A Multivariate Self-Tuning Controller for Run-To-Run Process Control under Shift and Trend Disturbances

Abstract

Many manufacturing systems are controlled with PID-type controllers. In some industries, such as semiconductor manufacturing, specifications or changing conditions impose a need for adjusting such controllers on a run-to-run basis. This need has originated a collection of techniques called run-to-run process control. Self-tuning control, where model estimation is done on-line, has been shown to be a feasible tool for run-to-run control in single input–single output systems. This paper presents a self-tuning multiple input-multiple output controller for run to run control. The controller compensates for a variety of disturbances frequently found in semiconductor manufacturing, such as offsets or shifts and trends. The controller also compensates for autocorrelated responses or noise terms, for coupled responses, and for non-square systems (i.e., the number of inputs may be greater than the number of outputs). A sensitivity analysis is presented to show the performance of the controller under various system-noise combinations. A performance measure is developed to compare the behavior of the controller with that of a minimum variance multivariate controller. A multivariate EWMA monitoring chart is added to the controller as a deadband in order to trade-off the number of recipe (setpoint) changes against the variance of the outputs. This approach is contrasted with the classical strategy of trading-off input versus output variances.

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Notes on contributors

Enrique Del Castillo

Enrique Del Castillo is assistant professor of Industrial Engineering at the University of Texas at Arlington. He holds a M.Eng. degree in OR from Cornell University and a Ph.D. degree in IE from Arizona State. He is Associate Editor of IIE Transactions, and a member of the editorial board of the Journal of Quality Technology. Dr Del Castillo’s interests are experimental optimization and process control. He is a member of IIE, ASQC, and ASA. He has published papers in the Journal of Quality Technology, IIE Transactions, International Journal of Production Research, Metrika, and Journal of the Operational Research Society, among other journals.