A multivariate EWMA controller for linear dynamic processes

Sheng Tsaing Tseng, Hsin Chao Mi, I-Chen Lee

Research output: Contribution to journalArticle

4 Citations (Scopus)

Abstract

Most research of run-to-run process control has been based on single-input and single-output processes with static input-output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1, 1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32% and 43%, respectively.

Original languageEnglish
Pages (from-to)104-115
Number of pages12
JournalTechnometrics
Volume58
Issue number1
DOIs
Publication statusPublished - 2016 Jan 2

Fingerprint

Exponentially Weighted Moving Average
Linear Process
Dynamic Process
Controller
Controllers
Output
Mean square error
Disturbance
Error Reduction
Semiconductor Manufacturing
Self-tuning
Discount
Process Control
Stability Condition
Process control
Tuning
Simulation Study
Semiconductor materials

All Science Journal Classification (ASJC) codes

  • Statistics and Probability
  • Modelling and Simulation
  • Applied Mathematics

Cite this

Tseng, Sheng Tsaing ; Mi, Hsin Chao ; Lee, I-Chen. / A multivariate EWMA controller for linear dynamic processes. In: Technometrics. 2016 ; Vol. 58, No. 1. pp. 104-115.
@article{df9745daf5e64f69bca1527c74587828,
title = "A multivariate EWMA controller for linear dynamic processes",
abstract = "Most research of run-to-run process control has been based on single-input and single-output processes with static input-output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1, 1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32{\%} and 43{\%}, respectively.",
author = "Tseng, {Sheng Tsaing} and Mi, {Hsin Chao} and I-Chen Lee",
year = "2016",
month = "1",
day = "2",
doi = "10.1080/00401706.2015.1006795",
language = "English",
volume = "58",
pages = "104--115",
journal = "Technometrics",
issn = "0040-1706",
publisher = "American Statistical Association",
number = "1",

}

A multivariate EWMA controller for linear dynamic processes. / Tseng, Sheng Tsaing; Mi, Hsin Chao; Lee, I-Chen.

In: Technometrics, Vol. 58, No. 1, 02.01.2016, p. 104-115.

Research output: Contribution to journalArticle

TY - JOUR

T1 - A multivariate EWMA controller for linear dynamic processes

AU - Tseng, Sheng Tsaing

AU - Mi, Hsin Chao

AU - Lee, I-Chen

PY - 2016/1/2

Y1 - 2016/1/2

N2 - Most research of run-to-run process control has been based on single-input and single-output processes with static input-output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1, 1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32% and 43%, respectively.

AB - Most research of run-to-run process control has been based on single-input and single-output processes with static input-output relationships. In practice, many complicated semiconductor manufacturing processes have multiple-input and multiple-output (MIMO) variables. In addition, the effects of previous process input recipes and output responses on the current outputs might be carried over for several process periods. Under these circumstances, using conventional controllers usually results in unsatisfactory performance. To overcome this, a complicated process could be viewed as dynamic MIMO systems with added general process disturbance and this article proposes a dynamic-process multivariate exponentially weighted moving average (MEWMA) controller to adjust those processes. The long-term stability conditions of the proposed controller are derived analytically. Furthermore, by minimizing the total mean square error (TMSE) of the process outputs, the optimal discount matrix of the proposed controller under vector IMA(1, 1) disturbance is derived. Finally, to highlight the contribution of the proposed controller, we also conduct a comprehensive simulation study to compare the control performance of the proposed controller with that of the single MEWMA and self-tuning controllers. On average, the results demonstrate that the proposed controller outperforms the other two controllers with a TMSE reduction about 32% and 43%, respectively.

UR - http://www.scopus.com/inward/record.url?scp=84975758257&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=84975758257&partnerID=8YFLogxK

U2 - 10.1080/00401706.2015.1006795

DO - 10.1080/00401706.2015.1006795

M3 - Article

VL - 58

SP - 104

EP - 115

JO - Technometrics

JF - Technometrics

SN - 0040-1706

IS - 1

ER -