A method for computing the partial derivatives of experimental data

Yeow, Y. Leong; Isac, Jordan; Khalid, Fathullah A.; Leong, Yee-Kwong; Lubansky, A.S.

doi:10.1002/aic.12236

Cited by 8 publications

(13 citation statements)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…With the imposition of the additional condition of negative second derivatives (if required), it has been successful in converting experimentally measured oxide layer thickness data into monotonic decreasing instantaneous rate of oxide growth. This success is attributed to the adjustable regularization parameter that maintains a fine balance between noise amplification inherent of numerical differentiation and the retention of as much of the physical information in the time‐thickness data as possible . This is a major improvement over unregularized numerical differentiation procedure such as the various finite difference schemes or differentiation based on spline curves such the popular Savitzky–Golay method …”

Section: Discussionmentioning

confidence: 99%

Obtaining model‐independent growth rates from experimental data of dry thermal oxidation of silicon

2014

Self Cite

View full text Add to dashboard Cite

Empirical time-oxide layer thickness data of dry thermal oxidation of silicon were converted numerically into instantaneous growth rates by Tikhonov regularization. These growth rates are independent of any assumed kinetics of oxidation or functional form of the original data and can, therefore, be used in model testing of this important industrial process. A number of numerical issues in the Tikhonov regularization computation, for example, the expected monotonic decrease in growth rate with time and the large time span of some of the datasets, are addressed. Numerical results indicate that kinetic data presented in the form of growth rate-oxide layer thickness plots are more sensitive than the traditional time-oxide thickness plots for use in model testing and for parameter determination. The advantages of this new approach are demonstrated by three case studies covering the complete oxide thickness spectrum of interest to the microelectronic industry.

show abstract

Section: Discussionmentioning

confidence: 99%

Obtaining model‐independent growth rates from experimental data of dry thermal oxidation of silicon

2014

Self Cite

View full text Add to dashboard Cite

show abstract

“…Finally, it should be noted that, while this estimation scheme was applied here in the context of modifier adaptation, the theory is by no means limited to this context and could perhaps find use in other fields where gradient estimation is important [13], [14], [15].…”

Section: Discussionmentioning

confidence: 99%

Exploiting local quasiconvexity for gradient estimation in modifier-adaptation schemes

Bunin

François

Bonvin

2012

2012 American Control Conference (ACC)

View full text Add to dashboard Cite

Abstract-A new approach for gradient estimation in the context of real-time optimization under uncertainty is proposed in this paper. While this estimation problem is often a difficult one, it is shown that it can be simplified significantly if an assumption on the local quasiconvexity of the process is made and the resulting constraints on the gradient are exploited. To do this, the estimation problem is formulated as a constrained weighted least-squares problem with appropriate choice of the weights. Two numerical examples illustrate the effectiveness of the proposed method in converging to the true process optimum, even in the case of significant measurement noise.

show abstract

“…More advanced methods of estimating the gradient from discrete measurements are certainly possible (Yeow et al, 2010;Bunin et al, 2013a), but would require greater computational effort, whereas a least-squares regression is easily carried out within the 60-ms time constraint.…”

Section: Choice and Configuration Of Rto Algorithmmentioning

confidence: 99%

Iterative Controller Tuning by Real-Time Optimization

Bunin

François

Bonvin

2013

IFAC Proceedings Volumes

View full text Add to dashboard Cite

The present article looks at the problem of iterative controller tuning, where the parameters of a given controller are adapted in an iterative manner to bring the user-defined performance metric to a local minimum for some repetitive process. Specifically, we cast the controller tuning problem as a real-time optimization (RTO) problem, which allows us to exploit the available RTO theory to enforce both convergence and performance guarantees. We verify the effectiveness of the proposed methodology on an experimental torsional system and note that the results are particularly promising considering the simplicity of the method.

show abstract

A method for computing the partial derivatives of experimental data

Cited by 8 publications

References 11 publications

Obtaining model‐independent growth rates from experimental data of dry thermal oxidation of silicon

Obtaining model‐independent growth rates from experimental data of dry thermal oxidation of silicon

Exploiting local quasiconvexity for gradient estimation in modifier-adaptation schemes

Iterative Controller Tuning by Real-Time Optimization

Contact Info

Product

Resources

About