Inventory Control Structure and Throughput Manipulator Location

1. Wed AM Part 3: Regulatory («stabilizing») control Inventory (level) controlstructure • Location ofthroughput manipulator • Consistency and radiatingrule Structureofregulatorycontrollayer (PID) • Selectionofcontrolled variables (CV2) and pairingwithmanipulated variables (MV2) • Main rule: Control drifting variables and "pair close" Summary: Sigurd’srules for plantwidecontrol

2. 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

3. 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

4. TPM (Throughput manipulator) • Definition 1. TPM = MV used to control throughput (CV) • 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 • Reactor temperature can be a TPM, because it changes the reactor conversion, • Pressure of gas product can be a TPM, because it changes the gas product flowrate • Fuel cell: Load (current I) is usually the TPM • 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

5. 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)

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

7. Production rate set at outlet:Inventory control opposite flow* TPM * Required to get “local-consistent” inventory control

8. Production rate set inside process* TPM * Required to get “local-consistent” inventory control

9. General: “Need radiating inventory control around TPM” (Georgakis)

10. Consistency of inventory control Consistency (required property): An inventory control system is said to be consistentif 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.

11. QUIZ 1 CONSISTENT?

12. 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

13. QUIZ 1 CONSISTENT?

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

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

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

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

18. 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: Separator controlAlternative TPM locations Compressor could be replaced by valve if p1>pG

20. Alt.2 Alt.1 Alt.4 Alt.3 Similar to original but NOT CONSISTENT (PC not direction of flow)

21. Example: Solid oxide fuel cell xH2?? xCH4,s CC PC CH4 CH4 + H2O = CO + 3H2 CO + H2O = CO2 + H2 2H2 + O2- → 2H2O + 2e- H2O (in ratio with CH4 feed to reduce C and CO formation) e- TPM = current I [A] = disturbance O2- Solid oxide electrolyte O2 + 4e- → 2O2- Air (excess O2) PC TC 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. 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”

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

25. DB-configuration OK??? TPM

26. DB-configuration: Level control NOT consistent by itself, but can still work* if we add one (or preferably two) composition/temperature loops cc TPM cc *But DB-configuration is notrecommended!

27. QUIZ * ** * Keep p ¸ pmin ** Keep valve fully open

29. QUIZ

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

31. 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.

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

33. 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)

34. First improvement: Located closer to bottleneck

35. 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”

36. 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”

37. 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, NitinKaistha*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 activeconstraints 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

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

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

40. 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

41. Structure of regulatory control layer (PID) Structureofregulatorycontrollayer (PID) • Selectionofcontrolled variables (CV2) and pairingwithmanipulated variables (MV2) • Main rule: Control drifting variables and "pair close" Summary: Sigurd’srules for plantwidecontrol

42. Regulatory layer II. Bottom-up • Determine secondary controlled variables (CV2) and structure (configuration) of control system (pairing, CV2-MV2) • A good control configuration is insensitive to parameter changes

43. Regulatory layer CV1 CV2 = ? 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)

44. Regulatory layer Objectives regulatory control layer • 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” • “stabilization” (practical sense) • Allow for “slow” control in layer above (supervisory control) • Make control problem easy as seen from layer above • Use “easy” and “robust” measurements (pressure, temperature) • Simple structure • Contribute to overall economic objective (“indirect” control) • Should not need to be changed during operation

45. Regulatory layer Stabilizing control: Use inputs MV2=u2 to control “drifting” variables CV2 Primary CV CV1 CV2s K u2 G CV2 Secondary CV (control for dynamic reasons) Key decision: Choice of CV2 (controlled variable) Also important: Choice of MV2=u2 (“pairing”) • Processcontrol: Typical «drifting» variables (CV2) are • Liquid inventories (level) • Vaporinventories (pressure) • Sometemperatures (reactor, distillationcolumnprofile)

46. Regulatory layer CV1 CV2s K u2 G CV2 Original DOF New DOF 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:

47. Regulatory layer CV1s CV1=c CC CV2s CV2=T TC Example: Exothermic reactor (unstable) Active constraints (economics):Product composition c + level (max) • u = cooling flow (q) • CV1 = composition (c) • CV2 = temperature (T) feed Ls=max LC product u cooling

49. Optimizer (RTO) Optimally constant valves CV1s Always active constraints y1=CV1 Supervisory controller (MPC) CV2s y2=CV2 Regulatory controller (PID) H H2 Physical inputs (valves) d y PROCESS Stabilized process ny u1 u2 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)

50. Regulatory layer Details Step 5 (Structure regulatory control layer) (a) What to control (CV2)? • Control CV2 that “stabilizes the plant” (stops drifting) • 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.* *Comment: usually not necessary with tight control of unconstrained CVs because optimum is usually relatively flat