Download - Some typical control loops
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Prof. Cesar de Prada, ISA, UVA 1
Some typical control loops
Prof. Cesar de Prada Dpt. Systems Engineering and Automatic Control
Univ. of Valladolid
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Prof. Cesar de Prada, ISA, UVA 2
Outline
• Flow control • Level Control • Pressure control • Temperature control
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Prof. Cesar de Prada, ISA, UVA 3
q a
Flow control
FC w u
Centrifugal pump
Flowmeter Control Valve
Pump, valve: sizing, placement
Flowmeter: Type, range
Right order: Pump, flowmeter, valve
Important element: valve selection
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Prof. Cesar de Prada, ISA, UVA 4
Sizing From a design point of view, control valves with a large Cv should be chosen, as they present a lower pressure drops, allowing the use of smaller pumps. Nevertheless, the use of smaller control valves gives wider flow changes making the process more controllable.
q
∆pv
a
∆p0 ∆pb
u
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Prof. Cesar de Prada, ISA, UVA 5
Example Design specifications
Flow: qs = 100 gpm Pressure drop in the line ∆pL = 40 psi Total Pressure difference ∆p0 = -150 psi density = 1 desired valve opening = 50%
Case 1: ∆pv = 20 psi Case 2: ∆pv = 80 psi
q
∆pv
a
∆p0 ∆pb
u Lvb0 pppp ∆+∆=∆+∆
Higher pressure in the line end
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Prof. Cesar de Prada, ISA, UVA 6
Example Case 1: ∆pv = 20 psi Case 2: ∆pv = 80 psi ∆pb = 150+40+20= 210 ∆pb = 150+40+80= 270
q
∆pv
a
∆p0 ∆pb
u 36.22C 72.44C
80C5.0100 20C5.0100
paCq
2v1v
2v1v
vvs
====
ρ∆
=
Lvb0 pppp ∆+∆=∆+∆
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Prof. Cesar de Prada, ISA, UVA 7
Range of operation Assuming that ∆pb is constant Case 1: a=1 , a=0.1 Case 2: a=1, a=0.1
gpm2.24q gpm3.33q
100q40120C1.0q
100q4060C1.0q
gpm141q 115gpmq
100
q40120C1q 100q4060C1q
120150270pp 60150210pp
paCq pppp
min21min
22min
2v2min
21min
1v1min
max21max
22max
2v2max
21max
1v1max
0b0b
vvLb0v
==
−=
−=
==
−=
−=
=−=∆+∆=−=∆+∆ρ
∆=∆−∆+∆=∆
The smaller valve provides a wider range of operation in q
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Prof. Cesar de Prada, ISA, UVA 8
Design
q
qpppCaq
q
qpppC1q
2
s
minLsb0vminmin
2
s
maxLsb0vmax
∆−∆+∆=
∆−∆+∆=
Size the pump (∆pb) and valve Cv as a function of the maximum and minimum flows required for the operation of the process, taking into account the design flow qs and pressures ∆p0, ∆pLs solving:
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Prof. Cesar de Prada, ISA, UVA 9
Design
1q
qa if equations for this existssolution Amin
maxmin <
Otherwise, use a split range control structure
q
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Prof. Cesar de Prada, ISA, UVA 10
q
∆pv
a h
∆p0 ∆pb
]ghq)AfL
Ca1(p[
LA
tdqd
)q(p Avq ALm qCa1p
gAhvAfLpA)pp(Atd
mvd
222
v2
20
22b
22v
2v
2vb0
−++β−αω+ρ
∆=
β−αωρ=∆=ρ=ρ=∆
ρ−ρ−∆−∆+∆=
Flow control
u
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Prof. Cesar de Prada, ISA, UVA 11
Linearized model
aK)p(Kqtdqd
]aqCa2)p([
q2)AfL
Ca1(
1
qtdqd
q2)AfL
Ca1(
LA
1
]aqCa2qq2)
AfL
Ca1()p([
LA
tdqd
]ghq)AfL
Ca1(p[
LA
tdqd
201
0
22v
30
022
v2
022
v2
0
22v
30
22v
20
222
v2
20
∆+∆∆=∆+∆
τ
∆
ρ+∆∆
++βρ=
=∆+∆
++β
∆
+∆
++β−ρ∆∆
=∆
−++β−αω+ρ
∆=
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Prof. Cesar de Prada, ISA, UVA 12
Changes in the operating point
02
2v
22v
22
022
v2
201
)A
CfLa1Ca(a
qK q2)
AfL
Ca1(
LA
1
aK)p(Kqtdqd
++β=
++β=τ
∆+∆∆=∆+∆
τ
q
t
