Transcript No Slide Title

C APEC
Ph.D. Summer school
Process and Tools Integration
Operability and Control for
Process Integration
17. August 2005
Sten Bay Jørgensen
CAPEC - Department of Chemical Engineering
Technical University of Denmark,
DK-2800 Lyngby, Denmark
Motivation for Process and Design Integration
No recycle of information flow (arrow) – Integration possible ?
Sequential design of
Heat integration
Issue 2
Issue 1
Mass integration
Control
Recycle of information flow – Integration possible?
Issue 1
Issue 2
Integrated design of
Heat and
mass integration
with control
Requirement: Measures for dynamic consequences of integration to be used
early in the design phase for control structuring and design
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Operability and Control for Process Integration
2
Dynamics and Control of Integrated Plants
• Process dynamics and control – a recap!
• Transfer functions, dynamics and stability
• Process integration structures
• Effects of process integration on dynamics and control
• Analysis of linear behaviour
• Implications upon control
• Nonlinear behaviour
• Dynamic consequences of optimal operation
• How to configure control?
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Operability and Control for Process Integration
3
Schedule for
Operability and Control of integrated plants
Lecture 1: Process dynamics and control recap 1
Lecture 2: Process dynamics and control recap 2
Lecture 3: Control of plants with units in series
Lecture 4: Dynamics of integrated processes
Lecture 5: Control effects of recycle
Lecture 6: Effects of process integration and optimization
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Operability and Control for Process Integration
4
Lecture 1: Process Dynamics and Control recap 1
• Chemical Process Dynamics Simplified
• Material Balance Control
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Operability and Control for Process Integration
5
Chemical Process Dynamics
A
A+ B
B
A → B
Heat Exchanger
Reactor
Separator
Standard process dynamics considers single simple standard
units with linear dynamics expressed in transfer functions
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Operability and Control for Process Integration
6
Material Balance P-Control exit flow
Fi
D(s)
LC
R(s)
S
Gc(s)
Gpd(s)
U(s)
S
Gp(s)
Y(s)
-
Fo
dV
 Fi  Fo
dt
Fo  Fo0  K c  (Vset  V )
y(t )  V (t )  V 0 (t )
u (t )  Fo (t )  Fo0 (t )
d (t )  Fi (t )  Fi 0 (t )
r (t )  Vset (t )  V 0 (t )
Y ( s) 
Gc ( s)G p ( s)
1  Gc ( s)G p ( s)
Gc ( s)  K c
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R( s) 
G pd ( s)
1  Gc ( s)G p ( s)
1
1
G p ( s) 
G pd ( s) 
s
s
Operability and Control for Process Integration
D( s )
7
Material Balance P-Control simulation
Fi
V
5
4.5
LC
4
Fo
0
2
4
6
8
10
0
2
4
6
8
10
dV
 Fi  Fo
dt
Fo  Fo0  K c  (Vset  V )
Fi 0  2.0 Fi  3.0
V (0)  Vset  4.0
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Fo
3
2.5
2
Operability and Control for Process Integration
8
Material Balance PI-Control
Fi
D(s)
LC
R(s)
S
Gc(s)
Gpd(s)
U(s)
S
Gp(s)
Y(s)
-
Fo
dV
 Fi  Fo
dt
Fo  Fo0  P(t )  I (t )
y(t )  V (t )  V 0 (t )
u (t )  Fo (t )  Fo0 (t )
d (t )  Fi (t )  Fi 0 (t )
r (t )  Vset (t )  V 0 (t )
Y ( s) 
Gc ( s)G p ( s)
R( s) 
G pd ( s)
D( s )
1  Gc ( s)G p ( s)
1  Gc ( s)G p ( s)

1 
1
1
dI (t ) K c


G
(
s
)

K

1

G
(
s
)

G
(
s
)

c 
p
pd


 (Vset (t )  V (t )), I (0)  0 c
T
s
s
s
i 

dt
Ti
P(t )  K c  (Vset (t )  V (t ))
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Operability and Control for Process Integration
9
Material Balance PI-Control simulation
Fi
5
V
4.5
LC
4
3.5
Fo
2
4
6
8
10
2
4
6
8
10
3.5
3
F
o
dV
 Fi  Fo
dt
Fo  Fo0  P(t )  I (t )
2.5
P(t )  K c  (Vset (t )  V (t ))
2
dI (t ) K c

 (Vset (t )  V (t )), I (0)  0
dt
Ti
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0
0
Fi 0  2.0 Fi  3.0 V (0)  Vset  4.0
Operability and Control for Process Integration
10
Material Balance P-Control inlet flow
4
V
Fi
3.5
LC
3
2
4
6
8
10
2
4
6
8
10
3
F
i
Fo
dV
 Fi  Fo
dt
Fi  K c  (Vset  V )
Fo0  2.0 Fo  3.0
0
2.5
2
0
V (0)  Vset  4.0
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Operability and Control for Process Integration
11
Material Balance PI-Control simulation
4.2
Fi
V
4
LC
3.8
3.6
3.4
4
6
8
10
0
2
4
6
8
10
F
i
3
2.5
P(t )  K c  (Vset (t )  V (t ))
2
dI (t ) K c

