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CHAPTER 18: LEVEL CONTROL
When I complete this chapter, I want to be
able to do the following.
Determine the proper location and volume
of liquid inventories in a process
Determine the dynamics of typical level
processes
Tune level controllers for two typical
control objectives
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Outline of the lesson.
Levels, where are they?
Levels - good and bad aspects
Level dynamics
Level tuning Determining inventory size
CHAPTER 18: LEVEL CONTROL
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1
2
3
15
16
17
LC-1
LC-3
LC-2
dP-1
dP-2
T5
T6
TC-7
AC-1
PC-1
P3
F3
F4
F7
F8
F9
T10
L4
CHAPTER 18: LEVEL CONTROL
Where are liquid inventories?
Why do we design equipment with inventories?
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CHAPTER 18: LEVEL CONTROL
Where are liquid inventories?
1
2
3
15
16
17
LC-1
LC-3
LC-2
dP-1
dP-2
T5
T6
TC-7
AC-1
PC-1
P3
F3F4
F7
F8
F9
T10
L4
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CHAPTER 18: LEVEL CONTROL
Where are liquid inventories? Why?
1
2
3
15
16
17
LC-1
LC-3
LC-2
dP-1
dP-2
T5
T6
TC-7
AC-1
PC-1
P3
F3
F4
F7
F8
F9
T10
L4
Liquid on trays, allows
liquid-vapor equilibrium
Liquid mixing
reduces effects of
composition
disturbances
Flow to tower can be
constant in spite of
fluctuation in feed
flow
Allows uninterrupted
reflux and product
flows in spite of
variable condensation
Uninterrupted
fluid flow to
pump
Liquid covers the heat
exchanger transfer
area
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CHAPTER 18: LEVEL CONTROL
How do inventories affect performance of the
process containing the liquid?
Strongly Weakly Insignificant
Volume of
chemical reactors,
volume has strong
effect on
conversion
Fast material
degradation (reduce
residence time)
Equilibrium stages,
both phases must
be present, but
amount beyond
minimum does not
affect process
Heat exchangers,
must have contact
with area
Drums and tanks,no change to
material properties
But these inventories
have strong effects
on the other processes
influenced by the flows
from these inventories
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CHAPTER 18: LEVEL CONTROL
What are ++ and -- for having liquid inventories?
NEGATIVE ASPECTSPOSITIVE ASPECTS
Conclusion: ??
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CHAPTER 18: LEVEL CONTROL
To design control, we
need to understand the
process dynamics
control objectives
algorithm & tuning
level sizing
Lets determine the
dynamics for each of the
designs
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CHAPTER 18: LEVEL CONTROL
Self-regulatory Non-self-regulatory
0 5 10 15 20 25 30 35 40 45-2
-1.5
-1
-0.5
0
Time
Level
0 5 10 15 20 25 30 35 40 450
0.5
1
1.5
2
Time
Flow
out
0 5 10 15 20 25 30 35 40 45-2
-1.5
-1
-0.5
0
Time
Level
0 5 10 15 20 25 30 35 40 450
0.5
1
1.5
2
Time
Flow
out
outin FFdt
dLA =
Fout does not depend on the level
outin FFdt
dLA =
Fout increases as level increases
Quick reminder of key property of dynamic process behavior
New steady stateNo new steady state
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CHAPTER 18: LEVEL CONTROL
0dt
dL
)( LKF
FFdtdLA
in
outin
=
=
21 PPKF
FFdt
dLA
in
outin
=
=
P1= pump head + gL
21 PPKF
FFdt
dLA
in
outin
=
=
P1
= P3
+ gL 0
0 5 10 1 5 20 2 5 3 0 35 4 0 4 5-2
-1.5
-1
-0.5
0
Time
Level
0 5 10 1 5 20 2 5 3 0 35 4 0 4 50
0.5
1
1.5
2
Time
Flow
out
Non-Self-regulatory
0 5 10 15 20 25 30 35 40 45-2
-1.5
-1
-0.5
0
Time
Level
0 5 10 15 20 25 30 35 40 450
0.5
1
1.5
2
Time
Flow
out
Self-regulatoryConstant
0 5 10 1 5 2 0 25 30 3 5 40 4 5-2
-1.5
-1
-0.5
0
Time
Level
0 5 10 1 5 2 0 25 30 3 5 40 4 50
0.5
1
1.5
2
Time
Flow
out
Non-Self-regulatory 0
Determine if each level is self-regulatory or not
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To design control, we
need to understand the
process dynamics
control objectives
algorithm & tuning
level sizing
Lets determine the
control objectivesfor level control
CHAPTER 18: LEVEL CONTROL
LC
Fin
Fout
What is important?
