Process Control Engineering (19CH5DCPCE)
Laboratory Manual
5
th
Semester
Department of Chemical Engineering
(Accredited by Washington accord Tier 1)
BMS COLLEGE OF ENGINEERING
BENGALURU-19
(Autonomous College under VTU)
Faculty In charge :
Department of Chemical engineering, BMSCE
PCE Lab
Department of Chemical Engineering
Process Control Engineering Manual
2017
Name of the Student:
USN:
Faculty In-charge:
PCE Lab
LABORATORY CERTIFICATE
This is to certify that Ms./Mr. has satisfactorily completed
the course of experiments in Practical Process Control Engineering prescribed by the
Visvesvaraya Technological University, Belgaum, for V Semester Chemical Engineering
course in the laboratory of the college in the year 2021.
Head of the Department Staff In-charge of the Batch
Date:
Marks
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Maximum
Obtained
USN:
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Signature of the Candidate
PCE Lab
DEPARTMENT OF CHEMICAL ENGINEERING
Process Control Engineering
Laboratory Manual
List of Experiments
Sl. No.
Title of the Experiment
Date
Page No.
1.
2.
3.
4.
5.
6.
7.
8.
9.
10.
PCE Lab
Time Constant Determination of a Thermo
meter
Aim:
(a) Determination of the response to the step input for a thermometer.
(b) Experimental determination of its time constant.
Apparatus: Experimental setup, stop watch, thermometer.
Theory:
The simplest possible dynamic system is one which satisfies a first order, linear,
differential equation. Such a system is known as a “first order system”. A block diagram
representation of the system is given below.
Input u(s) G(s) Output y(s)
The value of time constant will determine how quickly the system moves toward steady state.
The heat exchange between the thermometer and the measured medium takes time. That is
why there is always a delay in time in the registration of the actually prevailing temperature
in temperature measurement.
The response time is the time, which is needed by the thermometer after a temperature jump
to indicate a certain part of the temperature jump.
A thermometer„s response time depends on various factors
• Heat transfer values from thermometer to water or oil
• Heat transfer values in the structure of the thermometer
• Constructive structure of thermometer (geometry)
• Flow velocity of measured medium
• Heat transfer from measured medium to thermometer
• Heat capacity of measured medium
• Immersion depth of thermometer
PCE Lab
• Heat capacity of thermometer and material
The unsteady and steady state mass balance equations are written and solved to obtain the
response which is of the form,
)1()(
t
eAtY
(1)
Where
τ is the time constant, τ =
UA
MC
P
, here M is the mass of mercury, C
p
is the specific heat
of mercury, U is the overall heat transfer coefficient and A is the heat transfer area.
Procedure:
1. The stirrer as well as the heater is switched on and the thermometer is placed in the
water bath.
2. Temperature is allowed to reach the steady state and the temperature is noted down. The
room temperature is also noted down.
3. The thermometer is then removed from the bath and is allowed to cool to the room
temperature.
4. Once this is done, the thermometer is placed in the water bath again and immediately
the stop watch is started.
5. The temperature begins to rise rapidly and for every 5 seconds the time is noted down
until it reaches a steady state value.
6. The observations of this system are noted down.
7.
Next a test tube filled with oil is placed inside the water bath and allowed to attain
steady state. Once the temperature of the test tube is steady, a thermometer is
immediately placed inside the test tube and the stop watch is started simultaneously.
8.
The temperature begins to rise rapidly. Time is noted down for every 5 seconds until it
reaches a steady state value.
Table 1: Observations
Sl. No.
Water filled tube
Oil filled tube
Time, t
[s]
Temperature
[
o
C]
Time, t
[s]
Temperature
[
o
C]
1
2
5
PCE Lab
Model Calculations:
% change 100
io
no
TT
TT
(2)
where,
T
o
= Room Temp = Initial Temperature of Thermometer
T
n
= Bath Temp = Final Temperature of Thermometer
T
i
= Current Temperature of Thermometer
1) For water
2) For oil
Graph:
Plot a graph of % change vs. time in order to determine τ for both water and oil.
% change 100
io
no
TT
TT
Table 2: Results
Sl.
No.
Water filled tube
Oil filled tube
Time, t
[s]
Temperature
[
o
C]
% change
in Temp
Time, t
[s]
Temperature
[
o
C]
% change in
Temp
1
2
3
4
Nature of Graphs:
Figure 1: % Change in temperature vs time (in oil)
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140 160 180 200
% Change in temperature
→
Time (s) →
PCE Lab
Figure 2:% Change in temperature vs time (in water)
Results:
The response to a step input for the given thermometer was observed and plotted. The time
constants (τ) of the given thermometer were experimentally determined. τ for water = s and τ
for oil = s.
