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Strategies for Statistical Monitoring of Integral Control

However, nonÄ™ of the statistical monitoring schemes when combined with EPC consistently outperformed the others.

The purpose of this paper is to extend the initial work of the authors to the case of integrating statistical monitoring with the manipulatable variables of the process by examining the control actions taken as described in MacGregor (1990). Finally, integration strategies are developed based on the combined simulation results of the deviation from target and present (manipulated variable) study.

The Process Model

Harris and Ross (1991) and MacGregor (1992) discuss the reason for a wandering or drifting mean in terms of the inertial elements in the process such as tanks and reactors. In terms of these results, MacGregor (1990) postulates a different model for the process industries which is

y_t = u_t_i + n_t + et    (1)

where y_t is the output of the process at time period t, u_t.j is the effect of any control action taken after the (t - l)st observation, n_t is the effect of the underlying disturbances on the true process mean at time t, and is an independent random variable with mean 0 and varianceo^. In this model, the process mean follows an AR(1) process,

ⁿt = H-i + a_t    (2)

where -1 < <j> < 1 and a_t is an independent random variable with mean zero and variance a\. The MacGregor model given by equations (1) and (2) describes a process with a drifting mean, such as widely encountered in the Chemical and process industries. In such applications, we would typically find <J> > 0 (values of (j> which approach unity are not unusual). The control action is based on Box and Jenkins (1976). For the process model with a drifting mean as described above, MacGregor (1990) gives the following control action

m ⁼ H-i - (<f> -⁰ )yt    O)

where 0 is the parameter in the equivalent first-order autoregressive-moving average model representation of the total stochastic variation in the output. The derivation of eÄ…uation (3) is given in Messina (1992). The reader is referred to