Economic Plantwide Control Overview
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ECONOMIC PLANTWIDE CONTROL
Sigurd Skogestad
Dept. of Chemical Engineering, Norwegian University of Science and Technology,
Trondheim, Norway
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Trondheim
Oslo
UK
NORWAY
DENMARK
GERMANY
North Sea
SWEDEN
Arctic circle
Aurora Borealis = Northern Lights
Winter: No sun, but sometimes
Tromsø
NTNU,Trondheim
200 000 people
30 000 students
OUTLINE
•
INTRODUCTION
•
PROCEDURE FOR ECONOMIC PLANTWIDE CONTROL
•
REACTOR-SEPARATOR-RECYCLE CASE STUDY
•
PRACTICAL RULES
•
DYNAMIC SIMULATIONS
•
CONCLUSIONS
ECONOMIC PLANTWIDE CONTROL
Example of systems we want to operate optimally
•
Process plant
–
minimize J=economic cost
•
Runner
–
minimize J=time
•
«Green» process plant
–
Minimize J=environmental impact (with given economic cost)
•
General multiobjective:
–
Min J (scalar cost, often $)
–
Subject to satisfying constraints (environment, resources)
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Theory: Optimal operation
Objectives
Present state
Model of system
Theory:
•
Model of overall system
•
Estimate present state
•
Optimize all degrees of
freedom
Problems:
•
Model not available
•
Optimization complex
•
Not robust (difficult to
handle uncertainty)
•
Slow response time
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Excellent candidate for
centralized control
(Physical) Degrees of freedom
C
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Most (all?) large-scale engineering systems are controlled using
hierarchies of quite simple controllers
–
Large-scale chemical plant (refinery)
–
Commercial aircraft
•
100’s of loops
•
Simple components:
on-off + PI-control + nonlinear fixes + some feedforward
Same in biological systems
NEED A
SYSTEMATIC
APPROACH
Famous critique article on process control by Foss (1973):
The central issue to be resolved ... is the
determination of control system
structure
. Which
variables should be measured, which inputs
should be manipulated and which links should be
made between the two sets?
There is more than a suspicion that the work of a genius is needed
here, for without it the control configuration problem will likely
remain in a primitive, hazily stated and wholly unmanageable
form. The gap is present indeed, but contrary to the views of many,
it is the theoretician who must close it.
HOW DESIGN THE CONTROL
SYSTEM FOR A COMPLETE PLANT ?
MAIN OBJECTIVES FOR A CONTROL SYSTEM
1.
Economics:
Implementation of close-to-optimal
economic operation
2.
Regulation:
Stable operation
ARE THESE OBJECTIVES CONFLICTING?
•
Usually NOT
–
Different time scales
•
Stabilization fast time scale
–
Stabilization doesn’t “use up” any degrees of freedom
•
Reference value (setpoint) available for layer above
•
But it “uses up” part of the time window (frequency range)
PRACTICAL OPERATION: HIERARCHICAL STRUCTURE
Manager
Process engineer
Operator/
RTO
Operator/”
Advanced control”/MPC
PID-control
u = valves
Our Paradigm
CV1
Decompose the structural decisions into two
parts:
•
Top-down part
: F
ind a slow-time-scale
supervisory control structure that achieves
a close-to-optimal
economic
operation.
–
CV1 = Economic CVs
CV = Controlled variable
Figure 1: Typical control hierarchy in
a chemical plant
ECONOMIC PLANTWIDE CONTROL
PROCEDURE
Decompose the structural decisions into two
parts:
•
Top-down part
,
which attempts to find a
slow-time-scale supervisory control
structure that achieves a close-to-optimal
economic
operation.
•
Bottom - up part
: D
esign a robust fast-
time-scale
regulatory
control layer, which
stabilizes the plant and follows the
setpoints from the supervisory layer
.
–
CV2 = stabilizing CVs
Figure 1: Typical control hierarchy in
a chemical plant
ECONOMIC PLANTWIDE CONTROL
PROCEDURE
I.
Top Down
•
Step S1:
Define
operational objectives
(optimal
economic
operation)
–
Cost function J (to be minimized)
–
Operational constraints
•
Step S2:
Identify degrees of freedom (MVs) and
optimize
for expected disturbances
•
Step S3
:
Select primary controlled variables
CV
1
(economic CVs)
•
Step S4:
Where to set the production rate?
(TPM)
II.
Bottom Up
•
Step S5
:
Regulatory / stabilizing control
(PID layer)
–
What more to control
CV
2
(stabilizing CVs)?
–
Pairing of inputs and outputs
•
Step S6:
Supervisory control (MPC layer)
•
Step S7:
Real-time optimization (Do we need it?)
ECONOMIC PLANTWIDE CONTROL
STEPWISE PROCEDURE (Skogestad, 2004)
ECONOMIC PLANTWIDE CONTROL
Top-down part
(mainly steady-state):
:
•
Step S1
:
Define the
operational objectives
(economics) and constraints
.
