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ISSN : 1598-7248 (Print)
ISSN : 2234-6473 (Online)
Industrial Engineering & Management Systems Vol.9 No.3 pp.262-274
DOI :

Recursive Least Squares Run-to-Run Control with Time-Varying Metrology Delays

Shu-Kai Fan†, Yuan-Jung Chang
Department of Industrial Engineering and Management, Yuan Ze University
Received, March 10, 2010; Revised, July 2, 2010; Accepted, July 14, 2010

Abstract

This article investigates how to adaptively predict the time-varying metrology delay that couldrealistically occur in the semiconductor manufacturing practice. Metrology delays pose a great challenge for theexisting run-to-run (R2R) controllers, driving the process output significantly away from target if not adequatelypredicted. First, the expected asymptotic double exponentially weighted moving average (DEWMA) controloutput, by using the EWMA and recursive least squares (RLS) prediction methods, is derived. It has been foundthat the relationships between the expected control output and target in both estimation methods are parallel, andsix cases are addressed. Within the context of time-varying metrology delay, this paper presents a modifiedrecursive least squares-linear trend (RLS-LT) controller, in combination with runs test. Simulated single inputsingleoutput (SISO) R2R processes subject to various time-varying metrology delay scenarios are used as a testbedto evaluate the proposed algorithms. The simulation results indicate that the modified RLS-LT controller canyield the process output more accurately on target with smaller mean squared error (MSE) than the original RLSLTcontroller that only deals with constant metrology delays.

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