| Summary: | 碩士 === 南台科技大學 === 工業管理研究所 === 98 === Exponentially Weighted Moving Average (EWMA) controller is a popular run to run (R2R) controller. Due to its simplicity and effectiveness for process monitoring and controlling, it is widely used in semiconductor manufacturing. In practice, the problem of metrology delay often exists for a run to run control system. In general, products won’t be measured until they go through the entire production process; therefore, for a continuous process, time delay usually has occurred when any irregular feedback is detected, and such problem may ruin the stability of a run to run control system.
In recent literatures, many research have devoted to the study of stability and sensitivity of the EWMA control system for processes with metrology delay, but most of them are for models with white noise, uncorrelated noise, random walk, ARMA(1, 1), or IMA(1, 1) disturbance, but few for models with ARIMA(1, 1, 1) disturbance that is frequently seen in the semiconductor manufacturing. In this research, for time delay single-in single-out (SISO) processes under ARIMA(1, 1, 1) disturbance, process output and stability condition are derived explicitly. Efficiency and robustness of the controller under different combinations of the parameters ( , ) are studied with respect to various process gain (slope) estimation conditions, and to different degrees of initial biases via analytical and/or numerical ways.
In the long-run, our results indicate that for a delay with 2 to 5 runs, ranges of discount factor for stability depend on the value of . For short-term processes, results of optimal discount factor are influenced by both parameters and . With large and small and moderate ( ), even using the optimal discount factor, s-EWMA controller is unable to control the process, while with moderate , the process can be controlled well. Under latter condition, the process is controlled more stably when the process gain is under-estimated than over-estimated. Furthermore, to adjust processes with larger initial biases, larger values of discount factor are needed.
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