Abstract
Run-to-run (R2R) control plays a vital role in monitoring or adjusting the integrated-circuit (IC) manufacturing process. Recently, a dynamic quasi MMSE (qMMSE) controller has been proposed in literature to address R2R problem when the process dynamics and disturbance dynamics exit simultaneously. The controller, however, was constructed only based on a transfer function (TF) model with the process disturbance follows an IMA(1,1) model. Therefore, its control performances on stability conditions and total mean square error (TMSE) may not perform satisfactorily when the true process disturbance follows a general ARIMA(p,1,q) model. To overcome this difficulty, this article first proposed a modified dynamic quasi MMSE (qMMSE) controller and then, the corresponding long-term stability conditions and its limiting distribution are derived. Furthermore, when the process I-O model follows a second-order transfer function (TF) model with the ARIMA(2,1,2) disturbance, we also compared the control performance of our proposed controller with that of existing controllers by using a simulation study. The results demonstrates that using wrong controllers usually cause serious effects on the performances of stability conditions and total mean square error (TMSE).