Identify
•
A scalar cost function J [$/s]
J = cost feed + cost energy – value products
•
operational constraints
•
disturbances
d
and their ranges
•
Two main cases (modes/regions) depending on market conditions:
–
Mode 1
. Given feedrate
–
Mode 2
. Maximum production (max feedrate
)
ECONOMIC PLANTWIDE CONTROL
Top-down part
(mainly steady-state):
:
•
Step S2
: Determine the
degrees of freedom
and
find the steady-state
optimal operation.
Must optimize for the range of
expected disturbances
d
Requires a rigorous model (usually steady-state)
POTENSIALLY VERY TIME CONSUMING
Main goal: Identify the
ACTIVE CONSTRAINTS
ECONOMIC PLANTWIDE CONTROL
Top-down part
(mainly steady-state):
:
•
Step S3
: Select primary (economic)
controlled variables (
CV
1
)
Identify the candidate measurements
y
m
and
from these select a set
CV
1
(one CV for each
steady-state degree of freedom
)
:
•
Control the active constraints!
•
For the remaining
unconstrained
degrees of freedom:
Control
“
self-optimizing” variables
Figure 1: Typical control hierarchy in
a chemical plant
“Self-optimizing” variables:
Controlled variables (CV1), which when kept at constant setpoints,
indirectly achieve close-to-optimal operation in spite of unknown
disturbances
•
Minimize the need for
re-optimization
•
by moving optimization
into the control layer
–
Cost to be minimized, J=T
–
One degree of freedom (u=powe)
–
D
i
s
t
u
r
b
a
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c
e
(
d
)
=
h
i
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w
i
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d
–
What should we control?
Optimal operation - Runner
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100m. J=T
–
Active constraint control:
•
Maximum speed (”no thinking required”)
•
CV = power (at max)
Optimal operation - Runner
•
40 km. J=T
•
What should we control? CV=?
•
Unconstrained optimum
Optimal operation - Runner
2
.
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•
Any
self-optimizing variable
(to control at
constant setpoint)?
•
c
1
= distance to leader of race
•
c
2
= speed
Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
CV=speed
J=T
d=hill
CV
opt
Loss
•
Any
self-optimizing variable
(to control at
constant setpoint)?
•
c
1
= distance to leader of race
•
c
2
= speed
•
c
3
= heart rate
•
c
4
= level of lactate in muscles
Optimal operation - Runner
Self-optimizing control: Marathon (40 km)
CV=heart rate
J=T
d=hill
CV
opt
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c = heart rate
select one measurement
•
CV = heart rate is good “self-optimizing” variable
•
Simple and robust implementation
•
Disturbances are indirectly handled by keeping a constant heart rate
•
May
have infrequent adjustment of setpoint (c
s
)
Optimal operation - Runner
ECONOMIC PLANTWIDE CONTROL
Top-down part
(mainly steady-state):
•
Step S4
:
Select the location of
throughput manipulator
(TPM)
–
Where should the plant’s “gas pedal” (TPM) be located ?
•
Usually one for each plant
•
The location of the TPM is a
dynamic issue
but has an economic
impact
–
Answer: Often locate TPM at the feed, but
•
to maximize throughput (
M
ode 2
), should be located
close the production
bottleneck
•
to avoid “snowballing”,
locate inside recycle loop
ECONOMIC PLANTWIDE CONTROL
Bottom-up part
(mainly dynamic):
•
Step S5
: Select the control structure
for the
Regulatory Control layer
–
Q
1
:
What variables
(CV2)
should be controlled
to stabilize the plant operation ?
–
A
1
:
Select “drifting” process variables
CV
2
=
H
2
y
m
that need to be controlled to
ensure safe and stable operation
e.g. levels, pressures, temperatures.
–
Q
2
: H
ow should CV
2
be controlled (pairing)?
–
A
2
: Controllability analysis
Figure 1: Typical control hierarchy in
a chemical plant
ECONOMIC PLANTWIDE CONTROL
Bottom-up part
(mainly dynamic):
•
Step S6
:
Select the control
structure for the
Supervisory
(Advanced) Control layer
Objectives
–
Control economic controlled variables
CV
1
–
Look after regulatory layer (avoid
saturation of u
D
)
Two alternatives:
1.
Multivariable controller (e.g. MPC)
2.
Mix of various “advanced” controllers
including PID, selectors, feedforward…
ECONOMIC PLANTWIDE CONTROL
Bottom-up part
(mainly dynamic):
•
Step S7
:
Select the control structure
for the
Process Optimization layer
(RTO)
–
How should the optimal setpoints for
CV
1
be
updated ?
A good choice of controlled variables (CV1) may remove
the need for this layer.
Figure 1: Typical control hierarchy in
a chemical plant
REACTOR-SEPARATOR- RECYCLE
CASE STUDY (Luyben)
•
Feed
F
0
contains mostly
A.
•
Reactor (CSTR)
–
1
st
order
A
->
B
reaction
–
Constant temperature
•
Separator (distillation column)
–
Distillate
D
(mostly
A
): recycled
back to CSTR.