The level
The manipulated flow
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To design control, weneed to understand the
process dynamics
control objectives
algorithm & tuning
Lets determine the
control objectivesfor level control
To design control, we
need to understand the
process dynamics
control objectives
algorithm & tuning
level sizing
Lets determine the
algorithm & tuningfor level control
CHAPTER 18: LEVEL CONTROL
LC
Fin
Fout
1. Is the control in the figure
a. feedback
b. feedforward
c. neither
d. both
2. What makes control difficult?
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CHAPTER 18: LEVEL CONTROL
LC
Fin
Fout
1. Is the control in the figure
a. feedback
b. feedforward
c. neither
d. both
2. What makes control difficult?
Dead time makes feedback
difficult, but we see that
this process has negligibledead time!
Feedback: The flow out
has a causal effect on the
level.
Since this is feedback,
lets use the old
standard, PI control(D isnt needed).
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LC
D = Fin
MV = Fout
CV = L
CHAPTER 18: LEVEL CONTROL
Controller Tuning
Can we use the standard PI
tuning approach shown in
the schematic?
S-LOOP plots deviation variables (IAE = 608.1005)
0 5 10 15 20 25 30 35 40 45 500
0.2
0.4
0.6
0.8
1
Time
Ma
nipulatedVariable 0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
1DYNAMIC SIMULATION
Time
ControlledVariable
Determine a model
using the process
reaction curve
experiment.
Kc TI
Determine the initialtuning constants from
a correlation.
0 20 40 60 80 100 1200
0.5
1
1.5
S-LOOP plots deviation variables (IAE = 9.7189)
Time
ControlledVariable
0 20 40 60 80 100 1200
0.5
1
1.5
Time
ManipulatedVariable
Apply and fine tune
as needed.
IdttLL
T
tLLKtFt
SP
I
SPCout+
+=
0
'))'((1
))(()(
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LC
D = Fin
MV = Fout
CV = L
CHAPTER 18: LEVEL CONTROL
S-LOOP plots deviation variables (IAE = 608.1005)
0 5 10 15 20 25 30 35 40 45 500
0.2
0.4
0.6
0.8
1
Time
Ma
nipulatedVariable 0 5 10 15 20 25 30 35 40 45 50
0
0.2
0.4
0.6
0.8
1DYNAMIC SIMULATION
Time
ControlledVariable Cannot determine a
model using the
process reaction
curve experiment.
Kc TI
Cannot determine
the initial tuningconstants from
Ciancone (or Ziegler-
Nichols step)
correlation.
0 5 10 15 20 25 30 35 40 45Time
Level
0 5 10 15 20 25 30 35 40 45Time
Flow
out
Standard tuningcharts are not
applicable to a non-
self-regulating level.
The level process isunstable. Without
control, it never
reaches a new steady
state
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Gd(s)
GP(s)Gv(s)GC(s)
GS(s)
D(s)
CV(s)
CVm(s)
SP(s) E(s) MV(s)+
+
+
-LC
D = Fin
MV = Fout
CV = L
CHAPTER 18: LEVEL CONTROL
Lets build a model of the process with the controller, i.e, the closed-
loop system. We will ignore the fast sensor and valve dynamics.
Using block diagram algebra, we obtain
A = cross
sectional
area
)()(1
)(
)(
)(
sGsG
sG
sF
sL
PC
D
in+
=
With Gc(s) being eitherP-only of PI
For a non-self regulating level
AssGsG
DP1)()( ==
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LC
D = Fin
MV = Fout
CV = L
CHAPTER 18: LEVEL CONTROL
We substitute the appropriate models
for each process and controller to
obtain the following transfer function
models, which we can solve
analytically for a step disturbance!
