A pressure-measuring device has been analyzed and can be described by a model with the structure shown in figure a. In other words1 the device responds to pressure changes as if it were a first-order process in parallel with a second order process. Preliminary tests have shown that the gain of the firsts order process is ?3%/psi and the time constant equals 20 ruin, as shown in figure a. An additional test is made on the overall system. The actual output

Pm (not P?_m) resulting from a step change in P from 4 to 6 psi is plotted in figure b.

(a) Determine Q?(t).

(b) What arc the values of K, ?, and ??

(c) What is the overall transfer function for the measurement device P?m(s) / P?(s)?

(d) F1rd an expression for the overall process gain.

R'ts) + 21a +1 p'(s) Pte) -3 20s + 1 Q'te) 30 26 22 Pm (%) 18 24 10 40 60 80 100 Tirne (min) 20