Part 3: Regulatory («stabilizing») control
Inventory (level) control structure
– Location of throughput manipulator
– Consistency and radiating rule
Structure of regulatory control layer (PID)
– Selection of controlled variables (CV2) and pairing with manipulated
variables (MV2)
– Main rule: Control drifting variables and "pair close"
Summary: Sigurd’s rules for plantwide control
1
Outline
• Skogestad procedure for control structure design
I Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s)
– Active constraints
– Self-optimizing variables for unconstrained, c=Hy
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up
• Step S5: Regulatory control: What more to control (secondary CV’s) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
2
Step S4. Where set production rate?
• Very important decision that determines the structure of the rest of the
inventory control system!
• May also have important economic implications
• Link between Top-down (economics) and Bottom-up (stabilization)
parts
– Inventory control is the most important part of stabilizing control
• “Throughput manipulator” (TPM)
= MV for controlling throughput (production rate, network flow)
• Where set the production rate = Where locate the TPM?
– Traditionally: At the feed
– For maximum production (with small backoff): At the bottleneck
3
TPM and link to inventory control
•
Liquid inventory: Level control (LC)
– Sometimes pressure control (PC)
•
•
5
Gas inventory: Pressure control (PC)
Component inventory: Composition control (CC, XC, AC)
Production rate set at inlet :
Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory control
6
Production rate set at outlet:
Inventory control opposite flow*
TPM
* Required to get “local-consistent” inventory control
7
Production rate set inside process*
TPM
* Required to get “local-consistent” inventory control
8
General: “Need radiating inventory
control around TPM” (Georgakis)
9
Consistency of inventory control
•
Consistency (required property):
An inventory control system is said to be consistent if the steadystate mass balances (total, components and phases) are satisfied
for any part of the process, including the individual units and the
overall plant.
10
QUIZ 1
CONSISTENT?
11
Local-consistency rule
Rule 1. Local-consistency requires that
1. The total inventory (mass) of any part of the process must be locally
regulated by its in- or outflows, which implies that at least one flow in or
out of any part of the process must depend on the inventory inside that
part of the process.
2. For systems with several components, the inventory of each component of
any part of the process must be locally regulated by its in- or outflows or
by chemical reaction.
3. For systems with several phases, the inventory of each phase of any part
of the process must be locally regulated by its in- or outflows or by phase
transition.
12
Proof: Mass balances
Note: Without the word “local” one gets the more general consistency rule
QUIZ 1
CONSISTENT?
13
Local concistency requirement ->
“Radiation rule “(Georgakis)
14
Flow split: May give extra DOF
TPM
TPM
Split: Extra DOF (FC)
15
Flash: No extra DOF
Example: Separator control
(oil-gas separation offshore)
19
Example: Separator control
Alternative TPM locations
Compressor could be replaced by valve if p1>pG
20
Alt.1
Alt.3
21
Alt.2
Alt.4
Similar to original but
NOT CONSISTENT
(PC not direction of flow)
Example: Solid oxide fuel cell
xCH4,s
CC
PC
CH4
H2O
(in ratio with CH4 feed
to reduce C and CO formation)
Air
CH4 + H2O = CO + 3H2
CO + H2O = CO2 + H2
2H2 + O2- → 2H2O + 2eSolid oxide electrolyte
O2-
e-
TPM = current I [A] = disturbance
O2 + 4e- → 2O2-
(excess O2)
TC
PC
Ts = 1070 K
(active constraint)
22
LOCATION OF SENSORS
• Location flow sensor (before or after valve or pump): Does not matter
from consistency point of view
– Locate to get best flow measurement
• Before pump: Beware of cavitation
• After pump: Beware of noisy measurement
• Location of pressure sensor (before or after valve, pump or
compressor): Important from consistency point of view
23
Next slides: Exercises and solutions
24
25
FC
PC
FC
PC
PC
FC
FC
PC
PC
FC
For each of the five structures; Where is the TPM? Is it feasible?
FC
PC
FC
PC
PC
FC
FC
PC
FT
PT
Same sensor location as case 3.
Can you control both flow and
temperature using valves 2 and 3,
Valves 3 and 4?
26
Some more. For each of the five structures; Where is the TPM? Is it feasible?
FC
PC
TPM
FC
NO
PC
YES
TPM
PC
FC
TPM
FC
PC
NO
YES
(it does not matter
where the flow is
measured; the valve
determines the
location of the TPM)
TPM
PC
Solution according to radiation rule
FC
YES
TPM
27
Note: Can never control pressure at ends (upstream first control valve or downstream last valve)!