INFERENCE:
0
20
40
60
80
100
120
0 20 40 60 80 100 120 140 160 180 200
% Change in temperature
→
Time (s) →
PCE Lab
DYNAMICS OF A SECOND ORDER UNDERDAMPED: SYSTEM U-
TUBE MANOMETER
Aim:-
To study the dynamic behavior of a U-tube manometer and to determine the properties like
overshoot, decay ratio, rise time, period and natural frequency.
Apparatus:-
Experimental Setup, Stopwatch.
Theory:-
The dynamic behaviour of the U-tube liquid manometer with equal diameter columns
corresponds to an under-damped dynamic system. Improving the dynamic response
(decreasing the overshoot and the settling time, increasing the phase and delay margins) can
be achieved by increasing the connection tube length, by decreasing the columns diameter
and by using a high density liquid manometer
A system which can be represented by a linear second order differential equation is called as
a second order system. A U-Tube Manometer is a second order system. In many applications
the pressure difference to be measured may vary with time. The response time of the
measuring instrument and the connecting tubes decide the response time.
On applying force balance and solving the obtained equation, we get the transfer function for
this second order system as
12
)(
)(
)(
2
SS
k
sX
sY
sG
(1)
Where
k = Gain
Characteristic time
Damping Factor or Damping Coefficient
G(s) is the transfer function of the system under consideration
The dynamic behavior of the U-tube liquid manometer with equal diameter columns
corresponds to an under-damped dynamic system. Improving the dynamic response
(decreasing the overshoot and the settling time, increasing the phase and delay margins) can
be achieved by increasing the connection tube length, by decreasing the columns diameter
and by using a high density liquid manometer
PCE Lab
Procedure:-
1. Put on the vacuum pump and adjust the system to a particular vacuum.
2. Set the manometer level to zero by operating the valve above the manometer.
3. Press the solenoid valve and note down the trough and peak made by the oscillations and
respective time required.
4. Repeat the procedure for different vacuum pressure.
5. Plot the response curve and note down the overshoot, decay ratio, frequency etc.
Observation table:-
Table 1: Observations for pressure = 300 mmHg
Sl.
No.
Time
(s)
Manometer reading
(mm)
% change
1
2
3
Table 2 : Observations for pressure = 400 mmHg
Sl.
No.
Time
(s)
Manometer reading
(mmHg)
% change
1
2
3
Table 3 : Observations for pressure = 500 mmHg
Sl.
No.
Time
(s)
Manometer reading
(mmHg)
% change
1
2
3
5
PCE Lab
Specimen Calculations:-
For 300 mmHg:
Overshoot =
B
A
(3)
Overshoot =
2
1
exp
(4)
=
2
1
exp
From the graph, T =
f
s
-1
Rise Time from the graph = s
Response Time from the graph = s
Nature of Graphs:-
Figure 3: %change vs. time for 300 mmHg
0
50
100
150
0 0.5 1 1.5 2 2.5 3
% Change
Time (s)
A
B
Period T
Rise Time
Response Time
Decay Ratio =
2
B
A
(5)
Cyclical Frequency =
T
f
1
(6)
PCE Lab
Figure 4: %change vs. time for 400 mmHg
Figure 5: %change vs. time for 500 mmHg
Table 4: Results
Sl.
No.
Pressure
(mm
Hg)
Overshoot
(A/B)
Decay
Ratio
Time
Period
(T)
Frequency
(F)
Rise
Time,
s
[D]
Response
Time, s
[C]
1.
300
2
400
3
500
Results of experiment:
The dynamic behavior of a U tube manometer has been studied and properties such as
overshoot, decay ratio, cyclic frequency, damping factor, rise time and response time has
been determined.
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3
% Change
Time (s)
A
B
Rise Time
Response
Time
Period T
0
20
40
60
80
100
120
140
0 0.5 1 1.5 2 2.5 3
% Change
Time (s)
A
B
Period T
Rise Time
Response time
PCE Lab
Non-Interacting Tanks
Aim:
To study the dynamics and compare the theoretical response with the actual response for a
step input to a two-tank, non-interacting system.
Apparatus:
Experimental setup, bucket, stopwatch and measuring flask.
