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 condi...
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| Veröffentlicht in: | Technometrics 2017-07, Vol.59 (3), p.381-390 |
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| creator | Tseng, Sheng-Tsaing Chen, Pei-Yu |
| description | 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. |
| doi_str_mv | 10.1080/00401706.2016.1228547 |
| format | Article |
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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. 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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. 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| ispartof | Technometrics, 2017-07, Vol.59 (3), p.381-390 |
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| source | JSTOR Mathematics and Statistics; Jstor Complete Legacy |
| subjects | Computer simulation Control stability Control systems Controllers Dynamic model Dynamic models Error analysis Errors EWMA controller Input-output dynamical model Mathematical models Mean square errors Mean square values Process controls Quasi-MMSE controller Run-to-run control |
| title | A Generalized Quasi-MMSE Controller for Run-to-Run Dynamic Models |
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