 (Vset (t )  V (t )), I (0)  0
dt
Ti
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2
3.5
Fo
dV
 Fi  Fo
dt
Fi  Fi 0  P(t )  I (t )
0
Fo0  2.0 Fo  3.0 V (0)  Vset  4.0
Operability and Control for Process Integration
12
Lecture 2: Process Dynamics and Control recap!
• Transfer functions and single loop control
• Internal model based control
• Performance limitations in single loop control
• Control of Production Rate in Chemical Plant
• Front end control (Push)
• On demand control (Pull)
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Operability and Control for Process Integration
13
Transfer functions
Local Transfer Function
• zi a zero in left half plane
gives overshoot
• pj a pole in left half plane
gives exponential decay
X prod (s)
F(s)

 G (s) 

m
i 1
n
j1
(s  z i )
(s  p j )
Initially single variable transferfunctions are considered, i.e. all
signals are scalars: gi(s) = ni(s)/di(s)
Transfer functions will also be divided into g(s)=ga(s)gm(s)
where gm(s) is the minimum phase part
and ga(s) is the allpass part,
 s  zi
sT
ˆ
which contains all nonminimum
Ga (s)  e 
s  zi *
phase components:
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Operability and Control for Process Integration
14
Single Control Loop
Standard single variable open loop process:
d
gd
y = g u + gd d
y
u
gd
ggc
y
d
r
1  ggc
1  ggc
g
d
r
gd
u
g
gc
-1
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Standard single loop control:
• Significantly reduces sensitivity to
y disturbances at low frequences
• For high gain control the sensitivity to model
uncertainty is significantly reduced
• Control performance is limited for RHP
zeros, i.e. Nonminimumphase behaviour
Operability and Control for Process Integration
15
Internal Model Based Control Design
T heprocess G ( s) with the model Gˆ ( s)  Gˆ a ( s)Gˆ m( s)
where Gˆ m( s) is stable, and thedisturbanc e V ( s)  Va ( s)Vm( s)
is controlledwithT heminimum
the IMC- controller:
processG ( s ) with theintegral
modelG ^ ( s )  Gerror
^ ( s )G ^ ( by
s)
a


m

where G ^ m( s ) is stable, and thedist urbance V ( s )  Va ( s )Vm( s )
1
ˆ
GcIMC ( s)  GˆGmV(sm)  G^ G
V aG ^VVm
is controlledwith minimum integral
error by theIMC controller:
1
cIMC
m
m
a
1
m
y  G ^es
r  (1:G
G ^ cIMC
)d
For step disturbanc
(s)  Gˆ m 1 (s) The IMC regulator
For step dist urbances : GcIMC ( s )  G ^ m 1 ( s )
a
d
r
gives the closed loop:
gd
y
u
g
gcIMC
-ĝm
-1
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a
y  Gˆ a r  (1  Gˆ a) d
Thus the nonminimum phase in
Ĝa limits achievable performance!
Operability and Control for Process Integration
16
Control Performance Reducing Dynamics
• Local Transfer Function
X prod (s)
F(s)

 G (s) 

m
i 1
n
j1
(s  z i )
(s  p j )
– Real zero in right half plane
Xprod
• Zero Dynamics
Time
– Real pole into right half plane
Xprod
• Singularities (due to sensitivity to uncertainty)
– Complex pole pair into right half plane
Xprod
Time
Time
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Operability and Control for Process Integration
17
Material Balance P-Control
Fi
D(s)
R(s)
LC
S
Gc(s)
U(s)
Gpd(s)
Gp(s)
S
Y(s)
-
Fo
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G p ( s) 
u (t )  Fo (t )  Fo0 (t )
d (t )  Fi (t )  Fi 0 (t )
r (t )  Vset (t )  V 0 (t )
Gc ( s)G p ( s )
G pd ( s)
Y ( s) 
R( s) 
D( s )
1  Gc ( s)G p ( s )
1  Gc ( s)G p ( s )
dV
 Fi  Fo
dt
Fo  Fo0  K c  (Vset  V )
Gc ( s)  K c
y(t )  V (t )  V 0 (t )
1
1
G pd ( s) 
s
s
 Kc
1
R( s) 
D( s )
s  Kc
s  Kc
U ( s )  K c   R( s )  Y ( s ) 