–
Bottom product
B
(mostly
B
)
–
22 stages
–
Constant pressure
–
Constant relative volatility
Reactor-separator-recycle process
F
0
B
D
CASE STUDY: Step S1
Definition of optimal operation:
•
Given feedrate (Mode 1)
J =
cost feed + cost energy – value products
J =
c
F
F
0
+ c
V
V
B
– c
B
B
•
Since
F
0
= B
is given, this simplifies to
min
J = V
B
Reactor-separator-recycle process
CASE STUDY: Step S1
Definition of optimal operation:
•
Given feedrate (Mode 1)
J =
cost feed + cost energy – value products
J =
c
F
F
0
+ c
V
V
B
– c
B
B
•
Since
F
0
= B
is given, this simplifies to
min
J = V
B
•
Operational constraints
–
M
R
≤
2800 kmol
–
V
B
≤
50 kmol/min
–
x
B
≤
0.0105 (max. 1.05% A in product)
Reactor-separator-recycle process
CASE STUDY: Step S2
Step S2
: Determine the
degrees of freedom
and find the steady-state
optimal operation.
Given pressure and reactor temperature:
6 dynamic manipulated variables (valves)
•
u
D
=
{F0
,
V
B
, D, B, F, L
T
}
•
M
D
and M
B
have no steady-state
effect and need to be controlled
Steady state and given feed
F
0
:
•
3 steady-state degrees of freedom
Step S3: Must find 3 economic
variables to control (CV1)
???
Reactor-separator-recycle process
11 PRACTICAL RULES
(TO HELP WITH THE REMAINING
STEPS)
PRACTICAL RULES for
Step S3
•
Rule 1:
Control the active constraints
–
In general, process optimization is required to determine the active
constraints.
but a
good engineer can often guess the active constraints.
Step S3:
Selection of economic CV1
PRACTICAL RULES for
Step S3
•
Rule 1:
Control the active constraints
–
In general, process optimization is required to determine the active
constraints.
but a good engineer can often guess the active constraints
•
Rule 1A:
The purity constraint of the valuable
product is always active and should be controlled
.
–
This is to maximize valuable product and avoid product “give away”.
Step S3:
Selection of economic CV1
CASE STUDY
•
Rule 1
:
Control the active constraints
•
Rule 1A
:
The purity constraint of the
valuable product is always active and
should be controlled
.
Case study: Both M
R
(max) and x
B
(purity
valuable product) are active.
Need to find one more CV1
Reactor-separator-recycle process
Practical rules for Step S3:
Selection of economic CV
1
J=V
B
u = L
T
Unconstrained optimum
PRACTICAL RULES for Step S3
•
Rule 2
:
(for remaining unconstrained steady-state degrees of
freedom, if any):
Control “self-optimizing” variables
.
–
The two main properties of a good “self-optimizing” variable are:
•
Ι
ts
optimal
value is
in
sensitive to disturbances
–
s
o
F
=
Δ
C
V
1
,
o
p
t
/
Δ
d
i
s
s
m
a
l
l
•
Ι
t is
sensitive
to the plant inputs (= “flat optimum”)
–
s
o
t
h
e
p
r
o
c
e
s
s
g
a
i
n
G
=
Δ
C
V
1
/
Δ
u
i
s
l
a
r
g
e
Step S3:
Selection of economic CV
1
PRACTICAL RULES for Step S3
•
Rule 2
: (for remaining unconstrained steady-state degrees of
freedom, if any):
Control the “self-optimizing” variables
.
–
The two main properties of a good “self-optimizing” variable are:
•
Ι
ts optimal value is insensitive to disturbances (such that
F
=
Δ
CV
1
,
opt
/Δ
d
is small)
•
Ι
t is sensitive to the plant inputs (so the process scaled gain
G
=
Δ
CV
1
/Δ
u
is large).
The following rule combines the two desired properties:
•
Rule 2A
:
Select the set CV
1
such that the “ratio” G
-1
F is
minimized
.
–
This rule is often called the
“Maximum scaled gain rule”.
Step S3:
Selection of economic CV
1
CASE STUDY:
Self-optimizing variables
•
Rule 2
: (for remaining unconstrained
steady-state degrees of freedom, if any):
Control the “self-optimizing” variables
.
–
The two main properties of a good “self-
optimizing” variable are:
•
Ι
ts optimal value is insensitive to disturbances
(such that
F
=
Δ
CV
1
,
opt
/Δ
d
is small)
•
Ι
t is sensitive to the plant inputs (so the
process scaled gain
G
=
Δ
CV
1
/Δ
u
is large).
The following rule shows how to combine the two
desired properties:
•
Rule 2A
:
Select the set CV
1
such that the
ratio G
-1
F is minimized
.
–
This rule is often called the “Maximum
scaled gain rule”.
Practical rules for Step S3:
Selection of economic CV
1
“Sensitive variables” (with large scaled gain):
Some good candidates for CV
1,SOC
: {LT
/F , x
D
}.
PRACTICAL RULES for Step S3
•
Rule 3
:
(for remaining unconstrained steady-state degrees
of freedom, if any):
Never try to control the cost function J
(or any other variable with min or max at the optimal point)
.