Theory:
A non-interacting tank system includes two liquid tanks arranged in series with a linear
resistance attached to the outlet of each tank. When water or any fluid is introduced into the
system, it behaves as a second order system. The transfer function is developed as follows:
Figure 1: Two tank non-interacting system
Consider two tanks, tank 1 and tank 2 with resistances R
1
and R
2
arranged in series. When the
outflow from tank 1 is discharged into the atmosphere before entering tank 2 and the flow
through R
1
depends only on level h
1
and is independent of the level in tank 2 the system is
known as a non-interacting system. This implies that the variation in level h
2
does not affect
the transient response occurring in tank 1. Consider the two tanks in series as shown in the
figure above handling a liquid of constant density. It is assumed that these tanks:
q
0
h
1
A
1
R
1
q
1
R
2
A
2
h
2
q
2
Tank 1
1 11
Tank 2
222
PCE Lab
1. Have uniform cross-sectional area, A
1
and A
2
respectively
2. Have linear flow resistances
Since the resistances are linear, the outflow rate can be written in terms of the resistances as
Q
1
=
h
1
R
1
2
2
2
R
h
Q
Since these two systems do no interact, we can consider them as two individual first order
systems. Hence we obtain the desired transfer functions as:
2 2 2
2
0 1 2 1 2 1 2
()
( ) (1 )(1 ) ( ) 1
H s R R
Q s s s s s
Formulae:
Height of liquid in tank,
h
=
h
'
´sin
a
(1)
Deviation Variable,
H = h -h
s
(2)
Volumetric flow rate,
q =
WatercollectedinTank
10
´10
-6
(3)
Deviation Variable,
Q = q -q
s
m
3
/s
(4)
Time constant,
t
= A´R
(5)
Theoretical response for step change,
12
2 1 2
2 1 2 2 1
Theoretical
% 1 100
tt
H
ee
MR
(6)
Experimental response for step change,
22
22
Experimental
% 100
HH
MR MR
(7)
Procedure:
Part A: Determination of resistances and capacitances of the system.
1) The dimensions of both the tanks are measured.
2) The cross sectional areas of tanks A
1
and A
2
are the capacitances
C
1
and
C
2
respectively.
3) The inlet valve is kept fully open and the bypass valve is kept slightly open.
PCE Lab
4) The pump is then switched on and the system is allowed to reach steady state (when
there is no variation in the height of the tanks) and the levels in the two tanks are
noted down.
5) The steady state flow rates are noted by collecting water for a known duration of time.
6) The above procedure is repeated by gradually opening the bypass valve till its fully
open.
7) A graph of level v/s height for both tanks is plotted and the slopes determined give the
values for resistances
R
1
and
R
2
.
8) The product of the resistance and capacitance gives the time constants
t
1
and
t
2
.
Part B: Determination of time constant from response study for a step change in the
input flow rate.
1) A low flow rate is maintained and the level in tank 2 is noted with the corresponding
flow rate.
2) This is the initial steady state condition at time
t = 0
. The flow rate is now increased
at a stretch by opening the bypass valve for a higher flow rate.
3) The stopwatch is started and the change in the level of tank 2 with time is noted.
4) The change is constantly noted down till the conditions become steady and the
percentage change in level of tank 2 plotted against time. This is the required
experimental response curve.
5) The theoretical percentage change is calculated using formula (6) and the curve is
plotted.
Part A:
Table 1: Observations for steady state flow
Sl.no
Rotameter
reading
(LPM)
Tank 1
slant
height, h
1
(mm)
Tank 2
slant
height, h
2
(mm)
Water
collected in
tank 1 (mL)
Water
collected in
tank 2 (mL)
Time
(s)
1
5
2
10
3
15
PCE Lab
4
20
5
25
6
30
7
35
8
40
Model Calculations:
1) Height of liquid in tank 1,
h
1
=
h
1
'
´sin
a
=
2) Height of liquid in tank 2,
h
2
=
h
2
'
´sin
a
=
3) Deviation Variables,
1 1 1s
H h h
2 2 2s
H h h
4) Volumetric flow rate
1
Water collected in Tank 1
10
q
2
Water collected in Tank 2
10
q
5) Deviation Variables,
1 1 1s
Q q q
m
3
/s
2 2 2s
Q q q
m
3
/s.
Table 2: Results for steady state flow
Sl.no
Height,
1
h
(mm)
Height,
2
h
(mm)
Deviation
Variable,
1
H
(mm)
Deviation
Variable,
2
H
(mm)
Flow
rate,
1
q
(
m
3
/s)
Flow
rate,
2
q
(
m
3
/s)
Deviation
Variable,
1
Q
(m
3
.s)
Deviation
Variable,
2
Q
(m
3
/s)
1
2
3
4
5
1) Tank resistances,
R
1
= Slope of
H
1
v/s
Q
1
curve =
PCE Lab
R
2
= Slope of
H
2
v/s
Q
2
curve =
2) Tank capacitances (C/S Area),
1
A
m
2
2
A
m
2
3) Time constants,
1 1 1
AR
s
2 2 2
AR
s
Figure 2: H Vs Q for tank
Figure 3: H Vs Q for tank 2
0
0.01
0.02
0.03
0.04
0.05
0 0.0001 0.0002 0.0003 0.0004 0.0005
H
1
(m)
Q
1
(m
3
/s)
0
0.01
0.02
0.03
0.04
0.05
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
H
2
(m)
Q
2
(m
3
/s)
PCE Lab
Part B:
Table 3: Observations for step input
Sl.no
Time (s)
Tank 2 slant height,
h
2
'
(mm)
1
2
3
4
5
Model Calculations:
1) Height of liquid in tank 2,
h
2
=
h
2
'
´sin
a
=
Deviation Variable,
2 2 2s
H h h
2) Magnitude of step change,
M
LPM .
