Student Exercises—Feed-Forward Control

13	Use physical reasoning to discuss why the disturbance dead time must be greater than the process dead time to even have the possibility of perfect feed-forward disturbance compensation.
14	Let and . Design a feed-forward controller, gcf(s), for this system. Elaborate on its expected performance.
15	A mixing vessel is used to maintain a desired pH level in a stream flowing to a waste treatment plant. The pressure to the valve on an acid stream is used as the manipulated variable. Most of the variability in pH is due to waste stream 1, which is a caustic stream. It is desirable to implement a feed-forward controller to reject the pH disturbances due to this stream. The following data are relevant to this problem. Without control, a change in the inlet pH of 0.5 leads to a change of 0.25 pH in the outlet stream. The time delay is 10 minutes and the time constant is 30 minutes. A change in the acid stream valve-top pressure of 1 psig leads to a change in pH in the outlet stream of 0.4 pH. The time constant is 25 minutes and the time delay is 7.5 minutes. Design a feed-forward controller for this process. Show units.
16	Derive the following closed-loop relationship for IMC with feed-forward control, and show that there is no offset for a step load disturbance.