1.
The cost function J has no sensitivity to the plant inputs so G = 0,
(which violates Rule 2A)
Step S3:
Selection of economic CV
1
PRACTICAL RULES for Step S3
•
Rule 3
:
(for remaining unconstrained steady-state degrees
of freedom, if any):
Never try to control the cost function J
(or any other variable with min or max at the optimal point)
.
1.
The cost function J has no sensitivity to the plant inputs at the
optimal point and so G = 0, which violates Rule 2A.
2.
Potential infeasibility :
Step S3:
Selection of economic CV
1
J
u
CASE STUDY
•
Rule 3
: (for remaining unconstrained
steady-state degrees of freedom, if any):
Never try to control the cost function J
(or any other variable that reaches a min
or max at the optimal point)
.
•
Case study: Do
not
keep
V
B
constant
(but may be used as a TPM)
Practical rules for Step S3:
Selection of economic CV
1
PRACTICAL RULES for
Step S4
•
Rule 4
:
Locate the TPM close to the process bottleneck
.
–
This is to be able to maximize the production rate (Mode 2)
–
Gives a simpler transition between mode 1 (given feed) and mode 2
(Process bottleneck is defined as the last constraint to become active when
increasing the throughput rate.)
•
Rule 5
:
(for processes with recycle)
Locate the TPM inside the recycle loop.
–
This is to avoid “overfeeding” the recycle loop = “snowballing”
(Luyben)
Step S4:
Location of throughput manipulator (TPM)
CASE STUDY
•
Rule 4
:
Locate the TPM close to the
process bottleneck
.
•
Rule 5
: (for processes with recycle)
Locate the TPM inside the recycle loop.
According to Rules 4 and 5 the
best candidate for TPM
location is V
B.
Practical rules for Step S4:
Location of throughput manipulator (TPM)
PRACTICAL RULES for
Step S5
•
Rule 6
:
Arrange the inventory control loops
(for level,
pressures, etc.)
around the TPM location according to the
radiation rule
(Georgakis)
–
This ensures “local consistency” i.e. all inventories are controlled by
their local in or outflows
.
Step S5:
Structure of regulatory control layer
TPM
TPM
TPM
PRACTICAL RULES for Step S5
•
Rule 7
:
Select “sensitive/drifting” variables as controlled
variables CV
2
for regulatory control.
–
Typically include inventories (levels and pressures), reactor
temperature, or a sensitive temperature in a distillation column.
Step S5:
Structure of regulatory control layer
PRACTICAL RULES for Step S5
•
Rule 8
:
Economically important active constraints (CV
1
)
should be selected as CVs (CV
2
) in the regulatory layer
.
–
Economic variables
CV
1
are generally controlled in the supervisory
layer.
But moving
CV
1
to a faster layer may ensure tighter control with a
smaller back-off.
Step S5:
Structure of regulatory control layer
PRACTICAL RULES for Step S5
•
Rule 9
:
(“Pair-close” rule):
The pairings should be selected
such that, effective delays and loop interactions are
minimal
.
Step S5:
Structure of regulatory control layer
PRACTICAL RULES for Step S5
•
Rule 10
:
Avoid using MVs that may optimally saturate (at
steady state) to control CVs in CV
2
.
–
The reason is that we want to avoid re-configuring the regulatory
control layer.
To follow this rule, one needs to consider also other regions of
operation than the nominal.
Step S5:
Structure of regulatory control layer
CASE STUDY
•
Rule 7: Select “sensitive/drifting” variables
as controlled variables CV
2
for regulatory
control.
–
Typically include inventories (levels and
pressures), reactor temperature, or a
sensitive temperature in a distillation
column
•
Rule 6
:
Arrange the inventory control
loops (for level, etc.) around the TPM
location according to the radiation rule
.
•
Rule 8
: Economically important active
constraints (CV1) should be selected as CVs
(CV
2
) in the regulatory layer
•
Rule 9
: (“Pair-close” rule):
The pairings
should be selected such that, effective
delays and loop interactions are minimal
.
•
Rule 10
:
Avoid using MVs that may
optimally saturate (at steady state) to
control CVs in CV
2
.
•
Practical rules for Step S5:
Structure of regulatory control layer
PRACTICAL RULES for
Step S6
•
Rule 11
:
MVs that may optimally saturate (at steady
state) should be paired with the subset of CV
1
that may
be given up.
–
This rule applies for cases when we use decentralized control in the
supervisory layer and we have changes in active constraints
The idea is to avoid reconfiguration of loops.
This rule should be considered together with Rule 10.
Step S6:
Structure of supervisory control layer
CASE STUDY
•
Step S6:
Structure of supervisory control layer
•
Two remaining degrees of
freedom
–
L
T
–
F
•
Have two remaining variables to
control (CV1):
–
Active constraint x
B
–
Self-optimizing variable x
D
CASE STUDY: Final control structure
DYNAMIC SIMULATIONS
Initially
the TPM is ramped to achieve 40% increase in
fresh feed (F
0
), starting at 400 min till 600 min.