A = cross
sectional
area
A
KTand
K
AT
ss
K
T
sF
sL
CI
C
I
C
I
in
)(
2
1
12)(
)(22
=
=
++
=
Proportional-only control
Proportional-integral control
1
1
)(
)(
+
=
sK
A
K
sF
sL
C
C
in
+=
+
+=
sTKsG
IdttLLT
tLLKtF
I
CC
t
SP
I
SPCout
11)(
'))'((1
))(()(0
[ ]CC
SPCout
KsG
ItLLKtF
=+=
)(
)()(
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CHAPTER 18: LEVEL CONTROL
Stable, first order
Never underdamped
Non-zero s-s offset
Stable, second order
Underdamped when < 1(We want overdamped!)
Zero s-s offset
P-only PI
=
c
KAt
Cin eKFtL
/
11)('
=
c
KAt
in etA
FtL
2/
)('
Disturbance step response Disturbance step response
[ ] ItLLKtF SPCout += )()( IdttLLT
tLLKtFt
SP
I
SPCout+
+= 0 '))'((
1))(()(
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CHAPTER 18: LEVEL CONTROL
P-only Tuning
Determine the expected maximum step disturbance size (Fmax) and
calculate the Kc to give the maximum allowed change in the level(Lmax) .
LC
Fout
Fmax
Lmax
Note, level does
not return to its
set point.
When is this O.K?
Kc = - (Fmax)/ (Lmax)
Fout = ??
[ ] ItLLKtF SPCout += )()(
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CHAPTER 18: LEVEL CONTROL
PI Tuning
Determine the expected maximum step disturbance size (Fmax) andcalculate the Kc and TI to give the maximum allowed change in the level
(Lmax). Set tuning so that damping coefficient, = 1.
LCFout
Fmax
Lmax
Note, level returns
to its set point.
Fout = ??
Kc = - 0. 736 (Fmax)/ (Lmax) TI = 4 (2) A/(-Kc)
Fout
IdttLL
T
tLLKtFt
SP
I
SPCout +
+=
0
'))'((1
))(()(
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CHAPTER 18: LEVEL CONTROL
Lets use these results for averaging and tight level control.
LC
Fin
Fout
P-only control: Kc = - (Fmax)/ (Lmax)PI Control: K
c= - 0. 736 (F
max
)/ (Lmax
) TI
= 4 (2) A/(-Kc
)
Averaging level control, Lmax 40% of maximum rangeTight level control, Lmax 5% of maximum range
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To design control, we
need to understand the
process dynamics
control objectives algorithm & tuning
Lets determine the
control objectivesfor level control
To design control, we
need to understand the
process dynamics
control objectives
algorithm & tuning
level sizing
Lets look again at the
process
CHAPTER 18: LEVEL CONTROL
How do we determine the proper vessel volume?
LC
Fin
FoutV = ?
That is a good question.
Averaging level control will notprovide improvement unless the
vessel is large enough!
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CHAPTER 18: LEVEL CONTROL
One key design goal: maintain the rate of change of themanipulated flow below a maximum when using averaging
tuning. This protects the downstream units from fast
disturbances.
LCFout
Fmax
max
dt
dFout
V = ?
max
2max )(84.1
=
dt
dF
FV
out
The equation is based on a PI controller
with the averaging tuning recommended
in this chapter.See Chapter 18 for derivation
IdttLLT
tLLKtF
t
SP
I
SPCout +
+= 0 '))'((
1))(()(
Lmax
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To design control, we
need to understand the
process dynamics
control objectives
algorithm & tuning
level sizing
CHAPTER 18: LEVEL CONTROL
LC
Fin
Fout
Now, we understand control of a single level!
How small can we make the levels?
Do we have a guideline?
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CHAPTER 18: LEVEL CONTROL
Process plants have many units in series. Inventory control behavessimilar to a series of tanks. How should they be controlled?
