Nonlinear model reduction for simulation and control of rapid thermal processing

Aling, H.; Banerjee, S.; Bangia, Anil K.; Cole, Veronica; Ebert, J.L.; Emami-Naeini, Abbas; Jensen, Klavs F.; Kevrekidis, Ioannis G.; Shvartsman, Stanislav Y.

doi:10.1109/acc.1997.608956

Cited by 37 publications

(27 citation statements)

References 20 publications

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“…We conclude that the numerical technique developed produces accurate, low-order simulation results, especially at the collocation points of the coarse gridr which is most relevant to comparisons with experimental measurements. Further refinements to the numerical technique are currently under investigation, such as using the "acceleration" POD modes in place of the Bessel's functions ψ n (Aling, et al 1997;Sirovich, 1991).…”

Section: Results and Conclusionmentioning

confidence: 99%

“…Integrating the remaining ordinary differential equations in time subject to (7) defines the nonlinear Galerkin procedure (Aling, et al 1997;Deane, et al, . .. ... 1991; Dettori, et al, 1995;Graham, and Kevrekidis 1996;Sirovich, 1991).…”

Section: Nonlinear Weighted Residual Methodsmentioning

confidence: 99%

“…Because of the complexity of some of the simulators developed and the computational expenses of performing simulations for process optimization and control, interest in developing reduced-order models from the high fidelity simulations has emerged (Aling et al, 1996(Aling et al, , 1997Theodoropoulou et al, 1998). These models are based on collecting "snapshots" of the RTP system at points in time during processing cycles designed to excite as many spatial temperature modes as possible, and processing them with the Proper Orthogonal Decomposition method (Sirovich, 1987) to determine the dominant temperature spatial modes.…”

Section: Introductionmentioning

confidence: 99%

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Model reduction for a tungsten chemical vapor deposition system

Chang

Adomaitis

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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ISR develops, applies and teaches advanced methodologies of design and analysis toAbstract: A model of a tungsten chemical vapor deposition (CVD) system is developed to study the CVD system thermal dynamics and wafer temperature nonuniformities during a processing cycle. We develop a model for heat transfer in the system's wafer/susceptor/guard ring assembly and discretize the modeling equation with a multiple-grid, nonlinear collocation technique. This weighted residual method is based on the assumption that the system's dynamics are governed by a small number of modes and that the remaining modes are slaved to these slow modes. Our numerical technique produces a model that is effectively reduced in its dynamical dimension, while retaining the resolution required for the wafer assembly model. The numerical technique is implemented with only moderately more effort than the traditional collocation or pseudospectral techniques. Furthermore, by formulating the technique in terms of a collocation procedure, the relationship between temperature measurements made on the wafer and the simulator results produced with the reduced-order model remain clear.

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Section: Results and Conclusionmentioning

confidence: 99%

Section: Nonlinear Weighted Residual Methodsmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

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Model reduction for a tungsten chemical vapor deposition system

Chang

Adomaitis

1998

Proceedings of the 1998 American Control Conference. ACC (IEEE Cat. No.98CH36207)

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“…Assuming that the unresolved modes evolves on a much smaller time scale compared to the resolved modes, and considering that the resolved modes concentrate a higher energy than the unresolved ones (or equivalently the temporal p-modes exhibit much higher amplitudes than the q ones), the following approximate resolution of the second equation can be proposed [1,11]:…”

Section: Unresolved Modes Modeling With Nonlinear Galerkin Methodsmentioning

confidence: 99%

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

Artana¹,

Cammilleri²,

Carlier³

et al. 2012

Journal of Computational Physics

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In this work we propose and evaluate two variational data assimilation techniques for the estimation of low order surrogate experimental dynamical models for fluid flows. Both methods are built from optimal control recipes and rely on proper orthogonal decomposition and a Galerkin projection of the Navier Stokes equation. The techniques proposed differ in the control variables they involve. The first one introduces a weak dynamical model defined only up to an additional uncertainty time-dependent function whereas the second one, handles a strong dynamical constraint in which the dynamical system's coefficients constitute the control variables. Both choices correspond to different approximations of the relation between the reduced basis on which is expressed the motion field and the basis components that have been neglected in the reduced order model construction. The techniques have been assessed on numerical data and for real experimental conditions with noisy Image Velocimetry data.

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“…Some of them include additional dissipative models [12] or rely on nonlinear Galerkin projection techniques [1,4,13]. Robust techniques based on optimal control strategies have been also proposed for building reduced dynamical models from noisy data [9,15] and incomplete knowledge of the actual flow dynamics (i.e.…”

Section: Introductionmentioning

confidence: 99%

POD-spectral decomposition for fluid flow analysis and model reduction

Cammilleri

Guéniat

Carlier

et al. 2013

Theor. Comput. Fluid Dyn.

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We propose an algorithm that combines Proper Orthogonal Decomposition with a spectral method to analyse and extract from time data series of velocity fields, reduced order models of flows. The flows considered in this study are assumed to be driven by non linear dynamical systems exhibiting a complex behavior within quasi-periodic orbits in the phase space. The technique is appropiate to achieve efficient reduced order models even in complex cases for which the flow description requires a discretization with a fine spatial and temporal resolution. The proposed analysis enables to decompose complex flow dynamics into modes oscillating at a single frequency. These modes are associated with different energy levels and spatial structures. The approach is illustrated using time resolved PIV data of a cylinder wake flow with associated Reynolds number equal to 3900.

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Nonlinear model reduction for simulation and control of rapid thermal processing

Cited by 37 publications

References 20 publications

Model reduction for a tungsten chemical vapor deposition system

Model reduction for a tungsten chemical vapor deposition system

Strong and weak constraint variational assimilations for reduced order fluid flow modeling

POD-spectral decomposition for fluid flow analysis and model reduction

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