Later
the TPM is ramped down to its original value,
starting at 1800 min till 2000 min.
Important dynamic issue: TPM location
TPM = Throughput manipulator
Proposed structure: TPM at reboiler duty (V
B
)
TPM = Throughput manipulator
Alternative structure: TPM at feed (F0)
Alternative structure: TPM at the product stream – B
Alternative structure: TPM at the reactor effluent – F
•
Needs longer ramping
time to be feasible
Alternative structure: TPM at the recycle stream – D
RESULTS: TPM at feed – F0
Figure 5:
TPM at the feed –
F
0
.
Self-optimizing CV –
L
T
/F
.
RESULTS: TPM at the product stream – B
Figure 14:
TPM at the product stream –
B.
Self-optimizing CV –
L
T
/F
.
Alternative structure: TPM at the product stream – B
Figure 12:
TPM at the product stream –
B.
L
T
- constant.
Figure 3:
TPM at the feed -
F
0
.
L
T
– constant.
RESULTS: TPM at feed – F
0
RESULTS: TPM at the reactor effluent – F
Figure 4:
RESULTS: TPM at the reactor effluent – F
Figure 6:
RESULTS: TPM at reboiler’s steam supply – V
B
Figure 6:
TPM at reboiler’s steam supply –
V
B
.
L
T
– constant.
RESULTS: TPM at reboiler’s steam supply – V
B
Figure 8:
TPM at reboiler’s steam supply –
V
B
.
Self-optimizing CV –
L
T
/F
.
RESULTS: TPM at the recycle stream – D
Figure 9:
TPM at the recycle stream –
D.
L
T
– constant.
RESULTS: TPM at the recycle stream – D
Figure 11:
TPM at the recycle stream –
D.
Self-optimizing CV –
L
T
/F
.
CONCLUSIONS
SYSTEMATIC APPROACH TO PLANTWIDE CONTROL:
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Define the cost function and operational constraints
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Determine the active constraints
–
possibly
based on process insight
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Find CV1’s for each steady-state degree of freedom:
–
a
ctive constraints
–
+ "self-optimizing" unconstrained variables.
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Determine the TPM location
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Determine the structure of the control layers (pairing)
•
11 practical rules
ECONOMIC PLANTWIDE CONTROL
SUMMARY AND REFERENCES
•
V. Minasidis, N. Kaistha, S. Skogestad, “Simple rules for economic
plantwide control”, PSE-ESCAPE symposium, Copenhagen, June 2015
•
The following paper summarizes the procedure:
–
S. Skogestad, “Control structure design for complete chemical plant”,
Computers and Chemical Engineering
,
28
(1-2), 219-234 (2004).
•
The following paper updates the procedure:
–
S. Skogestad, “Economic plantwide control”, Book chapter in V. Kariwala and
V.P. Rangaiah (Eds),
Plant-Wide Control: Recent Developments and
Applications”,
Wiley (2012).
•
There are many approaches to plantwide control as discussed in the
following review paper:
–
T. Larsson and S. Skogestad, “Plantwide control: A review and a new design
procedure”,
Modeling, Identification and Control
,
21
, 209-240 (2000).
•
More information:
–
http://www.nt.ntnu.no/users/skoge/plantwide
•
2000 Italy (Adchem)
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2001 Korea (Dycops)
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2002 Spain (WC)
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2003 Hong Kong (Adchem)
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2004 USA (Dycops)
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2005 Czech Republic (WC)
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2006 Brazil (Adchem)
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2007 Mexico (Dycops-CAB)
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2008 Korea (WC)
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2009 Turkey (Adchem)
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2010 Belgium (Dycops-CAB)
•
2011 Italy (WC)
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2012 Singapore (Adchem)
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2013 India (Dycops-CAB)
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2014 South Africa (WC)
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2015 Canada (Adchem)
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Main international process
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Economic Plantwide Control is a critical concept in process engineering, aiming to optimize operation efficiency while minimizing costs and environmental impact. The approach involves multiobjective optimization, centralized control theory, and systematic design of control systems for complete plants. Case studies, practical rules, and dynamic simulations are key components to achieve optimal operation. Sigurd Skogestad's work at the Norwegian University of Science and Technology provides valuable insights into this field.
