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A process stream is heated using a shell and tube heat
Chapter 12, Problem 12.5(choose chapter or problem)
A process stream is heated using a shell and tube heat exchanger. The exit temperature is controlled by adjusting the steam control valve shown in Fig. E12.5. During an open-loop experimental test, the steam pressure \(P_{s}\) was suddenly changed from 18 to 20 psig and the temperature data shown below were
obtained. At the nominal conditions, the control valve and current-to-pressure transducers have gains of \(K_{v}=0.9\ \mathrm{psi} / \mathrm{psi}\) and \(K_{I P}=0.75\ \mathrm{psi} / \mathrm{mA}\), respectively. Determine appropriate PID controller settings using the following approaches:
(a) Internal Model Control (select a reasonable value of \(\tau_{c}\))
(b) ITAE (set point)
(c) ITAE (disturbance)
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\(T_{2m}\)(mA) |
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Equation Transcription:
Text Transcription:
P_{s}
K_{v}=0.9 psi/psi
K_{I P}=0.75 psi/mA
tau_{c}
T_{2 m}(m A)
T_2
T_2m
P_s
T_1
Questions & Answers
QUESTION:
A process stream is heated using a shell and tube heat exchanger. The exit temperature is controlled by adjusting the steam control valve shown in Fig. E12.5. During an open-loop experimental test, the steam pressure \(P_{s}\) was suddenly changed from 18 to 20 psig and the temperature data shown below were
obtained. At the nominal conditions, the control valve and current-to-pressure transducers have gains of \(K_{v}=0.9\ \mathrm{psi} / \mathrm{psi}\) and \(K_{I P}=0.75\ \mathrm{psi} / \mathrm{mA}\), respectively. Determine appropriate PID controller settings using the following approaches:
(a) Internal Model Control (select a reasonable value of \(\tau_{c}\))
(b) ITAE (set point)
(c) ITAE (disturbance)
\(t\)(min) |
\(T_{2m}\)(mA) |
0 |
|
1 |
|
2 |
|
3 |
|
4 |
|
5 |
|
6 |
|
7 |
|
8 |
|
9 |
|
10 |
|
11 |
|
12 |
Equation Transcription:
Text Transcription:
P_{s}
K_{v}=0.9 psi/psi
K_{I P}=0.75 psi/mA
tau_{c}
T_{2 m}(m A)
T_2
T_2m
P_s
T_1
ANSWER:
Problem 12.5A process stream is heated using a shell and tube heat exchanger. The exit temperature iscontrolled by adjusting the steam control valve shown in Fig. E12.5. During an open-loopexperimental test, the steam pressure Pswas suddenly changed from 18 to 20 psig and thetemperature data shown belowwere obtained. At the nominal conditions, the control valve and current-to-pressure transducershave gains of K = 0.9 psi/psi and K = 0.75 psi/mA, respectively. Determine appropriate PID v 1Pcontroller settings using the following approaches:(a) Internal Model Control (select a reasonable value oc )(b) ITAE(setpoint)(c) IT AE (disturbance) t(min) Tzm(mA) 0 12.0 1 12.0 2 12.5 3 13.1 4 14.0 5 14.8 6 15.4 7 16.1 8 16.4 9 16.8 10 16.9 11 17.0 12 16.9 Step-by-step solution Step 1 of 9 ^The plot with step response and a tangent line from the infection point from the given data isshown in Figure 1.\n Figure 1