τ grows when the opening of the valve increases K2 decreases when the opening of the valve increases
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Prof. Cesar de Prada, ISA, UVA 13
Linearized model
K2 decreases when the opening of the valve increases
a
u 100 %
A equal percentage valve compensates the change in gain
1
0
0 % uKa
tdad
vv ∆=∆+∆
τ
Valve dynamics must be taken into account very often. Let’s assume that it is approximated by:
q a
u
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Prof. Cesar de Prada, ISA, UVA 14
Block diagram
u %
+ -
W ( ) ( )1s
K1s
K 2
v
v
+τ+τ
Q
( )1sK1
+τ
∆P0
+ ( )sT
1sTK
i
ip +
Kp Ing /%
The transmitter dynamic can be neglected Choose the transmitter gain according to the maximum admissible flow
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Prof. Cesar de Prada, ISA, UVA 15
Field installation
q
The use of the manual valves allows to remove the control valve for repair without stopping the flow to the process
q
A A
A
C
C C
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Prof. Cesar de Prada, ISA, UVA 16
q a
Flow control
FC w u
PI Fast and noisy process Low Kp to decrease the noise effect (0.6 %/%) Low Ti to cancel soon the steady state error (0.1 min)
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Prof. Cesar de Prada, ISA, UVA 17
Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…
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Prof. Cesar de Prada, ISA, UVA 18
q
FC w
u
Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…
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Prof. Cesar de Prada, ISA, UVA 19
Minimum flow in the pump
q a
FC
w
u
FT
FC Fmin
Sometimes, in order to guarantee a minimum flow through the pump, an extra flow loop is added. When w > Fmin the recirculation valve is closed, but if w < Fmin then the extra flow loop opens the recycle to maintain the required flow
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Prof. Cesar de Prada, ISA, UVA 20
q
Flow control
FC w u
When the flow is high, instead of control valves, variable speed pumps are a sensible alternative that allows to save energy. A frequency converter (o similar device) connected to the pump asynchronous motor is required
M
∼
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Prof. Cesar de Prada, ISA, UVA 21
Flow control
FT
FC
Steam
Condensate
Reboiler
Destillation tower
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Prof. Cesar de Prada, ISA, UVA 22
Level Control
q
LC
w
u LT
qi
h
Different alternatives for the level transmitter
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Prof. Cesar de Prada, ISA, UVA 23
Level Control
q
LC w
u LT
qi
h
f0fat0
201
ii
i
phg)p( pghpp
aK)p(Kqtdqd
qqtdhdA qq
tdhdA
Ahm qqtdmd
∆−∆ρ=∆∆−ρ+=∆
∆+∆∆=∆+∆
τ
∆−∆=∆
−=
ρ=ρ−ρ=
uKatdad
vv ∆=∆+∆
τ
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Prof. Cesar de Prada, ISA, UVA 24
Block diagram
u
% +
-
W ( ) ( )1s
K1s
K 2
v
v
+τ+τ Q
( )1sK1
+τ
-∆Pf
+
Kp Ing /%
R(s) +
+
As1 H
gρQi
-
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Prof. Cesar de Prada, ISA, UVA 25
Block diagram
u
%
W ( ) ( )1s
K1s
K 2
v
v
+τ+τ
( )1sK1
+τ
∆Pf
+
Kp Ing /%
R(s) +
12 gKAssA
1sρ++τ
+τH
Qi
- + -
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Prof. Cesar de Prada, ISA, UVA 26
Level Control
q
LC w
u LT
qi
h aKq
tdqd: K smallor f
aK)p(Kqtdqd
qqtdhdA qq
tdhdA
Ahm qqtd
md
21
201
ii
i
∆=∆+∆
τ
∆+∆∆=∆+∆
τ
∆−∆=∆
−=
ρ=ρ−ρ=
uKatdad
vv ∆=∆+∆
τ
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Prof. Cesar de Prada, ISA, UVA 27
Block diagram
u
% +
-
W ( ) ( )1s
K1s
K 2
v
v
+τ+τ
Q
Kp Ing /%
R(s) +
As1 H Qi
-