3) Response for step change,
12
2 1 2
2 1 2 2 1
Theoretical
% 1 100
tt
H
ee
MR
Table 4: Results for step response
Sl.no
Time
(s)
Height,
h
2
(mm)
Deviation
variable,
H
2
(mm)
exp
H
mR
(%)
theo
H
mR
(%)
1
0
2
5
3
10
4
15
5
20
8
35
9
40
PCE Lab
Figure 6: Theoretical and experimental step responses v/s time
Results:
The dynamics of the two tank, non-interacting system has been studied. The theoretical and
actual responses are compared for a step change in input and have been tabulated.
Inference:
0
20
40
60
80
100
120
0 10 20 30 40 50 60
H/mR
Time (s)
% Change (theoretical)
% Change (experimental)
PCE Lab
SINGLE TANK SYSTEM
Aim:
To determine the time constant of a single tank system by
(i) evaluating the resistance and capacitance of the system.
(ii) from the response study to a step change in the inlet flow rate and to compare them.
Apparatus:
Stop watch, Experimental setup, measuring jar, bucket.
Theory:
A single tank system is one which consists of a liquid level tank of constant cross sectional
area with a linear resistance attached near the outlet. When such a system is made to undergo
a step change in the input flow rate of liquid, the system behaves as a first order system.
Consider a single tank system as shown below in the figure. The tank has a uniform cross
sectional area „A‟ where a liquid is flowing into the tank at volumetric flow rate q(t) and
flowing out at volumetric flow rate q
o
(t) through a resistance R such as valve. The density of
the liquid flowing through the tank is assumed to be constant.
q(t)
h(t) R
q
o
(t)
A first order system is characterized by a capacity to store material, energy or momentum and
the resistance associated with the flow of mass, energy or momentum reaching the capacity.
If a step input is applied to a capacity-dominated process such as a single tank, the output
begins to change instantaneously but does not reach its steady state value for a period of time.
PCE Lab
The time constant defined as the amount of time it takes to reach 63.2 % of its steady-state
value. For a single tank
= A
R
The transfer function of the given system can be written as
1
s
R
sQ
sH
1
1
ssQ
sQ
o
Procedure:
Determination of resistance and capacitances of the system
1. Measure the dimensions of the tank. The cross-sectional area of the tank is the
capacitance C.
2. Keep the inlet valve fully open and the bypass valve slightly open.
3. Switch on the pump and wait for the steady state to be reached.
4. Note down the level in the tank and also the corresponding steady state flow rate by
collecting water for known duration of time.
5. Repeat the above procedure by gradually opening the bypass valve till it is fully
open.
6. Plot a graph of level vs height in the tank and determine the slope which is the
resistance R1. The product of the resistance and capacitance gives the time constant
τ
1
.
Determination of the time constant from response study for a step change in the inlet
flow rate
1. Maintain a low flow rate and note down the level in the tank after steady rate is
reached and the corresponding flow rate. This is the initial steady state condition at
time t = 0.
2. Now increase the flow rate at a stretch by opening the bypass valve for a higher flow
rate and simultaneously start the stop watch. Note down the change in the level of
the tank with time.
3. Continue noting down till the condition becomes steady.
4. Plot percentage change in the level in the tank vs time which is the required
experimental response curve. Calculate theoretical percentage change and plot the
curve.
PCE Lab
Observations:
Table 1: Steady State Response
Sl. No.
Rotameter Reading
(Lpm)
Time (s)
Volume
(mL)
Height h'
(mm)
1
2
3
4
5
Model Calculation:
1. Volumetric flow rate (q) =
Volume
Time
q = m
3
/s
2.
sin
slantact
hh
3. Deviation Variable H
1
= h
1
-h
s
= m
Area of Tank
1
=
Area of Tank 2 =
Table 2: Results for Part A
Sl.
No.
Rotameter
Reading (lpm)
Volume
of water
collected
(m
3
/s)
Time
(s)
Q = q-
q
s
(m
3
/s)
Height h'
(mm)
h=h'sin30
(m)
H=h-
h
s
(m)
1
5
2
10
3
15
4
20
5
25
6
30
7
35
8
40
PCE Lab
Part B : Observations
Table 3: Step Response
Sl. No.
Time
(s)
Height (h’)
(mm)
1
2
3
4
5
6
7
8
9
Model Calculations:
1.
sin
slantact
hh
2. m = Final rotameter reading
Initial rotameter reading
m = Lpm
3.
AR
s
3.
exp
()Ht
mR
exp
()Ht
mR
exp
()
%%
Ht
mR
4.
t
thep
e
mR
tH
1
)(
()
theo
Ht
mR
PCE Lab
()
%%
theo
Ht
mR
Table 4 : Results for Part B
SL.
NO.