Operability and Control for Process Integration
18
Plant Production Rate – Front End 1
Raw
Material
Storage
Purchasing
dV1
 Fi  F1
dt
dV2
 F1  F2
dt
dV3
 F2  F3
dt
dVP
 F3  Fo
dt
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Final
Product
Storage
Fi
LC
LC
Fo
LC
Management or Production
Supervision
F1  F10  K c1 (V1, set  V1 )
F2  F20  K c 2 (V2, set  V2 )
F3  F30  K c 3 (V3, set  V3 )
Operability and Control for Process Integration
19
Plant Production Rate – Front End 2
Raw
Material
Storage
Final
Product
Storage
Fi
Purchasing
LC
LC
Fo
LC
Management or Production
Supervision
Y1 ( s) 
1
U 0 ( s)
s  K c1
U1 ( s)   K c1Y1 ( s)
 K c1
1
Y2 ( s) 
U1 ( s ) 
Y1 ( s )
s  Kc2
s  Kc2
Y3 ( s) 
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 Kc2
1
U 2 (s) 
Y2 ( s)
s  K c3
s  K c3
U 2 ( s)   K c 2Y2 ( s)
U 3 ( s)   K c 3Y3 ( s)
YP ( s) 
U 3 ( s )  D( s )  K c 3
1

Y3 ( s)  D( s)
s
s
s
Operability and Control for Process Integration
20
Plant Production Rate – Front End 3
Raw
Material
Storage
Purchasing
Final
Product
Storage
Fi
LC
LC
Fo
LC
Management or Production
Supervision
YP ( s) 
 K c 3  K c 2  K c1
1
1
U 0 ( s )  D( s )
s s  K c 3 s  K c 2 s  K c1
s
Simple strategy u0 (t )  d (t )  U 0 (s)  D(s)
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Operability and Control for Process Integration
21
Plant Production Rate - On Demand
Raw
Material
Storage
Purchasing
dV1
 Fi  F1
dt
dV2
 F1  F2
dt
dV3
 F2  F3
dt
dVP
 F3  Fo
dt
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Final
Product
Storage
Fi
LC
LC
LC
Fo
LC
Fi  Fi 0  K c1 (V1, set  V1 )
F1  F10  K c 2 (V2, set  V2 )
F2  F20  K c 3 (V3, set  V3 )
F3  F30  K cP (VP , set  VP )
Operability and Control for Process Integration
22
Lecture 3: Control of Plants with units in series
• Units in Series
• Disturbance effects
• Production rate – front end
• Production rate – on demand
• How to achieve changes in production rate
• Partial control
• Reactor control
• Examples of Production rate control
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Operability and Control for Process Integration
23
Units in Series - No Recycle
B
A
A B C
B C
C
• The plantwide control problem
is greatly simplified when there
is no recycle of mass or energy.
• The control system of each unit
is configured individually to
handle load disturbances.
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• Separation Example
Volatility order: A > B > C
Direct Sequence: The lightest
component is taken out of the
top of the first column.
Operability and Control for Process Integration
24
Production Rate - Front End
PC
FC
PC
LC
LC
CC
CC
B
A
A B C
B C
LC
LC
CC
CC
C
Disturbances propagate in the direction of mass flow
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Operability and Control for Process Integration
25
Production Rate - On Demand
PC
PC
LC
LC
CC
CC
B
A
A B C
B C
LC
LC
CC
CC
C
FC
Disturbances propagate in the opposite direction of mass flow
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Operability and Control for Process Integration
26
Production Plant without recycles
An ideal abstraction since energy and rawmaterials are not used very efficiently!
Raw Material
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Raw Material
Purification
Reactor
Product
Purification
Operability and Control for Process Integration
Product
27
Production Rate
• Changes in production rate can be achieved only
by changing the conditions in the reactor.
• Some variable that affects the reaction in the
reactor must vary.
Liquid Phase Reactors
• Hold-up
• Temperature
• Concentrations
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Gas Phase Reactors
• Pressure
• Temperature
• Concentrations
Operability and Control for Process Integration
28
Partial Control
• Often for reactors (and other units) the number of
control objectives exceed the number of
manipulated variables.
• We must assign manipulated variables to achieve
the control objectives, which must be important
for the operation of the plant and leave the rest of
the variables uncontrolled.
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Operability and Control for Process Integration
29
Plantwide Production Rate Control
• Production rate changes should be achieved by
modifying the setpoint of a partial control loop in
the reaction section.
• Separation section will not be significantly
disturbed.
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Operability and Control for Process Integration
30
Reactor Control
• Managing energy (temperature control)
• Keeping as constant as possible the composition
and flow rate of the total reactor feed stream
(Fresh feed and recycle).
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Operability and Control for Process Integration
31
Units in Series - Production Rate
A
A
A B
A B
B
 Ea 

R  V  k (T )  x A k (T )  A0 exp  
 RT
g 

R R
R R Ea

 
Sensitivities:
V V
T T RgT
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• How do we
specify and
control the plantwide production
rate of B, when
there is a reactor
in the plant?
• Reaction kinetics
has to be
considered!
R
R

