Improve Control: Level Loops
Improve Control: Level Loops
Improve Control: Level Loops
Reprinted with permission from CEP (Chemical Engineering Progress), June 2008.
Copyright 2008 American Institute of Chemical Engineers (AIChE).
Improve Control
of Liquid
Level Loops
Use this tuning recipe
for the classic integrating
process control challenge.
Robert Rice
Douglas J. Cooper
Control Station, Inc.
PV
Self-Regulating
CO
PV tracks up and
down with CO
PV
IntegratingBehavior
CO
PV at new value
when CO returns
Time
54
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June 2008
CEP
Integrating (non-self-regulating)
behavior in manual mode
The top plot of Figure 1 shows the open-loop (manual
mode) behavior of a self-regulating process. In this idealized response, the controller output (CO) signal and measured process variable (PV) are initially at steady state. The
CO is stepped up from this steady state and then back
down. As shown, the PV responds to the step, and ultimately returns to its original operating level.
The bottom plot of Figure 1 shows the open-loop
response of an ideal integrating process. The distinctive
behavior occurs when the CO returns to its original
value and the PV settles at a new operating level.
FT02
CT01
FLOW
CO2
CT04
FT01
FLOW
TT01
PT01
AT01
PT02
CT02
PRES
BALL
PSI
O2
TT02
AT02
PT03
TEMP
pH
PRES
CT03
BALL
Wild-Stream
Flow, gal/min
CO, %
Level PV / SP, %
TEMP
O2
LIC
shown in Figure 2 (p. 56), when the setpoint (SP) is initially at the design level of operation (DLO) in the first
moments of operation, then PV equals SP (the DLO is
where the setpoint and process variable are expected to be
during normal operation when the major disturbances are
at their normal or typical values).
The setpoint is then stepped up from the DLO on the
left side of the plot. The simple P-only controller is unable
to track the changing SP, and a steady error, called offset,
results. The offset grows as each step moves the SP farther
away from the DLO.
Midway through the process, a disturbance occurs, as
shown in the middle of the plot. (Its size was predetermined for this simulation to eliminate the offset.) When
the SP is then stepped back down (on the right) the offset
shifts, but again grows in a similar and predictable pattern.
CEP
June 2008
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55
65
60
55
50
60
55
50
45
65
3) shifting
the offset
1) Offset grows
2) then disturbance
load changes
50
100
200
300
400
500
600
Time
D, %
65
60
55
50
1) No offset
3) producing
sustained offset
60
50
40
54
2) ...then disturbance
load changes
52
50
40
80
120
160
Time
56
54
52
50
48
CO, %
60
Kc = 0.3
Modest oscillation
Kc = 1.2
PV oscillates
55
50
45
57
54
51
48
45
Kc = 1
PV oscillates
Kc = 4
Kc = 8
Overshoot but PV oscillates
no oscillation
100
80
60
40
20
150
300
450
600
750
75
Time
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June 2008
150
225
300
Time
56
CO, %
PV and SP, %
Kc = 0.3
No oscillation
PV and SP, %
D, %
Process Control
CEP
Figure 4 shows an ideal self-regulating process simulation that is controlled using this PI algorithm. Reset time,
Ti, is held constant throughout the simulation while controller gain, Kc, is doubled and then doubled again. As Kc
increases, the controller becomes more active, and, as
expected, this increases the tendency of the PV to display
oscillating (underdamped) behavior.
For comparison, consider PI control of an ideal integrating process simulation as shown in Figure 5. Ti, is
again held constant while Kc, is increased. A counter-intuitive result is that as Kc becomes small and as it becomes
large, the PV begins displaying an underdamped (oscillating) response behavior. While the frequency of the oscillations is clearly different between a small and large Kc,
when seen together in a single plot, it is not always obvious in what direction the controller gain needs to be
adjusted to settle the process, in particular, when seeing
such unacceptable performance on a control room display.
PI
PID
Kc
2Tc + p
Ti
Td
1
K *p (Tc + p )2
2Tc + p
2Tc + p
1
*
K p (Tc + 0.5 p )2
2Tc + p
0.25 p 2 + Tc p
2Tc + p
(3)
It is interesting to note when comparing these two models that individual values for the familiar process gain, Kp,
and process time constant, Tp, are not separately identified
for the FOPDT integrating model. Instead, an integrator
gain, Kp*, is defined that has units of the ratio of the process
gain to the process time constant, or:
K *p [=]
Kp
Tp
or
K *p [=]
PV
CO time
(4)
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57
Process Control
Disturbance
Flow, L/min
15.3
2.5
Setpoint, m
Tank
Level, m
4.0
LC
4.01
Controller
Output, %
70.0
Discharge
Flow, L/min
17.8
for tuning. Specifically, p is used as the basis for computing the closed-loop time constant, Tc.
Building on the popular internal model control (IMC)
approach to controller tuning, the closed-loop time constant is computed as Tc = 3p (3).
The controller tuning correlations for integrating
processes use this Tc, as well as the Kp* and p from the
FOPDT integrating model fit, in the correlations of Table 1.
2
0
80
75
70
20
CO
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CO, %
SP
PV
58
Level, m
Brine Feed
Flow, L/min
CEP
25
30
35
40
45
Time, min
the total flow into the tank is less than the flow pumped
out, the liquid level will fall and continue to fall.
Figure 7 is a plot of the pumped-tank behavior with the
controller in manual mode (open-loop). The CO signal is
stepped up, increasing the discharge flowrate out of the
bottom of the tank. The flow out becomes larger than the
total feed into the top of the tank and, as shown, the liquid
level begins to fall. As the situation persists, the liquid
level continues to fall until the tank is drained. The sawtoothed pattern occurs when the tank is empty because the
pump briefly surges every time enough liquid accumulates
for it to regain suction.
Figure 7 does not show that if the controller output were
to be decreased enough to cause the flowrate out to be less
than the flowrate in, the liquid level would rise until the
tank was full. If this were a real process, the tank would
overflow and spill, creating safety and profitability issues.
Slope2
Level, m
4.8
4.4
Slope1
4.0
75
CO1
70
(27, 5.2)
5.2
CO, %
CO, %
Level, m
5.2
CO2
65
4.8
(36, 4.6)
4.4
(24, 4.8)
4.0
75
CO1 = 65
70
CO2 = 75
65
20
25
30
35
40
20
25
Time, min
Level, m
(6))
4.8
4.4
P = 1 min
4.0
CO, %
40
5.2
and
dPV
dPV
dt
dt
2
K *p =
CO2 CO1
35
dPV
= K *p CO1 (t p )
dt 1
= K *p CO2 (t p )
30
Time, min
dPV
dt
(31, 5.2)
(7)
75
70
65
20
25
30
35
40
Time, min
June 2008
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59
D, %
Process Control
5.0
4.8
4.6
4.4
80
70
60
4
3
2
1
10
20
30
40
50
60
70
80
Time
Sample Time, T = 1 s
Kc =
1 2Tc + p
K *p (Tc + p )2
Ti = 2Tc + p
(8)
Distillation
Column
Kc =
Reflux Drum
FIC
L
FIC
D
Distillate Valve
Reflux Valve
Level PV / SP, %
50
40
Reflux Flow, %
Ti = 2( 3) + 1 = 7 miin
Lower Constraint
30
90
Literature Cited
80
70
60
50
40
30
20
0
12
16
20
24
28
Time, h
Using the tuning recipe for reflux drum (top) level control improves the
performance (bottom) with 95% less controller
output movement.
60
1 2( 3) + 1
= 18 m/%
0.025 ( 3 + 1)2
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