# One-Degree of Freedom Internal Model Control

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## 3.8 Modifying the Process to Improve Control System Performance

Another interesting feature of the process in Example 3.6 is that the response can be substantially improved by modifying the process. Let us rewrite Eq. (3.31) as

Equation 3.38a

If T0 in Eq. (3.38a) is taken as zero, then Eq. (3.38a) is the same as Eq. (3.31). If, however, T0 is taken as T, then Eq. (3.38a) becomes

Equation 3.38b

where p* = the modified process.

Now, our simple controller, given by Eq. (3.36), gives

Equation 3.38c

The above has an ISE of T, which is substantially better than that given by Eq. (3.35) using the optimal controller given by Eq. (3.32). Recall that when K = 2, the optimal ISE was 3T. This shows that small design changes to the process can lead to significant improvements in control system performance. Notice that the process given by Eq. (3.31) responds instantaneously to a step change in control effort. However, the process given by Eq. (3.38a), with T0 = T, responds to a step change in control effort only after a dead time of T units. Thus, we have improved control system performance by, in effect, increasing the deadtime of the process in going from Eq. (3.31) to Eq. (3.38a). For more information on how to improve performance by process modifications that increase certain dead times, see Psarris & Floudas (1990).