Minimum Variance Run-to-Run Controller for General Stochastic Time-Series-Based Disturbances

Abstract

Exponentially weighted moving average (EWMA) or double EWMA controllers are often employed to deal with various stochastic time-series disturbances for run-to-run control. If the disturbance model is known, then the best EWMA or double EWMA controller can be obtained by minimizing output variance with respect to controller parameters. However, from the theoretical view point, results are only sub-optimum because the control scheme may not be the best control scheme for the underlying stochastic disturbance. Therefore, investigating the best control scheme for the process disturbance following the general ARIMA time series process is worthwhile. In this paper, the predictive disturbance observer (PDOB) is developed based on minimum variance control for various ARIMA(p,r,q) stochastic disturbances. If the ARIMA(p,r,q) disturbance model is known, then the PDOB scheme generates one-step ahead prediction for this disturbance and then feeds it back to compensate the effect of stochastic disturbance on the system output; as a result, the system generates the minimum output variance or simply white noise variance.