x A x A
Operability and Control for Process Integration
32
Units in Series - Production Rate
PC
• The production rate
is controlled through
A
partial control of the
LC
reaction rate.
CC
A
A B
V controlled
CC
LC
xA controlled
T controlled (by ass.)
• Production rate may
LC
be changed by
CC
changing the setpoint
B
to the reactor CC or
A B
the reactor LC.
R  V  k (T )  x A
• Reactor LC change
will not change the
All three dominant reaction rate variables
composition fed to
controlled => SMALL variance.
the distillation col.
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Operability and Control for Process Integration
33
Units in Series - Production Rate
• One dominant
variable, xA, of the
A
reaction rate is
uncontrolled because
LC
CC
A
reactor composition
A B
measurement is not
LC
possible.
• Reaction rate and
LC
production rate may
fluctuate.
CC
B •
Production rate may
A B
be changed by
R  V  k (T )  x A
changing the setpoint
xA not controlled directly. This leads to
to the reactor FC or
larger variance in the production rate than
the reactor LC.
in the previous configuration.
• Rate set at front end.
PC
FC
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Operability and Control for Process Integration
34
Units in Series - Production Rate
PC
A
LC
CC
LC
A
A B
LC
CC
A B
R  V  k (T )  x A
xA not controlled directly. This leads to
larger variance in the production rate than
in the first configuration.
B
• On-Demand:
The production rate
is specified by setting
the FC of the bottom
product in the
distillation column.
• The disturbances
propagates in the
opposite direction of
the mass flow.
FC
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Operability and Control for Process Integration
35
Lecture 4: Process Integration and Dynamics
• Process Integration Structures
• Series – has been covered
• Parallel
• Recycle
• Example Recycle Plant models
• Disturbance Sensitivity of Recycle plant
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Operability and Control for Process Integration
36
Generic Production Plant
Energy Recycle
Raw Material
Raw Material
Purification
Reactor
Product
Purification
Product
Reactant Recycle
Process integration is mandatory for energy and rawmaterial efficiency!
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Operability and Control for Process Integration
37
Dynamic consequences of process integration
g4(s)
g1(s)
g2(s)
g3(s)
• Plant as an integration of different unit processes
• Relate behaviour of integrated plant to
• behaviour of individual units
• structure of interconnections
• Thereby existing knowledge of unit behaviour can be
exploited, for the analysis of linear behaviour
Hangos (1991) and Jacobsen (1999)
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Operability and Control for Process Integration
38
Interconnection Structures
Series
g1(s)
g2(s)
g2(s)
g1(s)
g1(s)
g2(s)
g ( s )  g 1( s ) g 2( s )
g 1( s )
1  g 1( s ) g 2( s )
n1d 2

d 1d 2  n1n 2
g (s) 
g ( s )  g 1( s )  g 2( s )
n1d 2  n 2 d 1

d 1d 2
n1n 2

d 1d 2
Zeroes and poles are the
union of those of units
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Recycle
Parallel
Zeroes are moved
Poles are the union
of those of units
Zeroes are the union of
those of n1 and poles of d2
Poles are moved!
Operability and Control for Process Integration
39
Summary: Process Integration Structures
• Series and parallel interconnections:
Realtively simple to deduce overall behaviour from unit
behaviours (only zeros are affected in parallel
interconnections).
• Recycle interconnections:
More complicated relation between overall behaviour and
unit behaviours (poles are moved).
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Operability and Control for Process Integration
40
Simple Recycle Example (1)
Recycle
Reactor Section
Feed
dx1
 a1 x1  b1u1
dt
dx2
 a2 x2  b2u2
dt
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Reactor
Effluent
Separation
Section
u1  u  x2
u2  x1
Operability and Control for Process Integration
Product
41
Simple Recycle Example (2)
dx1
 a1 x1  b1u1
dt
dx2
 a2 x2  b2u2
dt
Recycle
u1  u  x2
Reactor Section
Feed
Reactor
Effluent
Separation
Section
u2  x1
Product
Laplace Transformation
K1
X 1 (s) 
U1 ( s )
 1s  1
K2
X 2 ( s) 
X 1 (s)
 2s 1
Ki 
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bi
ai
i 
X2
U +
+
S
G2(s)
U1
1
ai
Operability
and Control for Process Integration
G1(s)
X1
42
Simple Recycle Example (3)
X 1 ( s)  G1 ( s)(U ( s)  X 2 ( s))
X
2
G2(s)
 G1 ( s)U ( s)  G1 ( s)G2 ( s) X 1 ( s)
K1K 2  1 :
G1 ( s )
+
X 1 (s) 
U ( s)
X1
U1
+
U
1  G1 ( s )G2 ( s )
S
G1(s)
K1
 1s  1
K1
K2

U (s)
G1 ( s) 
G2 ( s) 
K1
K2
 1s  1
 2s 1
1
 1s  1  2 s  1
K1 K 2  1 :
K1 ( 2 s  1)
K1
 2s 1

U ( s)
X
(
s
)

U (s)
( 1s  1)( 2 s  1)  K1 K 2
1
 1   2   1 2



s
s

1
K1
 2s 1

1   2

U ( s)


1  K1 K 2  1 2 s 2   1   2 s  1
1  K1 K 2 Operability
1  Kand
1 K Control
2
for Process Integration
8/8-2/9 2005
43
Simple Recycle Example (4)
K1K 2  1 :
X 1 ( s) 
K1
1  K1 K 2
K
 1 2
1  K1 K 2
 2s 1
1   2
2
s 
1  K1 K 2
U ( s)
s 1
 2s 1
U ( s)
2 2
 s  2s  1
K1
 1 2
1
( 1   2 ) 2
K

