The benefits of using corrected predictions will be illustrated by a simple example, a first-order-plus-time-delay model:
\frac{Y(s)}{U(s)}=\frac{5e^{-2s} }{15s+1} (20-34)
Assume that the disturbance transfer function is identical to the process transfer function, G_{d} (s)=G_{p}(s) . A unit change in u occurs at time t = 2 min , and a step disturbance, d = 0.15, occurs at t = 8 min. The sampling period is \Delta t = 1 min.
(a) Compare the process response y(k) with the predictions that were made 15 steps earlier based on a step-response model with N = 80. Consider both the corrected prediction \tilde{y} (k) and the uncorrected prediction \hat{y} (k) over a time period, 0 ≤ k ≤ 90.
(b) Repeat (a) for the situation where the step-response coefficients are calculated using an incorrect model:
\frac{Y(s)}{U(s)}= \frac{4e^{-2s} }{20s+1} (20-35)