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

ABSTRACT

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.

Keywords:

• Dynamic model
• EWMA controller
• Input-output dynamical model
• Quasi-MMSE controller
• Run-to-run control

Supplementary Materials

All the proofs are given in Appendices (Appendices.pdf).

Acknowledgments

The authors are grateful to the editor, associate editor, and anonymous referees for many insightful suggestions that significantly improve the quality of this article. The authors also thank Dr. I-C Lee and Miss Z-H Wu for her useful programming and suggestions. The work was partially supported by the Ministry of Science and Technology (Grant No: NSC-100-2221-E-007-060-MY3) of Taiwan, Republic of China (ROC).