Model-Based Control of Electroslag Remelting Process Using Unscented Kalman Filter

Seokyoung Ahn; Joseph J. Beaman; Rodney L. Williamson; David K. Melgaard

doi:10.1115/1.4000660

Journal of Dynamic Systems, Measurement, and Control | Volume 132 | Issue 1 | Research Paper

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Research Papers

Model-Based Control of Electroslag Remelting Process Using Unscented Kalman Filter

Seokyoung Ahn, Joseph J. Beaman, Rodney L. Williamson and David K. Melgaard

[+] Author and Article Information

Seokyoung Ahn

Department of Mechanical Engineering, University of Texas-Pan American, Edinburg, TX 78539

Joseph J. Beaman

Department of Mechanical Engineering, University of Texas at Austin, Austin, TX 78712

Rodney L. Williamson

Remelting Technologies, Albuquerque, NM 87112

David K. Melgaard

Sandia National Laboratories, Albuquerque, NM 87185-1134

J. Dyn. Sys., Meas., Control 132(1), 011011 (Dec 18, 2009) (9 pages) doi:10.1115/1.4000660 History: Received November 06, 2008; Revised October 01, 2009; Published December 18, 2009; Online December 18, 2009

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Abstract

Electroslag remelting (ESR) is used widely throughout the specialty metals industry. The process generally consists of a regularly shaped electrode, wherein a small amount is immersed in liquid slag at a temperature higher than the melting temperature of the electrode. Melting droplets from the electrode fall through the lower density slag into a liquid pool constrained by a crucible and solidify into an ingot. High quality ingots require that electrode melt rate and immersion depth be controlled at all times during the process. This can be difficult when process conditions are such that the temperature distribution in the electrode is not at steady state. This condition is encountered during the beginning and closing stages of the ESR process and also during some process disturbances such as when the melt zone passes through a transverse electrode crack. To address these transient melting situations, a new method of the ESR estimation and control has been developed that incorporates an accurate, reduced order melting model to continually estimate the temperature distribution in the electrode. The ESR process is highly nonlinear, noisy, and has coupled dynamics. An extended Kalman filter and an unscented Kalman filter were chosen as possible estimators and compared in the controller design. During the highly transient periods in melting, the unscented Kalman filter showed superior performance for estimating and controlling the system.

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Figure 1

ESR process schematic

Energy balance and coordinate setup in the ESR process

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Figure 2

Energy balance and coordinate setup in the ESR process

Descriptions of the boundary and immersion depth model of the ESR process

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Figure 3

Descriptions of the boundary and immersion depth model of the ESR process

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with perfect state estimation

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Figure 4

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with perfect state estimation

Plots of the commanded immersion depth, immersion depth controlled response, and ram velocity for case 1 with perfect state estimation

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Figure 5

Plots of the commanded immersion depth, immersion depth controlled response, and ram velocity for case 1 with perfect state estimation

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with perfect state feedback

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Figure 6

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with perfect state feedback

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with NLE estimated states

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Figure 7

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with NLE estimated states

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with NLE estimated states

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Figure 8

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with NLE estimated states

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with UKF estimated states

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Figure 9

Plots of the commanded melt rate, melt rate controlled response, and current for case 1 with UKF estimated states

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with UKF estimated states

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Figure 10

Plots of the exact and estimated thermal boundary layer thicknesses for case 1 with UKF estimated states

Plots of the commanded melt rate, melt rate controlled response, and current for case 2 with EKF estimated states

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Figure 11

Plots of the commanded melt rate, melt rate controlled response, and current for case 2 with EKF estimated states

Plots of the commanded melt rate, melt rate controlled response, and current for case 2 with UKF estimated states

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Figure 12

Plots of the commanded melt rate, melt rate controlled response, and current for case 2 with UKF estimated states

Plots of the exact and estimated thermal boundary layer thicknesses for case 2 with UKF estimated states

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Figure 13

Plots of the exact and estimated thermal boundary layer thicknesses for case 2 with UKF estimated states

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Ahn S, Beaman JJ, Williamson RL, Melgaard DK. Model-Based Control of Electroslag Remelting Process Using Unscented Kalman Filter. ASME. J. Dyn. Sys., Meas., Control. 2009;132(1):011011-011011-9. doi:10.1115/1.4000660.

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Model-Based Control of Electroslag Remelting Process Using Unscented Kalman Filter

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