PC
FC
TPM
NO
FC
PC
NO. New Rule:
Another controller
cannot cross the TPM,
Not even with a PC
TPM
FC
PC
NO, cannot cross TPM
TPM
FC
PC
NO
TPM
FT
PT
No, but OK if we
use valve 4 for PC
28
Some more. For each of the five structures; Where is the TPM? Is it feasible?
Where should we place TPM?
•
•
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
–
Gives inventory control “in direction of flow”
Consider moving TPM if:
1.
There is an important CV that could otherwise not be well controlled
– Dynamic reasons
– Special case: Max. production important: Locate TPM at process bottleneck* !
•
•
2.
TPM can then be used to achieve tight bottleneck control (= achieve max. production)
Economics: Max. production is very favorable in “sellers marked”
If placing it at the feed may yield infeasible operation (“overfeeding”)
–
If “snowballing” is a problem (accumulation in recycle loop), then consider placing TPM
inside recycle loop
BUT: Avoid a variable that may (optimally) saturate as TPM (unless it is at bottleneck)
–
Reason: To keep controlling CV=throughput, we would need to reconfigure (move TPM)**
*Bottleneck: Last constraint to become active as we increase throughput -> TPM must be used for bottleneck control
29
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally)
saturate with CV that may be given up”
Often optimal: Locate TPM at bottleneck!
• "A bottleneck is a unit where we reach a constraints which makes
further increase in throughput infeasible"
• If feed is cheap and available: Located TPM at bottleneck (dynamic
reasons)
• If the flow for some time is not at its maximum through the
bottleneck, then this loss can never be recovered.
37
Single-loop alternatives for bottleneck control
Traditional: Manual control of feed rate
Bottleneck.
Want max
flow here
TPM
Alt.1. Feedrate controls bottleneck flow (“long loop”…):
FC
Fmax
TPM
Alt. 2: Feedrate controls lost task (another “long loop”…):
Fmax
TPM
Alt. 3: Reconfigure all upstream inventory loops:
Fmax
38
TPM
May move TPM to inside recycle loop to
avoid snowballing
Example: Eastman esterification process
Alcohol recycle
Reach max mass transfer
rate: R increases sharply
(“snowballing”)
Ester product
Alcohol + water + extractive agent (e)
39
First improvement: Located closer to bottleneck
40
Final improvement: Located “at” bottleneck + TPM
is inside “snowballing” loop
Follows Luyben’s law 1 to avoid snowballing(modified): “Avoid having all
streams in a recycle system on inventory control”
41
CASE STUDY: Recycle plant (Luyben, Yu, etc.)
Part 1 -3
Recycle of unreacted A (+ some B)
5
Feed of A
4
1
Assume constant reactor temperature.
Given feedrate F0 and column pressure:
Dynamic DOFs:
Column levels:
Steady-state DOFs:
42
Nm = 5
N0y = 2
N0 = 5 - 2 = 3
2
3
Product (98.5% B)
Part 1: Economics (Given feed)
Recycle plant: Optimal operation
mT
1 remaining unconstrained degree of freedom, CV=?
43
J=V as a function of reflux L
Optimum
= Nominal point
44
With fixed active constraints:
Mr = 2800 kmol (max), xB= 1.5% A (max)
Control of recycle plant:
Conventional structure (“Two-point”: CV=xD)
LC
TPM
LC
XC
xD
XC
xB
LC
Control active constraints (Mr=max and xB=0.015) + xD
45
46
Luyben law no. 1 (to avoid snowballing):
“Fix a stream in the recycle loop” (CV=F or D)
Luyben rule: CV=D (constant)
LC
LC
XC
LC
47
“Brute force” loss evaluation:Disturbance in F0
Luyben rule:
Conventional
48
Loss with nominally optimal setpoints for Mr, xB and c
Loss evaluation: Implementation error
Luyben rule:
49
Loss with nominally optimal setpoints for Mr, xB and c
Conclusion: Control of recycle plant
Active constraint
Mr = Mrmax
Self-optimizing
50
L/F constant: Easier than “two-point” control
Assumption: Minimize energy (V)
Active constraint
xB = xBmin
Modified Luyben’s law to avoid snowballing
•
Luyben law no. 1 (“Plantwide process control”, 1998, pp. 57): “A
stream somewhere in all recycle loops must be flow controlled”
•
•
Luyben rule is OK dynamically (short time scale),
BUT economically (steady-state): Recycle should increase with
throughput
•
Modified Luyben’s law 1 (by Sigurd): “Consider moving the
TPM inside the recycle loop”
51
NOTE: There are actually two recycles
•
•
•
•
One through the reactor (D or F)
One through the column (L)
One flow inside both recycle loops: V
Alt.6: TPM=V if we want to break both recycle loops!