Time
(s)
Height(h’)
(m)
×10
3
Vertical
Height
h=h’sinα
(m)
H=h-h
s
(m)
()
theo
Ht
mR
(%)
exp
()Ht
mR
(%)
1
2
3
4
5
Nature of Graphs:
Figure 2: H vs Q
Figure 3: Theoretical and Experimental step responses v/s time
0
20
40
60
80
100
0 5 10 15 20 25 30 35 40 45
H/mR
Time (s)
(H/mR)Experimental
PCE Lab
Result:
The time constant of a single tank system was calculated by evaluating the resistance and
capacitance of the tank and it was found to be s.
The time constant was also determined from the response study to a step change in the inlet
flow rate and the values were compared. It was found that the theoretical values were greater
than the experimental values
Inference:
PCE Lab
Interacting Tanks
Aim:
To study the dynamics and compare the theoretical response with the actual response for a
step input to a two-tank, interacting system.
Apparatus:
Experimental setup, bucket, stopwatch and measuring flask.
Theory:
A two tank system arranged in series such that the liquid level in tank 2 is dependent on the
level in tank 1 is known as an interacting tank system. Such a system behaves as a complex
second order system. When this system is subjected to a step change in the input, the
corresponding transfer function is derived as follows:
Consider two tanks, tank 1 of uniform cross sectional area A
1
with a linear resistance R
1
and
tank 2 of uniform cross sectional area A
2
with a linear resistance R
2
.
Figure 1 : Two tank interacting system
When the outflow from tank 1 is directly discharged through R
1
into tank 2 without being
discharged into the atmosphere, flow through R
1
depends on the difference between h
1
and
h
2.
.Since the outflow of the liquid from tank 1 is dependent on the height of liquid in tank 2,
such a system is known as an interacting system
q
0
R
1
q
1
R
2
q
2
A
2
h
2
A
1
h
1
Tank 2
Tank 1
PCE Lab
The mass balance equation for the above system yields,
A
1
dh
1
dt
=q
0
-q
1
A
2
dh
2
dt
=q
1
-q
2
The linear resistances to flow are obtained from,
q
1
=
h
1
- h
2
R
1
q
2
=
h
2
R
2
Introducing deviation variables to the above equations and solving them, we get the
transfer function,
H
2
(s)
Q
0
(s)
=
R
2
t
1
t
2
s
2
+(
t
1
+
t
2
+ A
1
R
2
)s +1
Where,
t
1
= A
1
R
1
and
t
2
= A
2
R
2
.
For a step change in input, the roots of the denominator of the above equation (RHS) need
to be calculated. Let the roots be
p
1
and
p
2
. We get,
t
1
t
2
(s - p
1
)(s - p
2
)= 0
Let
-p
1
=
1
t
a
and
-p
2
=
1
t
b
where
t
a
,
t
b
are the effective time constants.
The above equation yields,
t
1
t
2
s +
1
t
a
( )
s +
1
t
b
( )
= 0
Deriving the response of the above equation at
t
a
¹
t
b
yields, (M= Magnitude)
%
H
2
MR
2
é
ë
ê
ù
û
ú
Theoretical
= 1-
t
a
t
b
t
a
-
t
b
æ
è
ç
ö
ø
÷
´
e
-
t
t
a
t
b
-
e
-
t
t
b
t
a
é
ë
ê
ê
ù
û
ú
ú
é
ë
ê
ê
ù
û
ú
ú
é
ë
ê
ê
ù
û
ú
ú
´100
Procedure:
Part A: Determination of resistances and capacitances of the system.
9) The dimensions of both the tanks are measured.
PCE Lab
10) The cross sectional areas of tanks A
1
and A
2
are the capacitances
C
1
and
C
2
Respectively.
11) The inlet valve is kept fully open and the bypass valve is kept slightly open.
12) The pump is then switched on and the system is allowed to reach steady state (when
there is no variation in the height of the tanks) and the levels in the two tanks are
noted down.
13) The steady state flow rate of tank 2 is noted by collecting water for a known duration
of time.
14) The above procedure is repeated by gradually opening the bypass valve till it‟s fully
open.
15) Graphs of level v/s flow rate are plotted and the slopes determined give the values for
resistances
R
1
and
R
2
.
16) The product of the resistance and capacitance gives the time constant (
t
1
,
t
2
).
Part B: Determination of time constant from response study for a step change in the
input flow rate.
6) A low flow rate is maintained and the level in tank 2 is noted with the corresponding
flow rate.
7) This is the initial steady state condition at time
t = 0
. The flow rate is now increased
at a stretch by opening the bypass valve for a higher flow rate.
8) The stopwatch is started and the change in the level of tank 2 with time is noted.
9) The change is constantly noted down till the conditions become steady and the
percentage change in level of tank 2 plotted against time. This is the required
experimental response curve.
10) The theoretical percentage change is calculated using formula (6) and the curve is
plotted.