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1 ECONOMIC PLANTWIDE CONTROL Sigurd Skogestad Dept. of Chemical Engineering, Norwegian University of Science and Technology, Trondheim, Norway 1 Economic Plantwide Control, July 2015
2 Trondheim, Norway 2
3 Arctic circle North Sea Trondheim SWEDEN NORWAY Oslo DENMARK GERMANY UK 3
4 Winter: No sun, but sometimes Aurora Borealis = Northern Lights Troms 4
5 NTNU,Trondheim 200 000 people 30 000 students 5
6 ECONOMIC PLANTWIDE CONTROL OUTLINE INTRODUCTION PROCEDURE FOR ECONOMIC PLANTWIDE CONTROL REACTOR-SEPARATOR-RECYCLE CASE STUDY PRACTICAL RULES DYNAMIC SIMULATIONS CONCLUSIONS 6
7 Optimal operation (economics) Example of systems we want to operate optimally Process plant minimize J=economic cost Runner minimize J=time Green process plant Minimize J=environmental impact (with given economic cost) General multiobjective: Min J (scalar cost, often $) Subject to satisfying constraints (environment, resources) 7
8 Theory: Optimal operation Objectives Theory: Model of overall system Estimate present state Optimize all degrees of freedom CENTRALIZED OPTIMIZER Present state Model of system Problems: Model not available Optimization complex Not robust (difficult to handle uncertainty) Slow response time Process control: Excellent candidate for centralized control (Physical) Degrees of freedom 8
10 HOW DESIGN THE CONTROL SYSTEM FOR A COMPLETE PLANT ? Famous critique article on process control by Foss (1973): The central issue to be resolved ... is the determination of control system structure. Which variables should be measured, which inputs should be manipulated and which links should be made between the two sets? There is more than a suspicion that the work of a genius is needed here, for without it the control configuration problem will likely remain in a primitive, hazily stated and wholly unmanageable form. The gap is present indeed, but contrary to the views of many, it is the theoretician who must close it. NEED A SYSTEMATIC APPROACH 10
11 MAIN OBJECTIVES FOR A CONTROL SYSTEM 1. Economics: Implementation of close-to-optimal economic operation 2. Regulation: Stable operation ARE THESE OBJECTIVES CONFLICTING? Usually NOT Different time scales Stabilization fast time scale Stabilization doesn t use up any degrees of freedom Reference value (setpoint) available for layer above But it uses up part of the time window (frequency range) 11
12 Our Paradigm PRACTICAL OPERATION: HIERARCHICAL STRUCTURE Manager Process engineer Operator/RTO CV1 Operator/ Advanced control /MPC PID-control u = valves 12
13 ECONOMIC PLANTWIDE CONTROL PROCEDURE Decompose the structural decisions into two parts: Top-down part: Find a slow-time-scale supervisory control structure that achieves a close-to-optimal economic operation. CV1 = Economic CVs CV = Controlled variable Figure 1: Typical control hierarchy in a chemical plant 13
14 ECONOMIC PLANTWIDE CONTROL PROCEDURE Decompose the structural decisions into two parts: Top-down part, which attempts to find a slow-time-scale supervisory control structure that achieves a close-to-optimal economic operation. Bottom - up part: Design a robust fast- time-scale regulatory control layer, which stabilizes the plant and follows the setpoints from the supervisory layer. CV2 = stabilizing CVs Figure 1: Typical control hierarchy in a chemical plant 14
15 ECONOMIC PLANTWIDE CONTROL STEPWISE PROCEDURE (Skogestad, 2004) I. Top Down Step S1: Define operational objectives (optimal economic operation) Cost function J (to be minimized) Operational constraints Step S2: Identify degrees of freedom (MVs) and optimize for expected disturbances Step S3: Select primary controlled variables CV1 (economic CVs) Step S4: Where to set the production rate? (TPM) II. Bottom Up Step S5: Regulatory / stabilizing control (PID layer) What more to control CV2(stabilizing CVs)? Pairing of inputs and outputs Step S6: Supervisory control (MPC layer) Step S7: Real-time optimization (Do we need it?) 15
16 ECONOMIC PLANTWIDE CONTROL Top-down part (mainly steady-state): : Step S1: Define the operational objectives (economics) and constraints. Identify A scalar cost function J [$/s] J = cost feed + cost energy value products operational constraints disturbances d and their ranges Two main cases (modes/regions) depending on market conditions: Mode 1. Given feedrate Mode 2. Maximum production (max feedrate) 16
17 ECONOMIC PLANTWIDE CONTROL Top-down part (mainly steady-state): : Step S2: Determine the degrees of freedom and find the steady-state optimal operation. Must optimize for the range of expected disturbances d Requires a rigorous model (usually steady-state) POTENSIALLY VERY TIME CONSUMING Main goal: Identify the ACTIVE CONSTRAINTS 17
18 ECONOMIC PLANTWIDE CONTROL Top-down part (mainly steady-state): : Step S3: Select primary (economic) controlled variables (CV1) Identify the candidate measurements ymand from these select a set CV1 (one CV for each steady-state degree of freedom): Control the active constraints! For the remaining unconstrained degrees of freedom: Control self-optimizing variables Figure 1: Typical control hierarchy in a chemical plant 18
19 Self-optimizing variables: Controlled variables (CV1), which when kept at constant setpoints, indirectly achieve close-to-optimal operation in spite of unknown disturbances Minimize the need for re-optimization by moving optimization into the control layer 19
Optimal operation - Runner 20 Optimal operation of runner Cost to be minimized, J=T One degree of freedom (u=powe) Disturbance (d) = hill or wind What should we control? 20