TC
57
PC
Alt. 6
TPM = V
PC
LC
LC
TC
XC L
F
TPM
LC
Simulations (to be done) confirm
This is the best!
58
L and F for composition control: OK!
XC
Alt. 7
What about keeping V constant?
(in addition to having another TPM)
PC
LC
TPM
F0
TC
L
LC
F
V
LC
59
With feedrate F0 fixed (TPM)
L for compostion control in bottom (xB)
Top composition floating
XC
NO! Never control cost J=V
Reactor-recycle process:
Want to maximize feedrate: reach bottleneck in column
Bottleneck: max. vapor
rate in column
TPM
60
Reactor-recycle process with max. feedrate
Alt.A: Feedrate controls bottleneck flow
Bottleneck: max. vapor
rate in column
TPM
Vs
61
FC
Vmax
V
Get “long loop”: Need back-off in V
Vmax-Vs=Back-off
= Loss
Reactor-recycle process with max. feedrate:
Alt. B Move TPM to bottleneck (MAX). Use
feedrate for lost task (xB)
Bottleneck: max. vapor
rate in column
MAX
TPM
62
Get “long loop”: May need back-off in xB instead…
=Alt.6 TPM
Reactor-recycle process with max. feedrate:
Alt. C: Best economically: Move TPM to bottleneck
(MAX) + Reconfigure upstream loops
LC
MAX
TPM
63
OK, but reconfiguration undesirable…
=Alt.6 TPM
Reactor-recycle process:
Alt.C’: Move TPM + reconfigure (permanently!)
LC
CC
TPM
F0s
64
For cases with given feedrate: Get “long loop” but no associated loss
=Alt.6 TPM
Alt.4: Multivariable control (MPC)
• Can reduce loss
• BUT: Is generally placed on top of the regulatory control system
(including level loops), so it still important where the production rate is
set!
•One approach: Put MPC on top that coordinates flows through plant
•By manipulating feed rate and other ”unused” degrees of freedom
(including level setpoints):
•E.M.B. Aske, S. Strand and S. Skogestad,
•``Coordinator MPC for maximizing plant throughput'',
•Computers and Chemical Engineering, 32, 195-204 (2008).
65
Conclusion TPM (production rate
manipulator)
• Think carefully about where to place it!
• Difficult to undo later
70
Session 5: Design of regulatory control layer
71
Outline
• Skogestad procedure for control structure design
I Top Down
• Step S1: Define operational objective (cost) and constraints
• Step S2: Identify degrees of freedom and optimize operation for disturbances
• Step S3: Implementation of optimal operation
– What to control ? (primary CV’s) (self-optimizing control)
• Step S4: Where set the production rate? (Inventory control)
II Bottom Up
• Step S5: Regulatory control: What more to control (secondary CV’s) ?
– Distillation example
• Step S6: Supervisory control
• Step S7: Real-time optimization
72
Regulatory layer
Step 5. Regulatory control layer
• Purpose: “Stabilize” the plant using a
simple control configuration (usually:
local SISO PID controllers + simple
cascades)
• Enable manual operation (by operators)
• Main structural decisions:
• What more should we control?
(secondary cv’s, CV2, use of extra
measurements)
• Pairing with manipulated variables
(mv’s u2)
CV1
CV2 = ?
74
Structure of regulatory control layer
(PID)
Main decisions:
1. Selection of controlled variables (CV2)
2. Pairing with manipulated variables (MV2)
Main rules:
75
1.
Control drifting variables
2.
«Pair close"
CV2
↕
MV2
Regulatory layer
Stabilizing control: Use inputs MV2=u2 to control
“drifting” variables CV2
CV2s
K
u2
G
CV1
Primary CV
CV2
Secondary CV
(control for
dynamic reasons)
Key decision: Choice of CV2 (controlled variable)
Also important: Choice of MV2=u2 (“pairing”)
Process control: Typical «drifting» variables (CV2) are
• Liquid inventories (level)
• Vapor inventories (pressure)
• Some temperatures (reactor, distillation column profile)
76
Regulatory layer
Degrees of freedom unchanged
• No degrees of freedom lost as setpoints y2s replace inputs u2 as new
degrees of freedom for control of y1
Cascade control:
CV2s
K
CV2s=New DOF
77
u2
G
CV1
CV2
MV2=Original DOF
Regulatory layer
Objectives regulatory control layer
1.