PCE Lab
Part A:
Table 1 : Observations for steady state flow
Sl.no
Rotameter
(LPM)
Tank 1 slant
height,
'
1
h
(mm)
Tank 2 slant
height,
'
2
h
(mm)
Water collected in
tank 2 (mL)
Time
(s)
1
2
3
4
5
Model Calculations:
Height of liquid in tank 1,
h
1
=
h
1
'
´sin
a
=
Height of liquid in tank 2,
h
2
=
h
2
'
´sin
a
=
Deviation Variables,
1 1 1s
H h h
2 2 2s
H h h
Volumetric flow rate for tank 2,
2
Water collected in Tank 2
10
q
=
m
3
/s.
Deviation Variable,
2 2 2s
Q q q
Table 2 : Results for steady state flow
Sl.no
Height,
h
1
(mm)
Height,
h
2
(mm)
Deviation
Variable,
H
1
(m)
Deviation
Variable,
H
2
(m)
Flow
rate,
q
2
(
m
3
/s)
Deviation
Variable,
Q
2
(
m
3
/s)
H
1
-H
2
(m)
1
2
3
4
5
PCE Lab
Tank resistances,
R
1
= Slope of
H
1
- H
2
v/s
Q
2
curve =
R
2
= Slope of
H
2
v/s
Q
2
curve =
Tank capacitances (C/S Area),
1
A
m
2
2
A
m
2
Time constants,
1 1 1
AR
s
2 2 2
AR
s
Figure 2 : Plot of (H
1
-H
2
) vs Q
2
Figure 3 : Plot of H
2
vs Q
2
0
0.004
0.008
0.012
0.016
0.02
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
H
1
-H
2
(m)
Q (m
3
/s)
0
0.01
0.02
0.03
0.04
0.05
0.06
0 0.0001 0.0002 0.0003 0.0004 0.0005 0.0006
H
2
(m)
Q (m
3
/s)
PCE Lab
Part B:
Table 4 : Observations for step response
Sl.no
Time (s)
Tank 2 slant height, h
2
(mm)
1
0
2
5
3
10
4
15
5
20
Model Calculations:
1) Height of liquid in tank 2,
h
2
=
h
2
'
´sin
a
=
2) Deviation Variable,
2 2 2s
H h h
.
3) Magnitude of step change,
M
LPM .
4) Effective time constants,
1)92.76087.0(79.7924.2)79.7924.2(1
2
2121
2
21
ss)sRA(s
767.0 ,05707.0177.18778.22
21
2
ppss
52.17
)05707.0(
111
1
1
p
p
a
a
s
304.1
)767.0(
111
2
2
p
p
b
b
s.
5) Response for step change,
1001%
2
2
a
t
b
t
ba
ba
lTheoretica
ba
ee
MR
H
2
2
%%
Experimental
H
MR
PCE Lab
Table 5 : Results for Part B
Sl.no
Time
(s)
Height,
2
h
=
sinαh
'
2
(mm)
Deviation
variable,
2
H
(mm)
exp
mR
H
(%)
theo
mR
H
(%)
1
2
3
4
5
Figure 4 : Plot of theoretical and experimental step responses v/s time
Results:
The dynamics of the two tank, interacting system has been studied.
The theoretical and actual responses are compared for a step change in input and have been
tabulated.
Inference:
0
20
40
60
80
100
120
0 10 20 30 40 50 60 70 80 90
% Change
Time (s)
Experimental
Theoretical
PCE Lab
STUDY OF VALVES
AIM: To study the On-off, Linear Percentage, Equal Percentage valves for a level process
and to plot the response curve for a step change in set point.
APPARATUS: Experimental setup, stop watch.
THEORY:
Regulating valves are the most important actuating devices in engineering processes. All the
valves are basically modelled with the same basic equation called the valve sizing equation
given by:
f
v
v
P
lCq
Where,
q
Liquid flow rate.
v
C
Valve co-efficient which is a function of percent valve opening, also called as lift (l).
v
P
Pressure drop across the valve.
f
fluid density.
The co-efficient is defined such that it is the flow rate in gpm of water at a pressure drop of 1
psi across a given valve. The manufacturers provide the characteristic curves of the different
valves which are plots between
max
Q
Q
and percent lift.
Here we study three general valves:
On-Off valve:
Here, most of the flow variation is introduced in the lower end of the lift and is used when we
want to deliver large flow rate as quickly as possible. The exact shape of the fast opening
valve is not defined in standards. Therefore, two valves one giving a 80% flow for a 50% lift
and other 90% flow for 60% lift, may both be regarded as having a On-Off characteristic. It is
a special case of proportional control. If the gain is made very high, the valve will move from
one extreme position to the other when there is a slight variation in the set point. This
sensitive action is called the on off action because either the valve is fully open or fully
closed.
max
Q
Q
=
1
l
, where α>0.
