(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The dynamic behavior of a pressure sensor/transmitter can be expressed as a first-order transfer function (in deviation variables) that relates the measured value Pm to the actual pressure, P:

Pm'(s)/P'(s)=1/(30s+1). Both Pm' and P' have units of psi and the time constant has units of seconds. Suppose that an alarm will sound if Pm exceeds 45psi. If the process is initially at steady state, and then P suddenly changes from 35 to 50 psi at 1:10 PM, at what time will the alarm sound?

2. Relevant equations

Pm'(s)/P'(s)=1/(30s+1)

3. The attempt at a solution

This is what I did however I don't think it's correct... :

If P'(s)=(50-35)/s=15/s

then Pm'(s)=[1/(30s+1)]*P'(s) --> Pm'(s)=15/[s(30s+1)] --> Inverse Laplace --> Pm'(t)=15(1-e^(-t/30))

Pm'(t)=Pm(t)-[P(t) steady state] --> Pm(t)=15[1-e^(-t/30)]+35

45=15*[1-e^(-t/30)]+35 --> t=33.3 s --> So the time would be 1:10:33 PM.

As I said I don't believe it's correct so any help would be greatly appreciated.

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# First Order Transfer Function

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