2.
3.
4.
5.
6.
7.
Allow for manual operation
Simple decentralized (local) PID controllers that can be tuned on-line
Take care of “fast” control
Track setpoint changes from the layer above
Local disturbance rejection
Stabilization (mathematical sense)
Avoid “drift” (due to disturbances) so system stays in “linear region”
–
78
“stabilization” (practical sense)
8. Allow for “slow” control in layer above (supervisory control)
9. Make control problem easy as seen from layer above
10. Use “easy” and “robust” measurements (pressure, temperature)
11. Simple structure
12. Contribute to overall economic objective (“indirect” control)
13. Should not need to be changed during operation
Regulatory layer
Example: Exothermic reactor (unstable)
Active constraints (economics):
Product composition c + level (max)
• u = cooling flow (q)
• CV1 = composition (c)
• CV2 = temperature (T)
feed
CV1s
CC
CV2s
TC
CV1=c
LC
CV2=T
u
79
Ls=max
product
cooling
Optimizer
(RTO)
Optimally constant valves
Always active constraints
CV1s
Supervisory
controller
(MPC)
y1=CV1
CV2s
u1
d
Regulatory
controller
(PID)
u2
y2=CV2
H2
Physical
inputs (valves)
PROCESS
y
Stabilized process
81
H
ny
Degrees of freedom for optimization (usually steady-state DOFs), MVopt = CV1s
Degrees of freedom for supervisory control, MV1=CV2s + unused valves
Physical degrees of freedom for stabilizing control, MV2 = valves (dynamic process inputs)
Regulatory layer
Details Step 5 (Structure regulatory control layer)
(a) What to control (CV2)?
1. Control CV2 that “stabilizes the plant” (stops drifting)
2. Select CV2 which is easy to control (favorable dynamics)
• In addition, active constraints (CV1) that require tight control
(small backoff) may be assigned to the regulatory layer.*
82
*Comment: usually not necessary with tight control of unconstrained CVs because
optimum is usually relatively flat
Regulatory layer
“Control CV2 that stabilizes the plant (stops drifting)”
In practice, control:
1. Levels (inventory liquid)
2. Pressures (inventory gas/vapor) (note: some pressures may be left
floating)
3. Inventories of components that may accumulate/deplete inside plant
•
•
•
E.g., amine/water depletes in recycle loop in CO2 capture plant
E.g., butanol accumulates in methanol-water distillation column
E.g., inert N2 accumulates in ammonia reactor recycle
4. Reactor temperature
5. Distillation column profile (one temperature inside column)
• Stripper/absorber profile does not generally need to be stabilized
84
Regulatory layer
Details Step 5b….
(b)
Identify pairings =
Identify MVs (u2) to control CV2, taking into account:
85
•
Want “local consistency” for the inventory control
– Implies radiating inventory control around given flow
•
Avoid selecting as MVs in the regulatory layer, variables that may
optimally saturate at steady-state (active constraint on some region),
because this would require either
– reassigning the regulatory loop (complication penalty), or
– requiring back-off for the MV variable (economic penalty)
•
Want tight control of important active constraints (to avoid back-off)
•
General rule: ”pair close” (see next slide)
Regulatory layer
Step 5b…. Main rule: “Pair close”
The response (from input to output) should be fast, large and in one direction.
Avoid dead time and inverse responses!
86
Cascade control in regulatory layer
• May be helpful to reduce nonlinearity and improve disturbance rejection
• Controller (“master”) gives setpoint to another controller (“slave”)
–
–
•
Without cascade: “Master” controller directly adjusts u (input, MV) to control y
With cascade: Local “slave” controller uses u to control “extra”/fast measurement (y’).
“Master” controller adjusts setpoint y’s.
Example: Flow controller on valve (very common!)
–
–
–
y = level H in tank (or could be temperature etc.)
u = valve position (z)
y’ = flowrate q through valve
WITHOUT CASCADE
flow in
WITH CASCADE
Hs
H
LC
flow in
Hs
H
LC
master
MV=z
MV=qs
valve position
FC
slave
flow out
87
q
z
flow out
measured
flow
What are the benefits of adding a flow
controller (inner cascade)?
qs
Extra measurement y’ = q
q
z
f(z)
1.