PCE Lab
Linear percentage:
To regulate the flow rates, we prefer this valve. The flow through this valve is proportional to
the valve opening or the lift at a constant differential pressure. A linear valve achieves this by
having a linear relationship between the valve lift and the orifice pass area. The steady state
gain of the valve will be a constant.
max
Q
Q
= l
Equal percentage:
This valve is also used when regulating the flow rates is required. The flow rate increases
more gradually with the valve position. With some non linear process, their steady state gain
may decrease with processing flow rate. If we implement an equal percentage valve in the
control system, we can now keep the system characteristic in terms of the product of the gain
of the process and the valve and we would not have to worry about retuning the controller as
much when the flow rate changes. The valve plug is so shaped such that each increment in
valve lift increases the flow rate by a certain percentage of the previous flow.
max
Q
Q
= R
(l–1)
where R= rangeability parameter.
The performance of all these valves can be judged by transient response of the output to
specific changes in the input.
PROCEDURE:
1. All the electrical circuits were connected.
2. The compressor was switched on and the air pressure was supplied more than 25 psi
to the regulators and the air regulator output pressure was set to 20 psi.
3. The bypass valve and the process outlet valve for On-Off valve was kept completely
open whereas of the other valves were completely closed.
4. By turning the knob, we set the lift to different positions like 25%. 50% till 100 % in
forward and backward movement and measure the time for rise in water level in the
tank for 10 mm.
5. We then calculate the volumetric flow rate and the maximum value of it.
6. We then plot
max
Q
Q
and percent lift and study the valve characteristic for both forward
and backward movement and get a hysteresis curve.
7. The same procedure is followed for linear and equal percentage valves also.
PCE Lab
OBSERVATION TABLE:
Table 4: Observation table for On-Off valve.
Sl No.
Percentage
opening of
the valve
(%)
Time
(s)
Height of
water in the
level tank
(mm)
1
0
2
25
3
50
4
75
5
100
6
75
7
50
8
25
Table 5: Observation table for Linear Percentage Valve.
Sl No.
Percentage
opening of
the valve
(%)
Time (s)
Height of
water in
the level
tank (mm)
1
0
2
25
3
50
4
75
5
100
6
75
7
50
8
25
PCE Lab
Table 6: Observation table for Equal Percentage valve
Sl No.
Percentage
opening of
the valve
(%)
Time
(s)
Height of
water in
the level
tank (mm)
1
0
2
25
3
50
4
75
5
100
6
75
7
50
8
25
MODEL CALCULATIONS:
For Observation No:2 :-
ON-OFF VALVE:
Volumetric flow rate ,
t
Ah
Q
;
Where h= Height of water in the level tank = 20 mm
A= Area of the tank = 0.1 m
2
.
t= Time taken by water for 20 mm rise in the level tank.
0
0
Q
1
Q
hrm /07.0
98
36001.01020
3
3
Similarly
max4
QQ
So,
max
1
Q
Q
LINEAR PERCENTAGE VALVE:
Volumetric flow rate ,
t
Ah
Q
;
PCE Lab
Where h= Height of water in the level tank = 20 mm =
3
1020
m.
A= Area of the tank = 0.1 m
2
.
t= Time taken by water for 20 mm rise in the level tank.
0
0
Q
1
Q
hrm /0847.0
85
36001.01020
3
3
Similarly
max4
QQ
=0.1946 m
3
/hr
So,
max
1
Q
Q
EQUAL PERCENTAGE VALVE:
Volumetric flow rate ,
t
Ah
Q
;
Where h= Height of water in the level tank = 20 mm =
3
1020
m.
A= Area of the tank = 0.1 m
2
.
t= Time taken by water for 20 mm rise in the level tank.
0
0
Q
1
Q
Similarly
max4
QQ
So,
max
1
Q
Q
RESULT TABLE:
Table 7: Result table for On-Off controller
SL
NO.
Volumetric flow rate
(m
3
/hr),
Q
max
Q
Q
1
2
3
4
5
6
7
8
PCE Lab
.
Table 8: Result table for Linear Percentage valve.
SL NO.
Volumetric flow
rate (m
3
/hr),
Q
max
Q
Q
1
2
3
4
5
6
7
8
Table 9: Result table for Equal Percentaage valve.
SL NO.
Volumetric flow
rate (m
3
/hr),
Q
max
Q
Q
1
2
3
4
5
6
7
8
PCE Lab
GRAPHS:
Figure 1: Q/Q
max
versus % Opening of Valve
RESULT:
The On-off, Linear Percentage, Equal Percentage valves were studied and the response curve
for step change in the set point was plotted for all the three valves.
INFERENCE:
0
0.2
0.4
0.6
0.8
1
1.2
0 20 40 60 80 100 120
Q/Q
max
Percentage Lift
Q/Q
max
vs Percentage Lift
PCE Lab
STUDY OF CONTROL SYSTEMS
Aim:
To study the transient response of a liquid flow system for a step change in the set point using
different controllers like Proportional (P), Proportional–Integral (PI), and Proportional–
Integral–Derivative (PID) controllers respectively.
