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Technical Briefs

Multirate Estimation for Discrete Processes Under Multirate Noise With Application to the Grinding Process

[+] Author and Article Information
Cheol W. Lee

Industrial and Manufacturing Systems Engineering, University of Michigan–Dearborn, Dearborn, MI 48128cheol@umich.edu

J. Dyn. Sys., Meas., Control 131(4), 044502 (May 18, 2009) (6 pages) doi:10.1115/1.3117199 History: Received February 25, 2008; Revised January 11, 2009; Published May 18, 2009

Asynchronous measurement of process output characterizes a series of discrete process cycles in batch production. A multirate Kalman filtering scheme was proposed by Lee (2008, “Estimation Strategy for a Series of Grinding Cycles in Batch Production,” IEEE Trans. Contr. Syst. Technol., 16(3, pp. 556–561)) for estimating immeasurable variables through integration of other sensor signals with postprocess inspection data. In this paper, a new state-space model structure for a series of discrete process cycles is proposed based on a semicontinuous system under the process noise of multiple frequencies due to the within-cycle drift and the cycle-to-cycle variation. An improvement is made to the previous estimation scheme by deriving the propagation of estimation errors between consecutive cycles under the multirate noise. Following a simulation demonstrating the advantage of the proposed change, experiments are conducted on an actual grinding process to validate the estimation scheme.

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Copyright © 2009 by American Society of Mechanical Engineers
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Figures

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Figure 6

Results of estimation and prediction for the surface roughness with experimental data from a mix of different grinding cycles: (a) estimated model parameter, R0; and (b) comparison of Ra and its a priori estimate, R̂a−, at the end of each cycle

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Figure 5

Estimation of Vw′, s0, and v with experimental data from a mix of different grinding cycles: (a) measured versus estimated accumulated metal removals; (b) estimated model parameter, s0; and (c) command infeed rate u versus estimated actual infeed rates

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Figure 4

Results of estimation for the wheel diameter with experimental data from the first batch: (a) measured versus estimated radial wheel wears and (b) estimated model parameter, G1

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Figure 3

Results of estimation and prediction for the surface roughness with experimental data from the first batch: (a) estimated model parameter, R0; and (b) comparison of Ra and its a priori estimate, R̂a−, at the end of each cycle

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Figure 2

Estimation of Vw′, s0, and v based on two measurement settings with experimental data from the first batch: (a) measured versus estimated accumulated metal removals; (b) estimated model parameter, s0; and (c) command infeed rate u versus estimated actual infeed rates

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Figure 1

Comparison of estimation based on two different methods of prior updates of error covariance P between cycles. For both trials, the following filter parameters were used: P0=diag[0 0.002 0], Qi,k=4×diag[0.01 10−710−9], and Qi=diag([0 0.002 0]): (a) true and estimated time constants and (b) errors in estimating the time constant.

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