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)
Control Active constraints + self-optimizing variables
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 (Throughput manipulator)
Definition 1. TPM = MV used to control throughput (CV)
= “MV used to set production rate”
Definition 2 (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.
The TPM is the “gas pedal” of the process
Value of TPM: Usually set by the operator (manual control)
Operators are skeptical of giving up this MV to the control system (e.g. MPC)
The TPM is usually a flow (or closely related to a flow), e.g. main feedrate, but not always.
It can be a setpoint to another control loop
Example: Reactor temperature can be a TPM, because it changes the reactor conversion,
Example: Pressure of gas product can be a TPM, because it changes the gas product flowrate
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

4. TPM and link to inventory control
Liquid inventory: Level control (LC)
Sometimes pressure control (PC)
Gas inventory: Pressure control (PC)
Component inventory: Composition control (CC, XC, AC)

5. 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 steady-state mass balances (total, components and phases) are satisfied for any part of the process, including the individual units and the overall plant.
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).
* Previously called self-consistency 9

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.
Proof: Mass balances
Note: Without the word “local” one gets the more general consistency rule

12. QUIZ 1
CONSISTENT?

13. Dynamic simulation case (d)

14. Local concistency requirement -> “Radiation rule “(Georgakis)

15. Flow split: May give extra DOF
TPM
Extra DOF (FC)
No extra DOF

16. Consistent? Local-consistent? QUIZ 2 Note: Local-consistent is
more strict as it implies
consistent

17. Closed system: Must leave one inventory uncontrolled
QUIZ 3
Closed system: Must leave one inventory uncontrolled

18. OK? (Where is production set?
QUIZ 4
OK? (Where is production set?
TPM1
TPM2
NO. Two TPMs (consider overall liquid balance).
Solution: Interchange LC and FC on last tank

19. Example 1: Alternative TPM locations
Compressor could be replaced by valve if p1>pG

20. Alt.1
Alt.2
Alt.3
Alt.4
NOT CONSISTENT

21. Example Reactor-recycle process: Given feedrate (production rate set at inlet)
TPM

23. Alt.1
Alt.2
Alt.3
Alt.4

24. 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:
There is an important CV that could otherwise not be well controlled
Dynamic reasons
Special case: Max. production important: Locate TPM at process bottleneck* !
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
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

25. QUIZ. Distillation. OK?
LV-configuration
TPM

26. DB-configuration OK???
TPM

27. TPM

29. Additional problems
See “Kida slides”
Exercise 4

30. Example * **
* Keep p ¸ pmin
** Keep valve fully open

33. 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.

34. Single-loop alternatives for bottleneck control
Want max flow here
Traditional: Manual control of feed rate
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
TPM

35. Possible improvements
Alt. 1D: Feedrate controls bottleneck flow + “feedforward”: FC
Fmax
TPM
Alt. 2D: Feedrate controls lost task + “feedforward”:
Fmax
TPM
Alt. 4: MPC

36. Bottleneck: max. vapor rate in column
Example
Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column
Bottleneck: max. vapor rate in column
TPM

37. Bottleneck: max. vapor rate in column
Example
Reactor-recycle process with max. feedrate Alt.1: Feedrate controls bottleneck flow
Bottleneck: max. vapor rate in column
TPM Vs FC
Vmax V
Vmax-Vs=Back-off
= Loss
Get “long loop”: Need back-off in V

38. Bottleneck: max. vapor rate in column
Example
Reactor-recycle process with max. feedrate: Alt. 2 Better economically: Move TPM to bottleneck (MAX). Feedrate used for lost task (xb)
Bottleneck: max. vapor rate in column
MAX
TPM
Get “long loop”: May need back-off in xB instead…

39. Reactor-recycle process with max. feedrate: Alt
Reactor-recycle process with max. feedrate: Alt. 3: Even better economically: Move TPM to bottleneck (MAX). Reconfigure upstream loops
Example
MAX LC
TPM
OK, but reconfiguration undesirable…

40. Reactor-recycle process: Alt.3: Move TPM + reconfigure (permanently!)
Example
Reactor-recycle process: Alt.3: Move TPM + reconfigure (permanently!) LC CC
TPM
F0s
For cases with given feedrate: Get “long loop” but no associated loss

41. Bottleneck: max. vapor rate in column
Example
Reactor-recycle process with max. feedrate Alt.1D: Alt. 1 “Long loop” + “feedforward”
Bottleneck: max. vapor rate in column
TPM
F/F0 Vs FC
“Feedforward”:
Send feed change to ALL
flows upstream bottleneck
Less back-off in V because F closer to V

42. Example
Reactor-recycle process with max. feedrate Alt.2D: Alt. 2 “Long loop” + “feedforward”
F/F0
MAX
TPM
“Feedforward”:
Send flow change to ALL
flows upstream bottleneck
Less back-off in xB because F closer to xB

43. Alt.4: Multivariable control (MPC)
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, (2008).

44. 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)

45. First improvement: Located closer to bottleneck

46. Final improvement: Located “at” bottleneck + TPM is inside “snowballing” loop

47. Where should we place TPM?
TPM = MV used to control throughput
Traditionally: TPM = Main feed valve (or pump/compressor)
Operators like it. Gives inventory control “in direction of flow”
Consider moving TPM if:
There is an important CV that could otherwise not be well controlled
Dynamic reasons
Special case: Max. production important: Locate TPM at process bottleneck* !
Because max. production is very favorable in “sellers marked”
TPM can then be used to achieve tight bottleneck control (= achieve max. flow)
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
**Sigurd’s general pairing rule (to reduce need for reassigning loops): “Pair MV that may (optimally) saturate with CV that may be given up”

48. Conclusion TPM (production rate manipulator)
Think carefully about where to place it!
Difficult to undo later

49. 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 noise
Etc.
Location of pressure sensor (before or after valve, pump or compressor): Important from consistency point of view

50. Moving TPM
A purely top-down approach: Start by controlling all active constaints at max. throughput (may give moving TPM)
Economic Plantwide Control Over a Wide Throughput Range: A Systematic Design Procedure
Rahul Jagtap, Nitin Kaistha*and Sigurd Skogestad
Step 0: Obtain active constraint regions for the wide throughput range
Step 1: Pair loops for tight control of economic CVs at maximum throughput
Most important point economically
Most active constraints
Step 2: Design the inventory (regulatory) control system
Step 3: Design loops for ‘taking up’ additional economic CV control at lower throughputs along with appropriate throughput manipulation strategy
Warning: May get complicated, but good economically because of tight control of active constraints

51. TPM for < max throughput
Figure 5. Plantwide control structure for maximum throughput operation of recycle process (Case Study I)
A + B  C
B + C  D
Stripper
Column
A, B Recycle B A C D FC PC LC TC X RC
CCD
CCB
V1MAX
V2MAX
0.98%
0.02%
LVLRxrMAX
TPM for < max throughput
165 °C
xBRxr Opt
HS3
TRxrOpt
HS2
LS1
SP1
SP3
LC2
SP2
SP1 > SP2 > SP3
LC1
LC3
LS2
TRxrMAX