Apparatus:
Experimental Setup
Theory:
A control system is one that controls the value of the controlled variable for either a change
in Set Point (Servo problem), a change in Load (Regulator problem), or a change in both. The
comparator measures the error and the controller provides the necessary signal to actuate the
final control element, which is usually a valve.
The simplest type of controller is the proportional controller. (The on/off control is actually
the simplest, but it is a special case of the proportional controller). The proportional controller
can reduce the error, but cannot eliminate it. If we can accept some residual error,
proportional control may be the proper choice for the situation. The proportional Action may
be represented as:
Where, ε is the error and P
b
is the bandwidth.
If any residual error cannot be tolerated, an additional control mode has to be introduced. If
integral control is added to a proportional controller, the PI, or proportional–integral
controller is obtained. The integral mode ultimately drives the error to zero. This controller
has two adjustable parameters, the gain and the integral time. PI control is given by:
p = (K
c
´
e
)+ p
s
Þ
P(s)
e
(s)
= K
c
1
K
c
P
b
p = (K
c
´
e
)+ p
s
+
K
c
t
I
( )
´
e
dt
0
t
ò
é
ë
ê
ù
û
ú
Þ
P(s)
e
(s)
= K
c
1+
1
t
I
s
æ
è
ç
ö
ø
÷
PCE Lab
Derivative control is another mode that can be added to our proportional or proportional–
integral controllers. It acts upon the derivative of the error, so it is most active when the error
is changingrapidly. It serves to reduce process oscillations.
The PID mode, however, is a combination of all the P and PI and PD modes of control. It is
described by the relationship:
Procedure:
1) All the electrical circuits are connected as shown and the compressor is switched on to
build up the pressure.
2) The bypass valve and process outlet valve are kept half open.
3) The computer is switched on and the process control software is accessed.
4) The process parameters are entered such that the set point remains constant.
5) The time of logging into the software is set to a desired value and the bandwidth,
integral value and derivative value are set for one of the values in the range in which
the process is feasible (Range for P = 50 to 150, I = 20 to 80, D = 20 to 100).
6) The parameters are locked in as per the controller under study.
7) For P control, only the bandwidth is varied with integral and derivative values set at
zero. For PI control, the bandwidth for which the least offset is obtained for the P
control is noted and set constant, then the integral is varied. For PID control, the
above process is done for both P and I values and then the derivative value is varied.
8) The process is started. The graph and the table for the given values of bandwidth,
integral and derivative is noted.
9) The offset is then determined from the graph.
P(s)
(s)
K
c
1
1
I
s
D
s
PCE Lab
Observations:
Part 1: Proportional Control
Log Interval = 25 s and Set Value = 12 LPM
Table 1: Part 1 Observation Table
Sl. No.
Time
(s)
Process Value for
P = 50 (LPM)
Process Value for
P = 100 (LPM)
Process Value for
P = 180 (LPM)
1
2
3
4
5
6
Figure 1: P Controller – Graph of Process Variable(LPM) vs Time(sec)
0
1
2
3
4
5
6
7
8
9
0 100 200 300 400 500 600
Process Variable (LPM)
Time (sec)
P CONTROLLER
P=50
P=100
P=180
PCE Lab
Table 2: Part 1 Result Table
Sl. No.
Bandwidth (P)
Process Value at Infinite Time
Offset
1
50
2
100
3
180
Part 2: PI – Control
Bandwidth (P) = 50, Log Interval = 25 s, and Set Value = 12 LPM
Table 3: Part 2 Observation Table
Sl. No.
Time (s)
Process Value for
I = 50 (LPM)
Process Value for
I = 150 (LPM)
Process Value for
I = 240 (LPM)
1
2
3
4
5
PCE Lab
Figure 2: PI Controller – Graph of Process Variable(LPM) vs Time(sec)
Table 4: Part 2 Result Table
Sl. No.
Integral Value (I)
Process value at infinite time
Offset
1
50
2
150
3
240
Part 3: PID – Control
Bandwidth (P) = 50, Integral (I) = 50, Log Interval = 25 s, and Set Value = 12 LPM
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500 600 700 800
Process Variable (LPM)
Time (sec)
PI CONTROLLER
I=50
I=150
I=240
SV
PCE Lab
Table 5: Part 3 Observation Table
Sl.
No.
Time
(s)
Process Value for D =
30 (LPM)
Process Value for D =
50 (LPM)
Process Value for D =
300 (LPM)
1
2
3
4
5
Figure 3: PID Controller – Graph of Process Variable(LPM) vs Time(sec)
Table 6: Result table for PID Control
Sl. No.
Derivative Value (D)
Process value at infinite time
Offset
1
2
3
0
2
4
6
8
10
12
14
16
0 100 200 300 400 500 600 700
Process Variable
(LPM)
Time (sec)
PID Controller
D=30
D=50
D=300
SV
PCE Lab
Result:
The transient response of the of a liquid flow system for step change in set point is
determined using P, PI, and PID controllers and the values for offset is tabulated as shown
above.
Inference:
