提升 Double EWMA 控制器績效之研究

A Study on the Enhancement of Double EWMA Control Scheme

張玉琪(Yu-Chi Chang)

指導教授 ： 桑慧敏 ； 曾勝滄

國立清華大學/工學院/工業工程與工程管理學系/博士(2007年)

https://doi.org/10.6843/NTHU.2007.00267

摘要

本論文之研究目標為提高單投入單產出 (SISO) 的批次控制的績效，本研究以降低double EWMA (dEWMA) 控制器所造成的產出偏差 (bias) 為研究的切入點，本研究提出一個以 dEWMA 為基礎的控制器，並將此控制器命名為起始截距項估計值控制器（initial intercept iteratively adjusted (IIIA) scheme，簡稱IIIA控制器），利用逐次調整起始截距項的技巧來消除 dEWMA 控制器所造成的產出偏差（bias）。

為了驗證IIIA 控制器的績效表現，本研究進行了IIIA 控制器、dEWMA與遞迴最小平方法（recursive least squares, RLS）控制器的績效比較，績效之比較標準為產出之均方差（MSE），結果發現在參數未提示的情形下， IIIA 控制器略勝一籌。

為了增進對折扣因子的瞭解，本研究也提出了兩個 dEWMA 與 IIIA 之折扣因子與均方差間關係的性質，藉由這兩個性質可以很快找出 dEWMA 與 IIIA 的最佳折扣因子，從不同參數的 IIIA 最佳折扣因子的值，我們歸納出當製程模型之干擾項為白干擾時，第三批次後 IIIA 最佳折扣因子為（0.001, -0.001）。

關鍵字

批次控制 ； HASH(0x8a520dc) ； 遞迴最小平方法 ； 起始截距項估計值控制器 ； 最佳折扣因子 ； 區域最小值

並列摘要

The research objective of this thesis is improving the performance of single-input-single-output (SISO) feedback control. The strategy of our approach begins from eliminating the bias of double Exponential Weighted Moving Average (dEWMA) controller. We propose an initial intercept iteratively adjusted (IIIA) control scheme, which is based on the dEWMA controller. The methodology of the IIIA controller is adjusting the initial intercept estimate run by run.

An analytic expression of the process output and its MSE of the IIIA controller are revealed in this study. Furthermore, the performance of IIIA controller is compared with dEWMA and recursive least squares (RLS) controller in this research, and we found that IIIA controller is better than the other two controllers in most of our studied cases when the parameters of the process are assumed unknown.

We also reveal two important properties on the discount factors of the dEWMA and IIIA controllers for a linear process. These two properties are helpful for the efficiency of selecting the optimal discount factors.

並列關鍵字

Run to run control ； Double EWMA controller ； Recursive least squares ； Initial intercept iteratively adjusted (IIIA) controller ； optimal discount factors ； local optimal ； dEWMA controller ； IIIA controller

參考文獻

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