Optimal setup adjustment and control of a process under ARMA disturbances

Fangyi He, Huiliang Xie and Kaibo Wang

IISE Transactions, 2015, vol. 47, issue 3, 230-244

Abstract: Process adjustment uses information from past runs to adjust settings for the next run and bring the output to its target. The efficiency of a control algorithm depends on the nature of the disturbance and dynamics of the process. This article develops a control algorithm when the disturbance is a general ARMA(p, q) process, in the presence of measurement error and adjustment error together with a random initial bias. Its optimality property is established and the stability conditions are derived. It is shown that the popular Exponentially Weighted Moving Average (EWMA) controller is a special case of the proposed controller. In addition, Monte Carlo simulations are conducted to study the finite sample behavior of the proposed controller and compare it with the proportional–integral–derivative controller when the disturbance is an ARMA(1,1) process and with the EWMA controller when the disturbance is an IMA(1,1) process. The ARMA controller is also implemented to control an ARMA(2,1) disturbance and its performance is compared with the other two controllers. All of the results reflect the new controller’s superiority when multiple sources of uncertainty exist or a general ARMA(p, q) disturbance is incurred.

Date: 2015
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DOI: 10.1080/0740817X.2014.928959

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