Counteracts nonlinearity in valve, f(z)
•
2.
88
1
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2
(FC reacts faster than outer level loop)
0
0
1 z
(valve opening)
Regulatory layer
Sigurd’s pairing rule for regulatory layer:
“Avoid using MVs that may optimally
saturate (at steady state) to control CV2s”
•
Main reason: Minimizes need for reassigning loops
. loop
LV
Ts
TC
TC
(a) Normal: Control T using V
•
•
•
89
TS
(b) If V may saturate: Use L
Important: Always feasible (and optimal) to give up a CV when optimal MV saturation occurs.
–
Proof (DOF analysis): When one MV disappears (saturates), then we have one less optimal CV.
Failing to follow this rule: Need some “fix” when MV saturates to remain optimal, like
–
reconfiguration (logic)
–
backoff (loss of optimality)
BUT: Rule may be in conflict with other criteria
–
Dynamics (“pair close” rule)
–
Interactions (“avoid negative steady-state RGA” rule)
–
If conflict: Use reconfiguration (logic) or go for multivariable constraint control (MPC which may provide “built-in” logic)
Regulatory layer
Why simplified configurations?
Why control layers?
Why not one “big” multivariable controller?
• Fundamental: Save on modelling effort
• Other:
–
–
–
–
–
–
90
easy to understand
easy to tune and retune
insensitive to model uncertainty
possible to design for failure tolerance
fewer links
reduced computation load
Hierarchical/cascade control: Time scale separation
•
With a “reasonable” time scale separation between the layers
(typically by a factor 5 or more in terms of closed-loop response time)
we have the following advantages:
1. The stability and performance of the lower (faster) layer (involving y2) is not
much influenced by the presence of the upper (slow) layers (involving y1)
Reason: The frequency of the “disturbance” from the upper layer is well inside
the bandwidth of the lower layers
2. With the lower (faster) layer in place, the stability and performance of the
upper (slower) layers do not depend much on the specific controller settings
used in the lower layers
Reason: The lower layers only effect frequencies outside the bandwidth of the
upper layers
91
Cascade control
distillation
ys
y
With flow loop +
T-loop in top
X
C
Ts
T
TC
Ls
L
92
X
C
FC
z
QUIZ: What are the benefits of adding a flow
controller (inner cascade)?
qs
Extra measurement y2 = q
1.
93
z
Counteracts nonlinearity in valve, f(z)
•
2.
q
With fast flow control we can assume q = qs
Eliminates effect of disturbances in p1 and p2
Summary: Rules for plantwide control
• Here we present a set of simple rules for economic plantwide control
to facilitate a close-to-optimal control structure design in cases where
the optimization of the plant model is not possible.
• the rules may be conflicting in some cases and in such cases, human
reasoning is strongly advised.
94
Rules for Step S3: Selection of primary (economic) controlled variables, CV1
Rule 1: Control the active constraints.
•
In general, process optimization is required to determine the active constraints,
but in many cases these can be identified based on a good process knowledge
and engineering insight. Here is one useful rule:
• Rule 1A: The purity constraint of the valuable product is
always active and should be controlled.
•
•
•
95
This follows, because we want to maximize the amount of valuable product
and avoid product “give away” (Jacobsen and Skogestad, 2011). Thus, we
should always control the purity of the valuable product at its specification.
For “cheap” products we may want to overpurify (purity constraint may not be
active) because this may reduce the loss of a more valuable component.
In other cases, we must rely on our process knowledge and engineering
insight. For reactors with simple kinetics, we usually find that, the reaction and
conversion rates are maximized by operating at maximum temperature and
maximum volume (liquid phase reactor). For gas phase reactor, high pressure
may increase the reaction rate, but this must be balanced against the
compression costs.
Rule 2: (for remaining unconstrained steady-state degrees of freedom, if any):
Control the “self-optimizing” variables.
•
This choice is usually not obvious, as there may be several alternatives, so this rule is in itself not very
helpful. The ideal self-optimizing variable, at least, if it can be measured accurately, is the gradient of
the cost function. Ju, which should be zero for any disturbance. Unfortunately, it is rarely possible to
measure this variable directly and the “self-optimizing” variable may be viewed as an estimate of the
gradient Ju
The two main properties of a good “self-optimizing” (CV1=c=Hy) variable
are:
1. Its optimal value is insensitive to disturbances (such that the optimal
sensitivity dcopt/dd =Fc HF = is small)
2. It is sensitive to the plant inputs (so the process gain dc/du = G = HGy
is large).
