23 May assessment
1. A 5 to 20 bar reverse acting proportional pressure controller has an output
of 4 to 20 mA. The set point is 11 bar. Determine:
(a) the measured value pressure which gives an output of 15 mA when
the proportional band setting of the controller is 40%
(b) the proportional band setting which will give an output of 8 mA when
the measured value is 14 bar and the desired value is 11 bar.
2. FIGURE 1(a) shows a flow control system whose output Qo is regulated
by using a proportional controller to control Q1. (Note that Q2 is not
controlled). The control system can be represented by the block diagram
shown in FIGURE 1(b).
(a) Derive a relationship between Qo and Q2, B, C and DV, where C is
the gain of the controller.
(b) If Q2 is 3000 m 3 h–1 when the bias B is 1000 m3 h–1, the PB setting of
the controller is 40% and the desired value of the controller is
4000 m3 h–1, determine the resultant value of Qo.
(c) If Q2 now changes to 2500 m 3 h–1, determine the new bias figure
required to ensure that Qo is maintained at its original flow rate
value.
2
Teesside University Open Learning (Engineering)
© Teesside University 2011
FIG. 1
Q1
Q2
FC
F
Dv
Mv
Qo
ε Dv C
B
Proportional controller
+ –
+ +
+ +
1.0
Qo
F = Flowmeter
Q2
Q1
(a)
(b)
3
Teesside University Open Learning (Engineering)
© Teesside University 2011
3. (a) With the aid of a sketch explain how proportional action is produced
in a pneumatic controller whose output is 0.2 to 1.0 bar. Assume that
the controller is direct acting.
(b) Show, mathematically, that the output is dependent on the difference
between the measured and desired values.
(c) With the aid of a well annotated sketch describe the construction and
operation of a P + I + D controller having a pneumatic output.
4. (a) FIGURE 2 shows an electronic ‘black box’ whose output is ten times
the difference between its two input signals. Show how the ‘black
box’ could be realised using just two operational amplifiers and five
resistors. Give the relative values of the resistors.
FIG. 2
(b) With the aid of circuit diagrams show diagrammatically, and prove
mathematically, how op-amps are utilized to produce:
(i) integral action
(ii) derivative action.
(c) Show how generation of the above actions are combined with
proportional action generation to produce a three term electronic
output controller.
Vo = 10(V2 – V1)
V1
V2
4
Teesside University Open Learning (Engineering)
© Teesside University 2011
5. The proportional control system of FIGURE 3(a) has an input, θ1, of 10 units. The uncontrolled input, θ2, has a value of 50 units, prior to a step change down to 40 units. The result of this disturbance upon the
output, θo, is shown in FIGURE 3(b).
(a) Calculate the change in offset in the output produced by the step
change.
(b) Draw a modified block diagram to show how the offset could be
minimised by the inclusion of another control action. Also, show by
means of a sketch how the modification might be expected to affect
the output response.
(c) Show, by drawing a modified block diagram, how the magnitude of
the disturbance could be minimised by the inclusion of a third type of
control action.
FIG. 3(a)
G 9
+ –
θ1 + +
θo
θ2
H 0.1
+ –
+ +
5
Teesside University Open Learning (Engineering)
© Teesside University 2011
FIG. 3(b)
6. FIGURE 4(a) shows a flow control system that is controlled by a P + I
controller. The control objective is to maintain a constant flow rate, Qo,
for varying values of input flow rate, Q2. The system can be represented
by the block diagram shown in FIGURE 4(b).
Assume that the following initial conditions apply.
DV = 2000 ε = 0 I = 1000 C = 0.2
Q2 = 1000 Ki = 0.8
Show that following a permanent step disturbance in Q2 from 1000 m 3 h–1
to 1200 m3 h–1, the resulting offset is eliminated.
You should continue your calculations until Qo is within 4 m 3 h–1 of its
final value for two successive calculations.* Derive any formulae used.
*A spreadsheet can be used to advantage here!
0 10 20 30 40 50 60
Time (minutes)
θo
6
Teesside University Open Learning (Engineering)
© Teesside University 2011
FIG. 4
Q1
Q2
Qo
DVFC
F
(a)
+ –
Dv + +C Qo
Q1
Q2
I
εCε
Ki ∫
++
1.0 Qo
(b)
7
Teesside University Open Learning (Engineering)
© Teesside University 2011
7. (a) FIGURE 5 shows the input and output waveforms for a proportional
plus integral controller. State:
(i) the controller’s proportional gain
(ii) the controller’s integral action time.
FIG. 5
0
Input
Output
0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0
Time (minutes)
8
Teesside University Open Learning (Engineering)
© Teesside University 2011
(b) FIGURE 6 shows a proportional plus derivative controller that has a
proportional band of 20% and a derivative action time of 0.1 minutes.
Construct the shape of the output waveform for the triangular
input waveform shown, if the input rises and falls at the rate of 4 units
per minute.
FIG. 6
8. (a) FIGURE 7 shows the closed-loop response of a plant to a step input
when the proportional only gain was set to 4. Use the ‘Quarter
Amplitude Response Method’ to estimate the required settings of a P
+ I + D controller.
FIG. 7 Plant Response to Step Input
(b) If the same plant was ‘tuned’ using the ‘Ultimate Cycle Method’,
estimate the P + I + D controller settings if a proportional only gain
of 6 was required to produce steady oscillations.
Time (seconds)
P ro
ce ss
o ut
pu t
+5
–5
10 20 30 40 50 600
P+Dθi θo
1 minute
9
Teesside University Open Learning (Engineering)
© Teesside University 2011
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