Optimal operation - Runner 21 1. Optimal operation of Sprinter 100m. J=T Active constraint control: Maximum speed ( no thinking required ) CV = power (at max) 21
Optimal operation - Runner 22 2. Optimal operation of Marathon runner 40 km. J=T What should we control? CV=? Unconstrained optimum J=T u=power uopt 22
Optimal operation - Runner 23 Self-optimizing control: Marathon (40 km) Any self-optimizing variable (to control at constant setpoint)? c1 = distance to leader of race c2 = speed d=hill J=T Loss CVopt CV=speed 23
Optimal operation - Runner 24 Self-optimizing control: Marathon (40 km) Any self-optimizing variable (to control at constant setpoint)? c1 = distance to leader of race c2 = speed c3 = heart rate c4= level of lactate in muscles d=hill J=T CVopt CV=heart rate 24
Optimal operation - Runner 25 J=T Conclusion Marathon runner c=heart rate copt select one measurement c = heart rate CV = heart rate is good self-optimizing variable Simple and robust implementation Disturbances are indirectly handled by keeping a constant heart rate May have infrequent adjustment of setpoint (cs) 25
26 ECONOMIC PLANTWIDE CONTROL Top-down part (mainly steady-state): Step S4: Select the location of throughput manipulator (TPM) Where should the plant s gas pedal (TPM) be located ? Usually one for each plant The location of the TPM is a dynamic issue but has an economic impact Answer: Often locate TPM at the feed, but to maximize throughput (Mode 2), should be located close the production bottleneck to avoid snowballing , locate inside recycle loop 26
27 ECONOMIC PLANTWIDE CONTROL Bottom-up part (mainly dynamic): Step S5: Select the control structure for the Regulatory Control layer Q1: What variables (CV2) should be controlled to stabilize the plant operation ? A1: Select drifting process variables CV2= H2ymthat need to be controlled to ensure safe and stable operation e.g. levels, pressures, temperatures. Q2: How should CV2be controlled (pairing)? A2: Controllability analysis Figure 1: Typical control hierarchy in a chemical plant 27
28 ECONOMIC PLANTWIDE CONTROL Bottom-up part (mainly dynamic): Step S6: Select the control structure for the Supervisory (Advanced) Control layer Objectives Control economic controlled variables CV1 Look after regulatory layer (avoid saturation of uD) Two alternatives: 1. Multivariable controller (e.g. MPC) 2. Mix of various advanced controllers including PID, selectors, feedforward 28
29 ECONOMIC PLANTWIDE CONTROL Bottom-up part (mainly dynamic): Step S7: Select the control structure for the Process Optimization layer (RTO) How should the optimal setpoints for CV1be updated ? A good choice of controlled variables (CV1) may remove the need for this layer. Figure 1: Typical control hierarchy in a chemical plant 29
30 REACTOR-SEPARATOR- RECYCLE CASE STUDY (Luyben) Feed F0 contains mostly A A. . Reactor (CSTR) 1st order A -> B reaction Constant temperature Separator (distillation column) Distillate D (mostly A ): recycled back to CSTR. Bottom product B (mostly B ) 22 stages Constant pressure Constant relative volatility D F0 B Reactor-separator-recycle process 30
31 CASE STUDY: Step S1 Definition of optimal operation: Given feedrate (Mode 1) J = cost feed + cost energy value products J = cFF0+ cVVB cBB Since F0 = B is given, this simplifies to min J = VB Reactor-separator-recycle process 31
32 CASE STUDY: Step S1 Definition of optimal operation: Given feedrate (Mode 1) J = cost feed + cost energy value products J = cFF0+ cVVB cBB Since F0 = B is given, this simplifies to min J = VB Operational constraints MR 2800 kmol VB 50 kmol/min xB 0.0105 (max. 1.05% A in product) Reactor-separator-recycle process 32
33 CASE STUDY: Step S2 Step S2: Determine the degrees of freedom and find the steady-state optimal operation. Given pressure and reactor temperature: 6 dynamic manipulated variables (valves) uD = {F0, VB, D, B, F, LT} MDand MBhave no steady-state effect and need to be controlled Steady state and given feed F0: 3 steady-state degrees of freedom Step S3: Must find 3 economic variables to control (CV1) Reactor-separator-recycle process ??? 33
34 11 PRACTICAL RULES (TO HELP WITH THE REMAINING STEPS) 34
35 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 1: Control the active constraints In general, process optimization is required to determine the active constraints. but a good engineer can often guess the active constraints. 35
36 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 1: Control the active constraints In general, process optimization is required to determine the active constraints. but a good engineer can often guess the active constraints Rule 1A: The purity constraint of the valuable product is always active and should be controlled. This is to maximize valuable product and avoid product give away . 36
37 CASE STUDY Practical rules for Step S3: Selection of economic CV1 Rule 1: Control the active constraints Rule 1A: The purity constraint of the valuable product is always active and should be controlled. Case study: Both MR (max) and xB (purity valuable product) are active. Need to find one more CV1 Unconstrained optimum J=VB Reactor-separator-recycle process u = LT 37
38 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 2: (for remaining unconstrained steady-state degrees of freedom, if any): Control self-optimizing variables. The two main properties of a good self-optimizing variable are: ts optimal value is insensitive to disturbances so F = CV1,opt / d is small t is sensitive to the plant inputs (= flat optimum ) so the process gain G = CV1/ u is large 38
