A Generalized Quasi-MMSE Controller for Run-to-Run Dynamic Models

This study proposes a generalized quasi-minimum mean square error (qMMSE) controller for implementing a run-to-run process control where the process input-output relationship follows a general-order dynamical model with added noise. The expression of the process output, the long-term stability conditions and the optimal discount factor of this controller are derived analytically. Furthermore, we use the proposed second-order dynamical model to illustrate the effects of mis-identification of the process I-O model on the process total mean square error (TMSE). Via a comprehensive simulation study, the model demonstrates that the TMSE may inflate by more than 150% if a second-order dynamical model with moderately large carryover effects is wrongly identified as that of a first-order model. This means that the effects of mis-identification of the process I-O model on the process total mean square error (TMSE) is not negligible for implementing a dynamic run-to-run (RTR) process control. Supplementary materials for this article are available online.