FINALS PROBLEMS Flashcards
Refer to the water-heating process below.
a. Determine the response of the outlet temp. for the tank to a step change in the inlet temp from 60 deg C. to 70 deg. C.
b. Determine the response of the outlet temp. of the tank to a step increase in heat input by 42 kW.
c. Determine the response for simultaneous change in given in a and b.
Ti = 60 deg C
m dot = 300 kg/min
V = 1500 L
T = 80 deg C
a. T’ (t) = 10 (1-e^-t/300)
b. T’ (t) = 2 (1-e^-t/300)
c. T’ (t) = 12 (1-e^-t/300)
The stirred-tank heater has a thermocouple with response time of 45s for a 90% response completed after step change. If the system is 1st-order:
a. Determine the transfer function.
b. For a step change in the inlet temp. of 10 deg. C, what is the change in Tm?
Ti = 60 deg C
m dot = 300 kg/min
V = 1500 L
T = 80 deg C
a. T’ m(s) / T’(s) = 1/(19.54s+1)
b. T’m (t) = 10-10.7e^(-t/300)+0.7e^(-t/19.5)
Reconsider the heating process with an overall block diagram shown in the figure where Tr = 80 deg C and Ti = 60 deg C. If the controller gain is 20 (unit = kW/deg C), what will be the change in heat input Q when the outlet temp drops to 70 deg C?
Ti = 60 deg C
m dot = 300 kg/min
V = 1500 L
T = 80 deg C
Tm=19.54 s
Q (t) = 200 (1-e^ (-t/0.326))
A first order 2000 L water heating tank is at steady-state with an inlet flow rate at 500 kg/min at 50 deg C and an outlet at 70 deg C. The process controller gain is 15 and the thermocouple has a response time of 1 min (90% complete for a step change).
a. Find the transfer function of the thermocouple.
b. Construct the block diagram of the system, including the transfer function of each component.
c. For an increase in set-point of 10°C, what is the outlet temperature after 5 min?
d. For a load change of 10 deg C, what is the measured temp of the sensor after 2 min?
e. If Tm is increased by 5 deg C, what is the outlet temp after 3 min?
a. T’m(s)/T’(s) = 1/(0.4343s+1)
b. Lantaw lang sa nb sa diagram.
c. T (5) = 70.051 deg C
d. Tm (2) = 73.208 deg C
e. T (3) = 69.981 deg C
A first-order 1500 L water heating tank is at steady-state with an inlet flow rate of 300 kg/min at 25 deg C and an outlet at 40 deg C. The process controller gain is 10 kJ/deg C, and thermocouple has a response time of 80 seconds (90% complete for a step change).
a. Construct the overall block diagram.
b. Considering a single pass on the components concerned, for an increase in the measured temp. of the thermocouple of 10 deg C, what is the outlet temperature after 2 min?
c. Considering a single pass on the components concerned, for a load increase of 10 deg C, what is the change in the measured temperature of the thermocouple after 2 min?
a. Naa pa ka Angelie ang pics
A unit step change in error is introduced into a PID controller. If Kc = 10, Ti = 1 and TD = 0.5, what is the response of the controller?
P(t) = 10 + 10t +5delta(t)
A PID temp. controller is at steady state with an output pressure 9 psig. The set point and process temperature are initially the same. At time t=0 , the set point is changed at the rate of 0.5 deg F/min to a lower temp. If Kc = 2 psig/deg F, TI=1.25 min, TD=0.4 min, what is the response and the actual response of the controller?
P’(t) = -(t+0.4t^2+0.4)
P(t) = 8.6-t-0.4t^2
Example 11.1 sa book (3rd edition)
Naa ra answers dadto sa book pud
Example 11.2
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Problem 11.1
a and b
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Problem 11.2
j
Problem 11.3
- C/R = 4/(3s+7)
- C(t) = 4/7-4/7e^(-7t/3)
Problem 11.4
- Y/X = 1/(s^2-2s+25)
- Y(t) = 1/25-1/25e^t cos(sqrt24)t+(1/(25sqrt24))e^t sin(sqrt24)t
A PID pneumatic temperature controller is at steady-state with an output pressure of 7 psig. At t=0, the set point temp is increased at a rate of 0.3°C/min. The controller has the ff parameters: Kc=3 psig/°C, Ti=2 min, TD=0.2 min. Considering a single pass in the controller, what is the pressure output after 5 min?
17.305 psig