 
1  K1 K 2
1  K1 K 2
2  1 2 (1  K1 K 2 )
0  K1K 2  1 :
1
( 1   2 ) 2
 
1
2  1 2 (1  K1 K 2 )
 2s 1
X 1 (s)  K
U ( s)
( A s  1)( B s  1)
8/8-2/9 2005

   

 1
 A      2 1
B
2
Operability and Control for Process Integration
44
Simple Recycle Example (5)
X 1 (s)  K
 2s 1
U ( s)
( A s  1)( B s  1)
1 red
K2  1 1  1  2  
4 blue
15



 A      2 1  B      2 1
A vs. K1
K vs. K1
20
K1
 1 2
1
( 1   2 ) 2
K

 
1  K1 K 2
1  K1 K 2
2  1 2 (1  K1 K 2 )

B vs. K1
1
100
0.9
80
0.8
60
0.7
40
0.6
20
10
5
0
8/8-2/9 2005
0
0.5
0.5
0
1
0
0.5
1
0
Operability and Control for Process Integration
0.5
1
45
Simple Recycle Example (6)
K2  1
 2s 1
X 1 (s)  K
U ( s)
( A s  1)( B s  1)
1  1
2 1
Unit Step Response
10
K1=0.9
8
Both the time
constant and the
steady-state gain
has been
dramatically
changed by the
recycle stream
X
1
6
K1=0.8
4
2
K1=0.4
0
0
8/8-2/9 2005
20
40
60
80
100
time
Operability
and Control for Process Integration
46
Snowball Effect
• Observation: Recycle systems has a large
tendency to exhibit large variations in the
magnitude of the recycle flow.
X2
U +
+
S
X 1 (s)  K
G2(s)
U1
G1(s)
X1
X 2 ( s) 

• Snowball effect: sensitivity of
recycle flow rates to small
disturbances
8/8-2/9 2005
 2s 1
U ( s)
( A s  1)( B s  1)
K2
X 1 ( s)
 2s 1
K2K
U ( s)
( A s  1)( B s  1)
K1
K
1  K1 K 2
Operability and Control for Process Integration
47
Snowball Effect – Static analysis
• Snowball effect: sensitivity of recycle flow rates to small disturbances
Only show composition of reactant A, i.e. x
All A is removed in Distillate, i.e. xB=0 and xD=1:
F, xF
D
Total balance:
FxF  BxB  VkxR
L
Component balance around reactor:
FxF  ( R  F ) xD  RxR  VkxR
R, xR
V
F ( xD  xF )  Vkx R F ( xD  xF )  FxF  BxB
R

