1. 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) (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

2. 2 Step S4. Where set production rate? 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

3. 3 TPM (Throughput manipulator) 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. 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

4. 4 Example Reactor-recycle process: Given feedrate with production rate set at inlet TPM

5. 5 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

6. 6 Production rate set at inlet : Inventory control in direction of flow* * Required to get “local-consistent” inventory control TPM

7. 7 Production rate set at outlet: Inventory control opposite flow TPM

8. 8 Production rate set inside process TPM

9. 9 Summary: “Radiation rule “(Georgakis)

10. 10 CONSISTENT? QUIZ 1

11. 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 local requirement one gets the more general consistency rule

12. 12 CONSISTENT? QUIZ 1

13. 13 Dynamic simulation case (d)

14. 14 TPM

15. 15 Consistent? Local-consistent? Note: Local-consistent is more strict as it implies consistent QUIZ 2

16. 16 Closed system: Must leave one inventory uncontrolled QUIZ 3

17. 17 OK? (Where is production set? NO. Two TPMs (consider overall liquid balance). Solution: Interchange LC and FC on last tank QUIZ 4

18. 18 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

19. 19 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.

20. 20 Single-loop alternatives for bottleneck control Bottleneck. Want max flow here Alt.1. Feedrate controls bottleneck flow (“long loop”…): FC F max Alt. 2: Feedrate controls lost task (another “long loop”…): F max Alt. 3: Reconfigure all upstream inventory loops: F max Traditional: Manual control of feed rate TPM

21. 21 Possible improvements Alt. 1D: Feedrate controls bottleneck flow + “feedforward”: FC F max Alt. 2D: Feedrate controls lost task + “feedforward”: F max Alt. 4: MPC TPM

22. 22 Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column Bottleneck: max. vapor rate in column TPM Example

23. 23 Reactor-recycle process with max. feedrate Alt.1: Feedrate controls bottleneck flow Bottleneck: max. vapor rate in column FC V max V V max -V s =Back-off = Loss VsVs Get “long loop”: Need back-off in V TPM Example

24. 24 MAX Reactor-recycle process with max. feedrate: Alt. 2 Optimal: Move TPM to bottleneck (MAX) Feedrate used for lost task (xb) Get “long loop”: May need back-off in xB instead… Bottleneck: max. vapor rate in column TPM Example

25. 25 Reactor-recycle process with max. feedrate: Alt. 3: Optimal: Move TPM to bottleneck (MAX) Reconfigure upstream loops MAX OK, but reconfiguration undesirable… TPM Example

26. 26 Reactor-recycle process: Alt.3: Move TPM + reconfigure (permanently!) F 0s For cases with given feedrate: Get “long loop” but no associated loss TPM Example

27. 27 Reactor-recycle process with max. feedrate Alt.1D: Alt. 1 “Long loop” + “feedforward” Bottleneck: max. vapor rate in column FC VsVs Less back-off in V because F closer to V F/F 0 “Feedforward”: Send feed change to ALL flows upstream bottleneck TPM Example

28. 28 MAX “Feedforward”: Send flow change to ALL flows upstream bottleneck F/F 0 Less back-off in xB because F closer to xB Reactor-recycle process with max. feedrate Alt.2D: Alt. 2 “Long loop” + “feedforward” TPM Example

29. 29 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! Alt.4: Multivariable control (MPC) 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). Example

30. 30 Conclusion production rate manipulator Think carefully about where to place it! Difficult to undo later

31. 31 QUIZ. Distillation. OK? LV-configuration TPM

32. 32 DB-configuration OK???

33. 33

34. 34

35. 35 QUIZ Cases 7–13, 15-23 Will it work? Where is throughput set (TPM)?

36. 36 LOCATE TPM? 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 TPM- variable 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)