Consider the data shown in Table 12E.1. The target value for this process is 200.

(a) Set up an integral controller for this process. Assume that the gain for the adjustment variable is g = 1.2 and assume that  = 0.2 in the EWMA forecasting procedure will provide adequate one-step-ahead predictions.
(b) How much reduction in variability around the target does the integral controller achieve?
(c) Rework parts (a) and (b) assuming that  = 0.4. What change does this make in the variability around the target in comparison to that achieved with  = 0.2?

TABLE 12E.! Process Data for Exercise 12.6 Observation Observation. 160.0 132.9 40 152.8 41 143.3 42 52.3 43 1113 143.6 129.9 46 122.9 126.2 133.2 49 145.0 129.5 38 39 13 174.3 14 166.5 15 157.3 166.6 1 160.6 18 55.6 19 152.5 164.9 159.0 174.2 143.6 163.1 189.7 1 215.8 2 1958 31913 4 185.3 27 1704 169.4 170.9 157.2 172.4 160.7 145.6 159.9 148.6 151.1 37 162 1 16 28 4 1853 216,0 1769 176,0 162.6 187.5 IO 1805 745 12 151.6 31 32 45 21 22 47 48 23 24 25 50