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
Prof. Cesar de Prada, ISA, UVA 2
Outline
• Flow control • Level Control • Pressure control • Temperature control
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
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
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
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 ∆+∆=∆+∆
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
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:
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
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
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
∆=
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
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
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
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
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)
Prof. Cesar de Prada, ISA, UVA 17
Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…
Prof. Cesar de Prada, ISA, UVA 18
q
FC w
u
Positive Displacement pumps Shaft,. Membrane,… Alternating compressors…
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
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
∼
Prof. Cesar de Prada, ISA, UVA 21
Flow control
FT
FC
Steam
Condensate
Reboiler
Destillation tower
Prof. Cesar de Prada, ISA, UVA 22
Level Control
q
LC
w
u LT
qi
h
Different alternatives for the level transmitter
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
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
-
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
- + -
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
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
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
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
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
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
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
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:
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 /%
+ - + -
Prof. Cesar de Prada, ISA, UVA 35
Pressure control
PT PC
Steam
Condensate
Cooling water
w
Column
Condenser
Slow process, PI / PID
Prof. Cesar de Prada, ISA, UVA 36
Pressure control
PT PC
Steam
Condensate
Cooling water
w
Column
Condenser
Slow process, PI / PID
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
Prof. Cesar de Prada, ISA, UVA 38
Temperature Control
TT
u TC
w
q T
The product flow cannot be changed independently
Prof. Cesar de Prada, ISA, UVA 39
Temperature Control
TT
u TC w
q T
Product by-pass Fast dynamics, low range of control
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
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
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
Prof. Cesar de Prada, ISA, UVA 43
Temperature Control
TT
TC
Steam
Condensate
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