xD  xR
xD  xR
A=>B
B , xB

VkF
Da F
1

F
x
Vk  FxF Da  xF
1 F
Da
Thus if Da = Vk/F approaches xF then R can become very large!
8/8-2/9 2005
Operability and Control for Process Integration
48
Control Implications of the Snowball Effect
X2
U +
+
S
G2(s)
U1
G1(s)
X1
Recycle
Reactor Section
Feed
Reactor
Effluent
Separation
Section
Product
Production rate can typically
NOT be set at the front end for
mass recycle systems.
8/8-2/9 2005
• Set the production rate at the
front end, I.e. by setting U.
• If the snowball effect is
dominant, K2*K >> 1, small
changes in U lead to large
changes in X2.
• Large changes in X2 implies
that the recycle valve goes
either fully open or closed.
• As X2 is large, X1 is also
large and this may overload
the separation section.
Operability and Control for Process Integration
49
Snowball Effect - Example
A
A
• Isothermal reactor
operation (perfect
temperature control)
• Produce pure B
A, B
• Be able to
manipulate the
production rate of B
B
• Select a control
structure that will
meet these objectives
A B
R  V  k (T )  x A
8/8-2/9 2005
Operability and Control for Process Integration
50
Snowball Effect - Example
• All flows in recycle
loop set by level
controllers
PC
FC
LC
CC
LC
LC
A B
R  V  k (T )  x A
SMALL flexibility index regarding
production rate.
CC
8/8-2/9 2005
• A small change in
the production rate
set front-end leads to
large changes in the
recycle loop flow
rates.
• No plantwide
control of inventory
of A.
Operability and Control for Process Integration
51
Snowball Effect - Example
PC
LC
• We cannot
manipulate production
rate directly by
manipulating the fresh
feed flow
CC
• The setpoint to the
reactor LC is used to
control production rate
LC
FC
LC
CC
• No snowball effect
due to FC in recycle
loop
A B
R  V  k (T )  x A
System inventory of A is controlled by the
reactor LC. This improves the flexibility index.
8/8-2/9 2005
Operability and Control for Process Integration
52
Snowball Effect - Example
PC
FC
LC
CC
LC
LC
CC
PC
LC
CC
LC
FC
LC
CC
8/8-2/9 2005
• To prevent the snowball effect, the
mass recycle loop must have a
flow controller.
• The plant inventory of A must be
controlled. It is not sufficient to
control the individual unit
inventories of A.
• In the upper flow sheet any
disturbance that increase the total
inventory of A in the process will
produce large increases in the
flowrates around the recycle loop.
Operability and Control for Process Integration
53
Snowball Effect - Example
PC
AB
FC
LC
CC
LC
LC
CC
PC
LC
CC
LC
FC
LC
CC
8/8-2/9 2005
R  V  k (T )  xA
• Consider a 20% production rate increase
of B.
• In the first control structure the separation
section must handle the entire load, as xA
must change with 20%. The feed to the
distillation column changes, as well as the
feed rate.
• In the second control structure both
reactor composition and volume changes.
So the separation section sees a smaller
load disturbance
• Production rate can only be changed by
changing the conditions in the reactor!
Operability and Control for Process Integration
54
Disturbance Sensitivity of single loop control
d
gd
Standard single variable process:
y = g u + gd d
y
u
g
Standard single loop control:
gd
g gc
d
gd
y
u
g
gc
-1
y = ----------d + ----------- r
1 + g gc
1 + g gc
Significantly reduces sensitivity to
disturbances at low frequences
What happens with process integration?
8/8-2/9 2005
Operability and Control for Process Integration
55
Disturbance Sensitivity with process recycle
d
gd
grec
y
g = gd/(1 – gd grec) = S gd
• The Sensitivity function S = 1/ (1 – gd grec) catches the effect
of recycle upon disturbance sensitivity.
• Instability is induced by recycle if gd grec is stable and
| gd grec (iωc)| > 1 and φ(gd grec (iωc)) = n 2π
where ωc is the critical frequency
• Note feedback may be positive or negative
• Control is based upon negative feedback
• Recycle introduces positive feedback
8/8-2/9 2005
Operability and Control for Process Integration
56
Feedback effects on Disturbance Sensitivity
• Negative feedback if | gd grec (0)| < 0
• Static Sensitivity |S(0)| < 1
Hence disturbance sensitivity is reduced at low frequences
• The critical frequency ωc > 0 – Increasing the loop gain will
yield a pair of complex poles crossing the imaginary axis.
• The closed loop response usually is faster
• Positive feedback if | gd grec (0)| > 0
• Static Sensitivity |S(0)| > 1
Hence disturbance sensitivity is increased at low frequencies
• The critical frequency may be at ωc = 0 – thus a real pole
crosses the imaginary axis for | gd grec (0)| > 1, i.e. static
multiplicity. Or at ωc = n 2π where a complex pair crosses.
• Thus the recycle loop response usually is slower if not unstable
8/8-2/9 2005
Operability and Control for Process Integration
57
Example Plant
Mixer Reactor
F, xFi
Separator
xF
L
xR
A+R=>2R
V
B =R, xB
8/8-2/9 2005
D=F, yD
Note autocatalytic reaction,
e.g. bioreactor
Main disturbance: xFi
Objective:
Maintain yD constant
Operability and Control for Process Integration
58
Example Plant – Unit models
Mixer – static:
M
Reactor:
Separator:
8/8-2/9 2005
FxFi  RxB  ( R  F ) xF
xF  kxB  (1  k ) xFi k  R /( R  F )
xR 
0. 6
xF  grxF
10 s  1
 yD 
L 
1  0.03 0.4  L 
  

   GD 
 xB  30s  1  0.03 2.2  xR 
 xR 
Operability and Control for Process Integration
59
Example Plant – Block Diagram
L
xFi
1-k
xF
gr
xR
yD
GD
xB
k
8/8-2/9 2005
Operability and Control for Process Integration
60
Example Plant: Disturbance Sensitivity
Effect of xFi on yD:
gD12
xFi
1-k
xF
gr
zF
yD
gD22
xB
k
• Sensitivity
S = 1/(1-kgrgD22)
Static loop gain: kgr(0) gD22(0) = 1.32 k thus positive feedback
Unstable for k > 0.76 (R/F > 3.1)
8/8-2/9 2005
Operability and Control for Process Integration
61
Summary on Sensitivity effects of Recycle
• Recycle of material or energy introduces positive feedback which
• increases low frequency disturbance sensitivity
• induces slower dynamics or instability
• Thus recycle implies a stronger need for control to reduce the
effect of disturbances and also to stabilize the plant
• How to handle the increased disturbance sensitivity?
8/8-2/9 2005
Operability and Control for Process Integration
62
Lecture 5: Control of Recycle Plants
• Feedback Control of Recycle Plants
• Control of variable in recycle path
• Control of variable not in recycle path
• Summary of control effects of recycle
• Conclusions on linear dynamics and control of Process Integrated
Plants
8/8-2/9 2005
Operability and Control for Process Integration
63
Feedback Control SISO versus recycle variable
u
d
g
y
gd
Perfect rejection of disturbance requires:
u = - (gd / g ) d
u
g
d
Standard single variable process:
y = g u + gd d
Control of variable in recycle loop:
y = (gu + gdd)/(1-gdgrec)= S(gu +gdd)
y
gd
grec
Perfect rejection of disturbance requires:
u = - (gd / g ) d
• Thus required input unaffected by recycle
8/8-2/9 2005
Operability and Control for Process Integration
64
Feedback Control of variable not in recycle 1
u
d
u2
g11
g21
g12
Control of variable not in recycle loop:
y
x
g22
y  g11 u  g12d  grecx 
grec
Thus the transfer
function from u to y
is affected by recycle!
But how?
8/8-2/9 2005
 y   g11 g12  u 
   