F0
LC LC LC
F1 F2 F3
Feed push with levels adjusting flows out
F0
LC LC LC
F1 F2 F3
Product pull with levels adjusting flows in
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CHAPTER 18: LEVEL CONTROL
For a series of levels, what is the importance of damping?
F0
LC LC LC
F1 F2 F3
Step
change
We see that flow variation increases with
number of levels in series
P-only control is not oscillatory
PI (=1) experiences overshoot PI (=0.5) experiences large oscillations
P-only
PI (=1)
PI (=0.5)
Best
Not acceptable
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CHAPTER 18: LEVEL CONTROL WORKSHOP 1
We can have a liquid inventory that is not controlled, if thevessel is large enough. Lets look at an example.
What is the minimum volume for
the storage tank?
Plot the level vs. time.
L
Fin
FoutTime (days)
Flow
rate
The flow in involves batches of 24,000 m3
delivered over 12 hours, with a batch
delivered every five days.
The flow out is the feed to the plant. It must
be continuous and have a constant value.
1/25
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CHAPTER 18: LEVEL CONTROL WORKSHOP 2
The principles we have learned for liquid level control
apply to solid and gas inventories as well.
1. Think of an example in a process plant in which we need to have
an inventory of
a. (granular) solids
b. gas
2. Describe the storage equipment for each.
3. Select a sensor to measure the inventory for each
4. Determine whether the inventory is self-regulating or non-self-
regulating.
5. Sketch the process with control.
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CHAPTER 18: LEVEL CONTROL WORKSHOP 3
Discuss how you determine the proper liquid
inventories for the following unit operations.
1. Liquid on the shell side of ashell and tube heat exchanger.
2. Liquid on a distillation tray
cooling
medium
TC
10
FC1
Bypass and
adjustable 3-way
mixing valve
1
2
3
15
16
17
LC-1
LC-3
AC-1
PC-1
F4
F7
F8
AC-1
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CHAPTER 18: LEVEL CONTROL WORKSHOP 3
3. Liquid in a flash drum
4. Liquid in a CSTR
Feed
Vaporproduct
Liquid
productProcessfluid
Steam
F1
F2 F3
T1 T2
T3
T5
T4
T6 P1
LC
A1
L. Key
Discuss how you determine the proper liquid
inventories for the following unit operations.
L
F
T
A
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CHAPTER 18: LEVEL CONTROL WORKSHOP 4
Calculate the level tuning for the situation described below.
Determine the tuning for tight and for averaging control.
LC
Fin
Fout
V = 50 m3
A = 25 m2
F = 1.5 m3/min
Fmax = 1.0 m3/min
For each tuning, what would be the maximum rate of change of the
manipulated flow for a step disturbance ofFmax = 1.0 m3/min?
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Lots of improvement, but we need some more study!
Read the textbook
Review the notes, especially learning goals and workshop
Try out the self-study suggestions Naturally, well have an assignment!
CHAPTER 18: LEVEL CONTROL
When I complete this chapter, I want to be
able to do the following.
Determine the location and volume of liquid
inventories in a process
Determine the dynamics of various level processes
Tune level controllers for both typical control
objectives
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CHAPTER 18: SUGGESTIONS FOR SELF-STUDY
1. Storing hazardous materials increases the risk in case of
an accident. Search the WEB for information on the
incident at Bhopal, India. Discuss the effect of the
storage volume of methyl isocyanate on the number of
deaths. A good place to start is
http://www.unu.edu/unupress/unupbooks/uu21le/uu21le00.htm#Contents
2. You are designing a reflux drum for a distillation tower
that operates at 10 atm. How does the cost of a carbon
steel, horizontal drum depend on the volume?3. Discuss how you would monitor the performance of
averaging level control. Based on plant data, define
rules for fine tuning the controller.
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CHAPTER 18: SUGGESTIONS FOR SELF-STUDY
4. Inventories are provided for all essential materials.
Discuss how you would determine the proper storage
inventory for some key materials, such as
a. Blood for transfusions
b. Food, e.g., grains and rice
c. Water for a city
5. Describe the physical principles for sensors to measure
the inventory of liquids, gases, and solids.