PID controllers
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Transcript of PID controllers
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Shell Global Solutions
Tuning Workshop
PID Controllers
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Shell Global Solutions 2
CP0420
FurnaceTT
TC
What is Controller?
Outlet temperature
Fuel flow
Feed flow
Set Value
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PID Controller Key Concepts
• The PID control algorithm does not "know" the correct output to bring the process to the set point.
• It merely continues to move the output in the direction which should move the process toward the set point.
• The algorithm must have feedback (process measurement) to perform
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Open Loop / Controller in Manual
e.g. Furnace, TC in MANUAL
TC
Process
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Closed Loop/ Auto Mode
TC
Process
e.g. Furnace, TC in AUTO
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PID Controller Tuning Parameters
• Proportional Band (Controller Gain)
• Integral Action ( Reset)
• Derivative Action
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Proportional action
CP0520
Controller output varies proportionally to input :
G = Controller Gainin = deviation or (PV-SV)
c
out = G * inc
= Proportional Band (PB)100%cG
Also:
Proportional action therefore provides a signal proportional to the size of the deviation
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Controller output
Controller input
0 50 100%20 80
100%
50
0
Output span: 100%
Input span: 60%
CP0585
Proportional-only control
( PV )
( MV )
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Proportional-only control
CP0560
Offset
Offset
Process variable
Deviation
Set value
Set value
Deviation
time
time
Low Gain
High gain
- smaller offset - less damping of measured value
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Proportional-only control - Offset
CP0550
tem
pera
ture
Disturbance in feed flow
Offset
Set value change by operator
Set value
Offset
Desired value
time
Process variable (actual measured value)
Process variable trend (if no feedback control)
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Proportional action• Proportional action gives an output signal proportional to the size
of the error.
• Proportional action can be tuned via the Controller Gain (Gc)
• Proportional action will leave an offset between SP and PV.
OP = K *
With:
= (PVP – SPP)
PVP = PV / “Range” * 100 % = PV / (PVEUHI – PVEULO) * 100 %
SPP = SP / “Range” * 100 % = SP / (PVEUHI – PVEULO) * 100 %
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Integral Action Definition
CP0570
Integral action therefore provides a signal which depends the length of time a deviation has existed.
Integral action time i is defined as the time taken for the
controller output to change by the same amount from integral action as that from proportional action.
out = (t) dt1
i
0
t
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Integral actionIntegral action
Deviation
TimeController Output
Integral Action Only
Time
Proportional + Integral ActionController Output
Proportional Action Only
Change due to the Proportional Action
i
Time
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Integral action at different ValuesIntegral action at different Values
Time
Proportional + Integral ActionController Output
Proportional Action Only
Change due to the Proportional Action
i
Time
Proportional + Integral ActionController Output
Proportional Action Only
Change due to the Proportional Action
i
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Proportional & Integral actionInitial kick in output from proportional action.
After that integral action increases output
Process value reaches set point – no off set due to integration
Proportional & Integral controller
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Time (minutes)
Set
po
int
/ P
roce
ss V
alu
e (E
U)
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Ou
tpu
t (%
)
SP
PV
OPInitial kick from proportional action
Integral action eliminates the off set
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Proportional & Integral action
• Proportional action gives an output signal proportional to the size of the error
• Integral action gives a signal which magnitude depends on the time the error has been there. The longer the error is present the higher the contribution of the Integral action to the total output.
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Proportional + Integral control
CP0590
Process Variable
Deviation
Set value
time
Long Integral action time
Short Integral action time Set value
Deviation
time
Process Variable
1
2
Integral Action removes offset
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Derivative Action
CP0610
time
Controller output
Derivative action only
Deviation
time
dtime
Proportional + Derivative actionController output
Proportional action only
change due to the Proportional action
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CP0600
Derivative action therefore provides a signal which depends on the rate-of-change of deviation
Derivative action therefore provides anticipatory action
Derivative action time d is the time taken for the change in controller output due to proportional action to equal the same change as that from derivative action
Derivative Action Definition
out = d ddt
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• Disturbance at t = 10 (min). Initial kick in output from proportional and derivative action; integral action increases OP further; when PV starts to move derivative action brings OP quickly back to steady state value.
PI controller - derivative action removed(Kp = 1; Tp = 6; Td = 2; Kc = 2.3; Ti = 6; Tder = 0)
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Time (minutes)
Set
po
int
/ P
ro
cess
Valu
e (
EU
)
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Ou
tpu
t (%
)
SP
PV
OP
Disturbance of - 5
PI controller - with derivative action(Kp = 1; Tp = 6; Td = 2; Kc = 2.3; Ti = 6; Tder = 0.6)
0
10
20
30
40
50
60
70
80
0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32 34 36 38 40
Time (minutes)
Set
po
int
/ P
ro
cess
Valu
e (
EU
)
0.00
10.00
20.00
30.00
40.00
50.00
60.00
70.00
80.00
90.00
100.00
Ou
tpu
t (%
)
SP
PV
OP
Disturbance of - 5
Proportional & Integral & Derivative action
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Proportional & Integral & Derivative action
• Proportional action gives an output signal proportional to the size of the error
• Integral action gives a signal which magnitude depends on the time the error has been there
• Derivative action gives a signal proportional to the change in the PV. It gives sort of “anticipatory” control. Sensitive to measurement noise !
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Proportional + Integral + Derivative control
CP0620
Process Variable
Deviation
Set value
time
P + I + D action
Set value
Deviation
time
P + I action (without Derivative action)
Process Variable
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PID controller actions - summary
• Proportional action
• Integral (reset) action
• Derivative action
• P + I + D controller
CP0630
out = (t).dt1
i0
t
out = d ddt
out = Gc * in = Gc *
Out = Gc * + (t).dt + d ddt
1
i0
t
for a P-only controller Out = Gc * + 50%
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Proportional controlProportional control
Proportional + Integral controlProportional + Integral control
without Derivative action with Derivative action
Long Integral action time vs. Short Integral action time
Low Gain vs. High Gain
OffsetOffset
CP800
Controller Responses
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Controller Selection
• P-Only Controllers:
•Used when offset is uncritical (some level applications).
• PI controllers are used in 95% of the applications:
•When offset is undesirable
• On applications having long dead time and time constant use PID except if the measurement is noisy.
•Examples
•Large Volume Pressure
•Temperature Control
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Controller Algorithm Selection - Type Td < 0.2*Tp 0.2*Tp < Td < Tp Tp < Td < 5*Tp Td >
5*Tp
Dominant first orderDominant dead time
- PI x x x x
- PID x x
- PIT x x x
- I-only x
- Td = process dead time (minutes)
- Tp = process time constant (minutes)
- Use PI as standard
- Use Derivative action (together with P& I action) only as exception; most effective when 0.5*Tp < Td < 5*Tp
- Proportional Integral Time-delay (PIT) controller when dead time exceeds time constant. Special algorithm and relatively easy to implement in DCS.
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Desired Response Desired Response
Response to a Step Change
Set Value
Time
Process Variable
One Overshoot
One Undershoot
• Desired behavior or response must be decided upon before loop can be tuned.
• Response below could be in general considered as “good” (fast and well damped).
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Valve Failure ActionValve Failure Action Spring to Close (Air Failure Close)
(Air to Open)
Spring to Open (Air Failure Open)(Air to Close)
Decision Fail Action is taken in Process/Safeguarding design
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Reverse and Direct Controller Polarity
If the measurement
increases
The controller output has to be reduced to
counter act
Reverse
PV↑ OP↓ Reverse
If the measurement
increases
The controller output has to be increased to counteract
Direct
PV ↑ OP ↑ Direct
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Controller Action
LC
C-1
Direct-Acting Controller
Output
Pump
(Air Failure Close)
increase of PV leads to increase of OP of controller with constant SP
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Reverse-Acting Controller
LC
C-2
Output
Pump
(Air Failure Close)
increase of PV leads to decrease of OP of controller with constant SP
Controller action
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Valve Linearity
Valves are usually non-linear.That is, the flow through the valve is not the same as the valve position. Several types of valves exist:
LinearSame gain regardless of valve position
Equal Percentage (most commonly used)Low gain when valve is nearly closedHigh gain when valve is nearly open
Quick OpeningHigh gain when valve is nearly closedLow gain when valve is nearly open
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End of The PID Controllers