a stratified storage tank.…”

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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State estimation of a stratified storage tank

Cited by 32 publications

References 16 publications

State estimation of a solid‐state polymerization reactor for PET based on improved SR‐UKF

State estimation of a solid‐state polymerization reactor for PET based on improved SR‐UKF

Discrete-Time Kalman Filter Design for Linear Infinite-Dimensional Systems

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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