The following rule shows how to combine the two desired properties:
• Rule 2A: Select the set CV1=c such that the ratio G-1Fc is minimized.
•
96
This rule is often called the “maximum scaled gain rule”.
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 maximum or minimum at the optimum)
J
J>Jmin
Jmin
J<Jmin
?
u
•
•
•
•
97
First, the cost function J has no sensitivity to the plant inputs at the optimal
point and so G = 0 which violates Rule 2A.
Second, if we specify J lower than its optimal value, then clearly, the
operation will be infeasible
Also, specifying J higher than its optimal value is problematic, as we have
multiplicity of solutions. As mentioned above, rather controlling the cost J, we
should control its gradient, Ju.
Rules for Step S4: Location of throughput manipulator (TPM)
Rule 4: Locate the TPM close to the
process bottleneck
.
• The justification for this rule is to take advantage of the large
economic benefits of maximizing production in times when product
prices are high relative to feed and energy costs (Mode 2). To
maximize the production rate, one needs to achieve tight control of the
active constraints, in particular, of the bottleneck, which is defined as
the last constraint to become active when increasing the throughput
rate (Jagtap et al., 2013).
98
Rule 5: (for processes with recycle)
Locate the TPM inside the recycle loop.
• The point is to avoid “overfeeding” the recycle loop which may easily
occur if we operate close to the throughput where “snowballing” in the
recycle loop occurs. This is a restatement of Luyben’s rule “Fix a Flow
in Every Recycle Loop” (Luyben et al., 1997). From this perspective,
snowballing can be thought of as the dynamic consequence of
operating close to a bottleneck which is within a recycle system.
• In many cases, the process bottleneck is located inside the recycle loop
and Rules 4 and 5 give the same result.
99
Rules for 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.
• The radiation rule (Price et al., 1994), says that, the inventory loops
upstream of the TPM location must be arranged opposite of flow
direction. For flow downstream of TPM location it must be arranged in
the same direction. This ensures “local consistency” i.e. all inventories
are controlled by their local in or outflows.
10
0
Rule 7: Select “sensitive/drifting”
variables as controlled variables CV2 for
regulatory control.
• This will generally include inventories (levels and pressures), plus
certain other drifting (integrating) variables, for example,
– a reactor temperature
– a sensitive temperature/composition in a distillation column.
• This ensures “stable operation, as seen from an operator’s point of
view.
• Some component inventories may also need to be controlled,
especially for recycle systems. For example, according to “Down’s
drill” one must make sure that all component inventories are “selfregulated” by flows out of the system or by removal by reactions,
otherwise their composition may need to be controlled (Luyben, 1999).
10
1
Rule 8: Economically important active
constraints (a subset of CV1), should be
selected as controlled variables CV2 in
the regulatory layer.
• Economic variables, CV1, are generally controlled in the supervisory
layer. Moving them to the faster regulatory layer may ensure tighter
control with a smaller backoff.
• Backoff: difference between the actual average value (setpoint)
and the optimal value (constraint).
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Rule 9: “Pair-close” rule: The pairings
should be selected such that, effective
delays and loop interactions are minimal.
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Rule 10: : Avoid using MVs that may
optimally saturate (at steady state) to
control CVs in the regulatory layer (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, for example, operating at
maximum capacity (Mode 2) where we usually have more active
constraints.
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Rules for Step S6: Structure of supervisory control layer.
Rule 11: MVs that may optimally saturate (at steady
state) should be paired with the subset of CV1 that
may be given up.
• This rule applies for cases when we use decentralized control in the
supervisory layer and we want to avoid reconfiguration of loops.
• The rule follows because when a MV optimally saturates, then there
will be one less degree of freedom, so there will be a CV1 which may
be given up without any economic loss. The rule should be considered
together with rule 10.
• Example: Gives correct answer for the process where we want to
control flow and have p>pmin: Pair the valve (MV) with CV1 (p)
which may be given up.
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Plantwide control. Main references
• The following paper summarizes the procedure:
– S. Skogestad, ``Control structure design for complete chemical plants'',
Computers and Chemical Engineering, 28 (1-2), 219-234 (2004).
• 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).
• 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).
• More information:
http://www.nt.ntnu.no/users/skoge/plantwide
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All papers available at: http://www.nt.ntnu.no/users/skoge/