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) ?
• Step S6: Supervisory control
• Step S7: Real-time optimization
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Step S4. Where set production rate?
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Where locale the TPM (throughput manipulator)?
Very important!
Determines structure of remaining inventory (level) control system
Set production rate at (dynamic) bottleneck
Link between Top-down and Bottom-up parts
TPM (Throughput manipulator)
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Definition (Aske and Skogestad, 2009). A TPM is a degree of freedom that
affects the network flow and which is not directly or indirectly determined by
the control of the individual units, including their inventory control.
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Comments:
– The TPM is the “gas pedal” of the process
– Usually set by the operator (manual control), often the main feedrate
– The TPM is usually a flow (or closely related to a flow) but not always.
• Example: Reactor temperature can be a TPM, because it changes the reactor conversion,
– Usually, only one TPM for a plant, but there can be more if there are
• parallel units or splits into alternative processing routes
• multiple feeds that do not need to be set in a fixed ratio
– If we consider only part of the plant then the TPM may be outside our control.
• throughput is then a disturbance
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Example Reactor-recycle process:
Given feedrate with production rate set at inlet
TPM
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Consistency of inventory control
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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.
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Local*-consistency (desired property):
A consistent inventory control system is said to be local-consistent if
for any part/unit the local inventory control loops by themselves
are sufficient to achieve steady-state mass balance consistency
for that unit (without relying on other loops being closed).
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* Previously called self-consistency
Production rate set at inlet :
Inventory control in direction of flow*
TPM
* Required to get “local-consistent” inventory control
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Production rate set at outlet:
Inventory control opposite flow
TPM
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Production rate set inside process
TPM
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Summary: “Radiation rule “(Georgakis)
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QUIZ 1
CONSISTENT?
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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.
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Proof: Mass balances
Note: Without the local requirement one gets the more general consistency rule
QUIZ 1
CONSISTENT?
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Dynamic simulation case (d)
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TPM
TPM
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QUIZ 2
Consistent?
Local-consistent?
Note: Local-consistent is
more strict as it implies
consistent
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QUIZ 3
Closed system: Must
leave one inventory
uncontrolled
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QUIZ 4
OK? (Where is production set?
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NO. Two TPMs (consider overall liquid balance).
Solution: Interchange LC and FC on last tank
Locate TPM = Where set the production rate?
• Very important decision that determines the structure of the rest of the
control system!
• May also have important economic implications
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Often optimal: Set production rate 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: Optimal to set production rate at
bottleneck
• If the flow for some time is not at its maximum through the
bottleneck, then this loss can never be recovered.
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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
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TPM
Possible improvements
Alt. 1D: Feedrate controls bottleneck flow + “feedforward”:
Fmax
FC
TPM
Alt. 2D: Feedrate controls lost task + “feedforward”:
Fmax
TPM
Alt. 4: MPC
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Example
Reactor-recycle process:
Want to maximize feedrate: reach bottleneck in column
Bottleneck: max. vapor
rate in column
TPM
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Example
Reactor-recycle process with max. feedrate
Alt.1: Feedrate controls bottleneck flow
Bottleneck: max. vapor
rate in column
TPM
Vs
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FC
Vmax
V
Get “long loop”: Need back-off in V
Vmax-Vs=Back-off
= Loss
Example
Reactor-recycle process with max. feedrate:
Alt. 2 Optimal: Move TPM to bottleneck (MAX)
Feedrate used for lost task (xb)
Bottleneck: max. vapor
rate in column
MAX
TPM
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Get “long loop”: May need back-off in xB instead…
Reactor-recycle process with max. feedrate:
Alt. 3: Optimal: Move TPM to bottleneck (MAX)
Example
Reconfigure upstream loops
MAX
TPM
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OK, but reconfiguration undesirable…
Example
Reactor-recycle process:
Alt.3: Move TPM + reconfigure (permanently!)
TPM
F0s
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For cases with given feedrate: Get “long loop” but no associated loss
Example
Reactor-recycle process with max. feedrate
Alt.1D: Alt. 1 “Long loop” + “feedforward”
Bottleneck: max. vapor
rate in column
TPM
Vs
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F/F0
FC
“Feedforward”:
Send feed change to ALL
flows upstream bottleneck
Less back-off in V because F closer to V
Example
Reactor-recycle process with max. feedrate
Alt.2D: Alt. 2 “Long loop” + “feedforward”
F/F0
MAX
TPM
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“Feedforward”:
Send flow change to ALL
flows upstream bottleneck
Less back-off in xB because F closer to xB
Example
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:
•E.M.B. Aske, S. Strand and S. Skogestad,
•``Coordinator MPC for maximizing plant throughput'',
•Computers and Chemical Engineering, 32, 195-204 (2008).
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Conclusion production rate manipulator
• Think carefully about where to place it!
• Difficult to undo later
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QUIZ. Distillation. OK?
LV-configuration
TPM
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DB-configuration OK???
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QUIZ
• Cases 7–13, 15-23
• Will it work? Where is throughput set (TPM)?
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LOCATE TPM?
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For step 4, locate TPM, the procedure is:
As the default choice place the TPM at the feed
Consider moving if there is an important active constraint that could otherwise
not be well controlled. That is, if the feedrate must be used for some other task
in order to get a local-consistent system with tight control of the constraint.
To avoid the need to move (reassign) the TPM, avoid variables that may
saturate.
Exception: The last constraint to become active when we reach optimum or
maximum throughput* is a good candidate TPM, because the bottleneck
situation is generally where the backoff losses are largest. Also, this TPM will
only saturate when it no longer can be increased, so no change in TPMvariable is ever needed.
*At optimum/maximum throughput, the throughput can no longer be set (because
it is used a degree of freedom for optimal operation)
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