In practice it behaves as a process with an integrator
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Prof. Cesar de Prada, ISA, UVA 28
Tight /Average control
LC w
u LT h
LC w
u LT qi h
qi
The level must be maintained tightly: PI with “active” tuning
Store liquid + smooth changes in qi : P with “loose” tuning
Surge/Supply tank
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Prof. Cesar de Prada, ISA, UVA 29
Average Control
q
LC
w
u LT
qi
h
Smooth disturbances
P control with low Kp: The level oscillates and there is steady state error but q changes smoothly
u = Kpe + bias
If w = 50%, Kp= 1 and bias = 50%, then u = 100 if h = 100%, u = 0 if h = 0
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Prof. Cesar de Prada, ISA, UVA 30
Units in series
LC w
u LT h
qi
LC w
u LT h
All level control must be placed in the same direction
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Prof. Cesar de Prada, ISA, UVA 31
Several streams
q
LC
w
u LT
qi
h
If possible, then choose the larger stream for control
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Prof. Cesar de Prada, ISA, UVA 32
Pressure control
PC PT
Fi
F
u
a
w
Many different dynamics and aims
Fast process
PI with “tight” tuning
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Prof. Cesar de Prada, ISA, UVA 33
Pressure control
{ }
aKFKptdpd
aap
ppFpaCppp
tdpd
pRTaCppVM
ppp
paCappCFtdpd
RTVM
ppaCFtdpd
RTVM
tankisothermal RTM
p Vm
ppaCFFFtdmd
2i1
0
2f
2
i
0v
2f
2
0v
2f
2
02f
2v02f
2vi
0
2f
2vi
2f
2vii
∆−∆=∆+∆
τ
∆
−
−∆
−
=∆+∆
−
∆
−−∆−−∆=
∆
−−=
ρ=ρ=
−−=−=
Fi
F a
p
pf
uKatdad
vv ∆=∆+∆
τValve:
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Prof. Cesar de Prada, ISA, UVA 34
Block diagram
u %
W ( ) ( )1s
K1s
K 2
v
v
+τ+τ
P
( )1sK1
+τ
∆Fi
( )sT
1sTK
i
ip +
Kp Ing /%
+ - + -
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Prof. Cesar de Prada, ISA, UVA 35
Pressure control
PT PC
Steam
Condensate
Cooling water
w
Column
Condenser
Slow process, PI / PID
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Prof. Cesar de Prada, ISA, UVA 36
Pressure control
PT PC
Steam
Condensate
Cooling water
w
Column
Condenser
Slow process, PI / PID
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Prof. Cesar de Prada, ISA, UVA 37
Temperature Control
TT
u TC
w
q T
Many architectures / processes Slow process PID Transmitter dynamics can be significant Be careful with the placement of the transmitter in order to avoid transport delays
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Prof. Cesar de Prada, ISA, UVA 38
Temperature Control
TT
u TC
w
q T
The product flow cannot be changed independently
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Prof. Cesar de Prada, ISA, UVA 39
Temperature Control
TT
u TC w
q T
Product by-pass Fast dynamics, low range of control
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Prof. Cesar de Prada, ISA, UVA 40
Temperature Control
TT
u TC
w
q T
The valves operate in opposition, one is air-open and the other one air-close The total product flow is not changed
u 100 %
100 %
B A
B
A
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Prof. Cesar de Prada, ISA, UVA 41
Temperature Control
TT
u TC
w
q T
Three ways valve
Mixing valve at the output or splitting valve at the input
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Prof. Cesar de Prada, ISA, UVA 42
Temperature Control
TT
u TC
w
q T
Heating fluid by-pass Slower dynamics
Configurations with two valves or one three ways valve
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Prof. Cesar de Prada, ISA, UVA 43
Temperature Control
TT
TC
Steam
Condensate