  u 2  d  grecx
 x   g 21 g 22  u 2 
1
S

(
1

g
22
g
rec
)
x  S g 21u  S g 22 d
 g11  g12 grecSg21 u  g12 Sd
1  g 22 grec / 11
g12
 g11
u
d
1  g 22 grec
1  g 22 grec
Operability and Control for Process Integration
65
Feedback Control of variable not in recycle 2
1  g 22 grec / 11
y  g 11
u
transfer function:
1  g 22 grec
The recycle
g 11 g 22
  
Det G
Recycle affetcs the static behaviour such that:
1. It will have more poles in the RHP than g11 if
g22(0)grec(0) >1 and λ11(0) ≠1
2. It will have more zeros in the RHP than g11 if g22(0)grec(0)/λ11(0) >1 and
λ11(0) ≠1.
The above two conditions are sufficient for moving a real pole or zero into the RHP.
Thus if g11 is stable and nonminimum phase the above two conditions imply that the
recycle system has RHP poles and RHP zeros respectively.
In Conclusion: Closing a control loop from y to u will most certainly be affected by
the dynamics introduced through recycle!
8/8-2/9 2005
Operability and Control for Process Integration
66
Plantwide Control Structure Design Procedure
(Luyben et al.)
•
•
•
•
•
•
•
•
•
Establish control objectives
Determine control degrees of freedom
Establish energy management system
Set production rate
Control production quality and handle safety,
environmental and operational constraints
Fix a flow in every recycle loop and control inventories
Check component balances
Control individual unit operations
Optimize economics and improve dynamic controllability
8/8-2/9 2005
Operability and Control for Process Integration
67
Summary on control effects of recycle
• Control of variables within the recycle loop
• Input required to reject a disturbance is unaffected by
recycle
• Control of variable not within the recycle loop
• Input required to reject a disturbance is affected by recycle
in fact the effect of control inputs relative to disturbance may
decrease significantly.
• Recycle may introduce RHP zeros
If acceptable control is not possible then redesign such that
recycle loop gain decreases
8/8-2/9 2005
Operability and Control for Process Integration
68
Conlusions on linear dynamics and control
• Plant dynamics may be strongly affected by recycles
• Recycle usually gives positive feedback
• increases low freqency sensitivity
• renders response slower or causes instability
• Controllability for variables outside the recycle loop may be
severely reduced by recycle, i.e. reduced efffect of control inputs
possibly combined with RHP zeros
• Recycle may significantly increase model uncertainty for units
in plant compared to that of individual units (not shown).
• Remedy: Redesign loop to decrease loop gain. Often that means
modify reactor design!
8/8-2/9 2005
Operability and Control for Process Integration
69
Lecture 6: Effects of Process Integration on
nonlinear behaviour
• The Control Hierachy and degrees of freedom
• Profit Optimizing Control
• Operational Implications
• Example: Continuous cultivation of yeast
• Analysis
• Experiment
• Example with Optimal operation of process integrated plant
• Ammonia reactor with feed-effluent heat exchange
8/8-2/9 2005
Operability and Control for Process Integration
70
Profit Optimizing Control
• Productivity in Continuous Process:
J  F  x prod  c  F  x raw
• Optimality requires : Max J
x prod
F

c  x raw  x prod
F
 RHS
x prod
F
8/8-2/9 2005
 RHS
x prod
F
Operability and Control for Process Integration
 RHS
x prod
F
 RHS
71
Gain Changes for Xprod vs. F
• Output Multiplicity
– Dynamic Consequence:
Instability when (dXprod/dF)<0
• Input Multiplicity
– Dynamic Consequence:
May be a zero in RHP, i.e.
unstable zero dynamics.
8/8-2/9 2005
Operability and Control for Process Integration
72
Control Performance Reducing Dynamics
• Local Transfer Function
X prod (s)
F(s)

