. Questions:
1) Proportional Controller is used for controlling temperature in melting process.
Temperature set point is 750°C and temperature
measuring tool range is 0 - 1000°C
.Proportional space is set at 15%. Pressure
output range from controller is 20 –100 kN/m2 and pressure
output rises when temperature increases.If pressure output is set
at 60 kN/m2 for temperature set point,
find
i. Temperature
for pressure output at 20 kN/m2
ii. Temperature
for pressure output at 100kN/m2
2 ) In a process, a Proportional Controller is used
to control the liquid level in the boiler. The level is set at 8 meters and the level range is 1 to 14
meters. Proportional band is at 20%.The output current has a range of 5 –
20mA. Determine:-
i. The output level when current is 5 mA.
ii. The output current at a level of 10 meters.
3) An air to open valve on the inflow
controls level in a tank. When the process is at the set point the valve
opening is 50%. An increase in outflow results in the valve opening
increasing to a new steady state value of 80%. What is the resulting offset
if the controller PB is:
i. 80%
ii. 40%
4) A temperature
controller has the following characteristic curve below:
The controller has a range of 100 0C to 400 0C.
The set‐point is 250 0C.
Calculate:
i. The controller Proportional Band
ii. The controller Proportional Gain
Answers:
1) i. P= 20 kN/m2 , P= 0%
P(t) = KpEp+P(0) , Kp = 100 , = 100
PB 15
P(t)= 100 Ep + 50
15
0= 100 Ep + 50
15
100 Ep = 0 - 50
15
Ep = -50 x 15
100
Ep = -7.5 %
Ep = SP - MV x 100%
Ep = SP - MV x 100%
range
-7.5 = 750 - MV x 100%
1000 - 0
-7.5(1000) = 750 - MV
100
-75 = 750 - MV
-75 - 750 = - MV
MV = 825°C
ii. P = 100 kN/m2 , P = 100%
P(t) = KpEp + P(0) , Kp = 100 = 100
PB 15
P(t) = 100 Ep + 50
15
100 = 100 Ep + 50
15
100 Ep = 100 - 50
15
Ep = 50 x 15
100
Ep = 7.5%
E = SP - MV x 100%
range
7.5 = 750 - MV x 100%
1000
7.5(1000) = 750 - MV
100
75 = 750 - MV
MV = 750 -75
MV = 675°C
2) i. SP - MV x 100%
range
Ep = 8 - 10 x 100%
14 - 1
Ep = -15.38
P(t) = KpEp + P(0)
P = 5(-15.38) + 50
P = -26.9%
-26.9 = Current - Min x 100%
Max - Min
-26.9 = MV - 1 x 100%
14 - 1
MV = -2.5
ii. Controller output = Current - Min x 100%
Max - Min
= 10 - 5 x 100%
20 - 5
= 5 x 20%
15
Co = 7m
3) i. 80%
Pb = 100
Kp
80% = 100
Kp
Kp = 100
80
Kp = 1.25
ii. 40%
Pb = 100
Kp
40 = 100
Kp
Kp = 100
40
Kp = 2.5
4) i. Positive error band
= 3°C x 100%
(400 - 100)°C
= 1.7%
= 1.7 - (-1.7)
= 3.4
Negative error band
= -5°C x 100%
(400 - 100)°C
= - 1.7%
ii. Pb = 100
Kp
3.4 = 100
Kp
Kp = 100
3.4
Kp = 29.42
-7.5 = 750 - MV x 100%
1000 - 0
-7.5(1000) = 750 - MV
100
-75 = 750 - MV
-75 - 750 = - MV
MV = 825°C
ii. P = 100 kN/m2 , P = 100%
P(t) = KpEp + P(0) , Kp = 100 = 100
PB 15
P(t) = 100 Ep + 50
15
100 = 100 Ep + 50
15
100 Ep = 100 - 50
15
Ep = 50 x 15
100
Ep = 7.5%
E = SP - MV x 100%
range
7.5 = 750 - MV x 100%
1000
7.5(1000) = 750 - MV
100
75 = 750 - MV
MV = 750 -75
MV = 675°C
2) i. SP - MV x 100%
range
Ep = 8 - 10 x 100%
14 - 1
Ep = -15.38
P(t) = KpEp + P(0)
P = 5(-15.38) + 50
P = -26.9%
-26.9 = Current - Min x 100%
Max - Min
-26.9 = MV - 1 x 100%
14 - 1
MV = -2.5
ii. Controller output = Current - Min x 100%
Max - Min
= 10 - 5 x 100%
20 - 5
= 5 x 20%
15
Co = 7m
3) i. 80%
Pb = 100
Kp
80% = 100
Kp
Kp = 100
80
Kp = 1.25
ii. 40%
Pb = 100
Kp
40 = 100
Kp
Kp = 100
40
Kp = 2.5
4) i. Positive error band
= 3°C x 100%
(400 - 100)°C
= 1.7%
= 1.7 - (-1.7)
= 3.4
Negative error band
= -5°C x 100%
(400 - 100)°C
= - 1.7%
ii. Pb = 100
Kp
3.4 = 100
Kp
Kp = 100
3.4
Kp = 29.42