39 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 2: (for remaining unconstrained steady-state degrees of freedom, if any): Control the self-optimizing variables. The two main properties of a good self-optimizing variable are: ts optimal value is insensitive to disturbances (such that F = CV1,opt / d is small) t is sensitive to the plant inputs (so the process scaled gain G = CV1/ u is large). The following rule combines the two desired properties: Rule 2A: Select the set CV1such that the ratio G-1F is minimized. This rule is often called the Maximum scaled gain rule . 39
40 CASE STUDY: Self-optimizing variables Practical rules for Step S3: Selection of economic CV1 Rule 2: (for remaining unconstrained steady-state degrees of freedom, if any): Control the self-optimizing variables. The two main properties of a good self- optimizing variable are: ts optimal value is insensitive to disturbances (such that F = CV1,opt / d is small) t is sensitive to the plant inputs (so the process scaled gain G = CV1/ u is large). The following rule shows how to combine the two desired properties: Rule 2A: Select the set CV1such that the ratio G-1F is minimized. This rule is often called the Maximum scaled gain rule . Sensitive variables (with large scaled gain): Some good candidates for CV1,SOC : {LT/F , xD}. 40
41 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 3: (for remaining unconstrained steady-state degrees of freedom, if any): Never try to control the cost function J (or any other variable with min or max at the optimal point). 1. The cost function J has no sensitivity to the plant inputs so G = 0, (which violates Rule 2A) 41
42 PRACTICAL RULES for Step S3 Step S3: Selection of economic CV1 Rule 3: (for remaining unconstrained steady-state degrees of freedom, if any): Never try to control the cost function J (or any other variable with min or max at the optimal point). 1. The cost function J has no sensitivity to the plant inputs at the optimal point and so G = 0, which violates Rule 2A. 2. Potential infeasibility : J u 42
43 CASE STUDY Practical rules for Step S3: Selection of economic CV1 Rule 3: (for remaining unconstrained steady-state degrees of freedom, if any): Never try to control the cost function J (or any other variable that reaches a min or max at the optimal point). Case study: Do not keep VBconstant (but may be used as a TPM) 43
44 PRACTICAL RULES for Step S4 Step S4: Location of throughput manipulator (TPM) Rule 4: Locate the TPM close to the process bottleneck. This is to be able to maximize the production rate (Mode 2) Gives a simpler transition between mode 1 (given feed) and mode 2 (Process bottleneck is defined as the last constraint to become active when increasing the throughput rate.) Rule 5: (for processes with recycle) Locate the TPM inside the recycle loop. This is to avoid overfeeding the recycle loop = snowballing (Luyben) 44
45 CASE STUDY Practical rules for Step S4: Location of throughput manipulator (TPM) Rule 4: Locate the TPM close to the process bottleneck. Rule 5: (for processes with recycle) Locate the TPM inside the recycle loop. According to Rules 4 and 5 the best candidate for TPM location is VB. 45
46 PRACTICAL RULES for Step S5 Step S5: Structure of regulatory control layer Rule 6: Arrange the inventory control loops (for level, pressures, etc.) around the TPM location according to the radiation rule (Georgakis) This ensures local consistency i.e. all inventories are controlled by their local in or outflows. TPM TPM TPM 46
47 PRACTICAL RULES for Step S5 Step S5: Structure of regulatory control layer Rule 7: Select sensitive/drifting variables as controlled variables CV2for regulatory control. Typically include inventories (levels and pressures), reactor temperature, or a sensitive temperature in a distillation column. 47
48 PRACTICAL RULES for Step S5 Step S5: Structure of regulatory control layer Rule 8: Economically important active constraints (CV1) should be selected as CVs (CV2) in the regulatory layer. Economic variables CV1are generally controlled in the supervisory layer. But moving CV1to a faster layer may ensure tighter control with a smaller back-off. 48
49 PRACTICAL RULES for Step S5 Step S5: Structure of regulatory control layer Rule 9: ( Pair-close rule): The pairings should be selected such that, effective delays and loop interactions are minimal. 49
50 PRACTICAL RULES for Step S5 Step S5: Structure of regulatory control layer Rule 10: Avoid using MVs that may optimally saturate (at steady state) to control CVs in CV2. The reason is that we want to avoid re-configuring the regulatory control layer. To follow this rule, one needs to consider also other regions of operation than the nominal. 50
51 CASE STUDY Practical rules for Step S5: Structure of regulatory control layer Rule 7: Select sensitive/drifting variables as controlled variables CV2for regulatory control. Typically include inventories (levels and pressures), reactor temperature, or a sensitive temperature in a distillation column Rule 6: Arrange the inventory control loops (for level, etc.) around the TPM location according to the radiation rule. Rule 8: Economically important active constraints (CV1) should be selected as CVs (CV2) in the regulatory layer Rule 9: ( Pair-close rule): The pairings should be selected such that, effective delays and loop interactions are minimal. Rule 10: Avoid using MVs that may optimally saturate (at steady state) to control CVs in CV2. 51
