A pressure-measuring device has been analyzed and can be
Chapter 6, Problem 6.7(choose chapter or problem)
A pressure-measuring device has been analyzed and can be described by a model with the structure shown in Fig. E6.7a. In other words, 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 first-order process is -3 and the time constant equals 20 min, as shown in Fig. E6.7a. An additional test is made on the overall system. The actual output \(P_{m}\) (not \(P_{m}^{\prime}\)) resulting from a step change in P from 4 to 6 psi is plotted in Fig. E6.7b.
(a) Determine Q'(t).
(b) What are the values of \(K, \tau \text {, and } \zeta ?\)
(c) What is the overall transfer function for the measurement device \(P_{m}^{\prime}(s) / P^{\prime}(s) ?\)
(d) Find an expression for the overall process gain.
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