Exercise 1.7 shows two possible ways to design a feedback control loop to obtain a desired rate of liquid flow, wxp. Assume that in both Systems I and II, the flow transmitter is direct acting (i.e., the output increases as the actual flow rate increases). However, the control valve in System I is ‘air-to-open,” meaning that an increasing pressure signal from the controller will open the valve more, thus increasing the flow rate. On the other hand, the control valve in System 11 is “air.-to-close.” The dynamics for both of the valves are negligible.

(a) For each of these valves, what is the sign of its gain, K?

(b) Which controller must be direct acting? reverse acting? Use physical arguments to support your answers.

(c) What sign should the controller gain have for each case?