 G (s) 

m
i 1
n
j1
(s  z i )
(s  p j )
– Real zero in right half plane
Xprod
• Zero Dynamics - input multiplicity
Time
– Real pole into right half plane
Xprod
• Singularities - output multiplicity
– Complex pole pair into right half plane
Xprod
Time
Time
8/8-2/9 2005
Operability and Control for Process Integration
73
Process Analysis:
Operational Implications of Optimality
Theorems based upon induction:
• Complex behaviour may be encountered
near an optimal operating point
• Optimised process integrated design
increases the likelihood of complex
behaviour
8/8-2/9 2005
Operability and Control for Process Integration
74
Continuous Cultivation of Yeast
• Bifurcation analysis reveals:
– Hysteresis curve, multiple steady-states at maximal
biomass productivity!
Chemostat, Sf = 28g/L
Biomass [g/L]
15
10
Stable
Unstable
5
0.3
8/8-2/9 2005
0.32
0.34
0.36
Dilution rate [1/hr]
f
0.38
Operability and Control for Process Integration
0.4
75
Adaptive Model Predictive Control

Parameter Estimation
Control Design
Controller Parameters
yref
Controller
u
Bioreactor
y
-1
8/8-2/9 2005
Operability and Control for Process Integration
76
Response to Etanol Setpoint Changes
8/8-2/9 2005
Operability and Control for Process Integration
77
Ethanol Concentration vs. Dilution Rate
8/8-2/9 2005
Operability and Control for Process Integration
78
Ammonia Reactors
3-bed quench reactor
simple reactor
Operating point:
Feed temperature
Feed concentration
Feed flow rate
Pressure
By-pass
No automatic control of
inlet temperature
Feed
8/8-2/9 2005
Operability and Control for Process Integration
79
Outlet Ammonia Mass Fraction [%]
Energy Integrated Ammonia Reactor
I II
III IV V VI I
20
15
10
5
0
1
2
3
Inlet Ammonia Mole Fraction [%]
 Subcritical Hopf
bifurcation from the
upper steady state
 Stable limit cycle
coexists with the
upper stable steady
state
! Safer to operate in
region with no stable
limit cycle
!
Stable Steady State
Stable Limit Cycle
Unstable Steady State Unstable Limit Cycle
Operability and Control for Process Integration
8/8-2/9 2005 Hopf Bifurcation
80
2.8
550
2.6
500
2.4
450
Hopf
2.2
400
Cyclic fold
2.0
350
1.8
300
200
0
50
100
150
Dimensionless time
8/8-2/9 2005
Bed Outlet temperature [C]
Inlet Ammonia Mole Fraction [%]
Dynamic Simulation
• Operate at ignited
steady state and
increase inlet
concentration:
– Passing Hopf at 2.3
mole%
– Large amplitude
oscillations
• Decrease inlet
concentration
– Passing cyclic fold at
2.1 mole%
– Stable steady state
Operability and Control for Process Integration
81
Conclusions on nonlinear analysis
• New process design tools should be developed to
account for possible nonlinear behaviours
• To operate near optimal operating points reliable
model identification and nonlinear control is
desirable - a profit margin of 3% has been
estimated!
• Is a combined process and nonlinear control
design optimization formulation solvable - to
exploit the nonlinearity?
8/8-2/9 2005
Operability and Control for Process Integration
82
General Plantwide Control Structure Design Procedure
• Top down analysis
–
–
–
–
Define operational objectives
Manipulated variables and degrees of freedom for control
Select primary controlled variables (given ¨via design goal)
Production rate: determine where to set this in the plant, often at some interior
position
– Investigate possible nonlinear complex behavioours near optimal operation
• Bottom up design
– Regulatory control layer
• Stabilization
• Local disturbance rejection
– Supervisory control layer
• Keep controlled outputs at optimal setpoints
– Optimization layer
• identify active constraints and determine optimal setpoints
– Validation simulations
Extention of Skogestad (2004)
8/8-2/9 2005
Operability and Control for Process Integration
83
Conclusions on Dynamics and Control of
Process Integrated Plants
• Linear Analysis explains large sensitivity of recycle plants
especially for control of variables not in recycle path.
• Optimizing Operation exploits nonlinearities, therefore
nonlinear analysis is recommendable.
• Nonlinear Analysis explains specific cases – it is therefore
difficult to generalise. It is however important to understand
how to avoid occurrence of potentially serious problems.
8/8-2/9 2005
Operability and Control for Process Integration
84
References and Further Reading
• Luyben, Tyreus, Luyben: Plantwide Process Control,
McGraw-Hill (1998), chap. 1-3
• Jacobsen, E.W.: On the dynamics of integrated plants –
non-minimum phase behaviour. Journal of Process Control
9 (1999) 439-451
• Skogestad, S. : Plantwide control: the search for the selfoptimizing control structure: Journal of Process Control 10
(2000) 487-507
• Skogestad, S.: Control structure design for complete
chemical plants. Comp. and Chem. Engineering
28(2004)219-234.
8/8-2/9 2005
Operability and Control for Process Integration
85
Monographs
• Buckley: Techniques of Process Control, Wiley
(1964)
• Shinskey: Process Control Systems, McGraw-Hill
(1988)
• Rijnsdorp: Integrated Process Control and
Automation, Elsevier (1991)
• Luyben, Tyreus, Luyben: Plantwide Process
Control, McGraw-Hill (1999)
• Ng, Stephanopoulos: Plant-wide control structures
and strategies, Academic Press (2000)
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86