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) ? –Distillation example Step S6: Supervisory control Step S7: Real-time optimization

2. 2 II. Bottom-up Determine secondary controlled variables and structure (configuration) of control system (pairing) A good control configuration is insensitive to parameter changes

3. 3 Regulatory control layer Purpose: “Stabilize” the plant using a simple control configuration (usually: local SISO PID controllers + simple cascades) Enable manual operation (by operators) Step S5: Regulatory / stabilizing control (PID layer) (a) What more to control (CV2=y 2 ; local CVs)? (Decision 2) (b) Pairing of inputs u 2 and outputs y 2 (Decision 4) y 1 = c y 2 = ?

4. 4 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) Optimizer (RTO) PROCESS Supervisory controller (MPC) Regulatory controller (PID) H2H2 H y 1 =CV 1 CV 2s y nyny d Stabilized process CV 1s y 2 =CV 2 Physical inputs (valves) Optimally constant valves Always active constraints u2u2

5. 5 Objectives regulatory control layer 1.Allow for manual operation 2.Simple decentralized (local) PID controllers that can be tuned on-line 3.Take care of “fast” control 4.Track setpoint changes from the layer above 5.Local disturbance rejection 6.Stabilization (mathematical sense) 7.Avoid “drift” (due to disturbances) so system stays in “linear region” –“stabilization” (practical sense) 8.Allow for “slow” control in layer above (supervisory control) 9.Make control problem easy as seen from layer above

6. 6 Details Step 5 (Structure regulatory control layer) (a) What to control? 1.Control CV2s (y2) that “stabilizes the plant” (stops drifting) –Select y2 which is easy to control (favorable dynamics) –Favor reliable measurements y2 2. 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

7. 7 A. “Mathematical stabilization” (e.g. reactor): Unstable mode is “quickly” detected (state observability) in the measurement (y 2 ) and is easily affected (state controllability) by the input (u 2 ). Tool for selecting input/output: Pole vectors –y 2 : Want large element in output pole vector: Instability easily detected relative to noise –u 2 : Want large element in input pole vector: Small input usage required for stabilization B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity): Intuitive: y 2 located close to important disturbance Maximum gain rule: Controllable range for y 2 is large compared to sum of optimal variation and measurement+control error More exact tool: Partial control analysis “Control CV2s that “stabilizes the plant” (stops drifting)”

8. 8 Recall maximum gain rule for selecting primary (economic) controlled variables c Control variables y 2 for which their controllable range is large compared to their sum of optimal variation and control error controllable range = range y 2 may reach by varying the inputs optimal variation: due to disturbances control error = implementation error n Restated for secondary controlled variables y 2 : Want small Want large

9. 9 “Control CV2s 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., amount of amine/water (deplete) in recycle loop in CO2 capture plant E.g., amount of butanol (accumulates) in methanol-water distillation column E.g., amount of 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

10. 10 2. “y 2 is easy to control” (controllability) 1.Steady state: Want large gain (from u 2 to y 2 ) 2.Dynamics: Want small effective delay (from u 2 to y 2 ) “effective delay” includes inverse response (RHP-zeros) + high-order lags Main rule: y 2 is easy to measure and located close to available manipulated variable u 2 (“pairing”)

11. 11 What should we control (y2)? Avoid closing too many loops because it increases complexity

12. 12 ( b) Identify pairings = Identify MVs (u2) to be used to control CV2, taking into account Want “local consistency” for the inventory control –Implies radiating inventory control around given flow Avoid selecting as MVs in the regulatory layer (u2), 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) Avoid variables u 2 where (frequent) changes are undesirable, for example, because they disturb other parts of the process. Want tight control of important active constraints (to avoid back-off) General rule: ”pair close” (see next slide) Comments: 1.Preferably, the regulatory layer should be independent of the economics (operating regions of active constraints) - without the need to reassigning loops depending on disturbances, price changes, etc. 2.The total number of theoretical pairing options is very large, but in practice, by following the above rules, the number is usually quite small (in some cases, there may be no feasible solution, so, for example, the radiating rule must be broken) Details Step 5b….

13. 13 Step 5b…. Further Rules for pairing of variables Main rule: “Pair close” 1.The response (from input to output) should be fast, large and in one direction. Avoid dead time and inverse responses! 2.The input (MV) should preferably effect only one output (to avoid interaction between the loops) 3.Try to avoid input saturation (valve fully open or closed) in “basic” control loops for level and pressure 4.The measurement of the output y should be fast and accurate. It should be located close to the input (MV) and to important disturbances. Use extra measurements y’ and cascade control if this is not satisfied 5.The system should be simple Avoid too many feedforward and cascade loops 6.“Obvious” loops (for example, for level and pressure) should be closed first before you spend to much time on deriving process models, RGA-analysis, etc.

14. 14 Why simplified configurations? Why control layers? Why not one “big” multivariable controller? Fundamental: Save on modelling effort Other: –easy to understand –easy to tune and retune –insensitive to model uncertainty –possible to design for failure tolerance –fewer links –reduced computation load

15. 15 Closing inner loops (cascade control): Use of (extra) measurements (y 2 ) as (extra) CVs GK y 2s u2u2 y2y2 y1y1 Key decision: Choice of y 2 (controlled variable) Also important: Choice of u 2 (“pairing”) Primary CV Secondary CV (control for dynamic reasons)

16. 16 Degrees of freedom unchanged No degrees of freedom lost by control of secondary (local) variables as setpoints become y 2s replace inputs u 2 as new degrees of freedom GK y 2s u2u2 y2y2 y1y1 Original DOF New DOF Cascade control:

17. 17 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 y 2 ) is not much influenced by the presence of the upper (slow) layers (involving y 1 ) 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

18. 18 XCXC TC FC ysys y LsLs TsTs L T z XCXC Cascade control distillation With flow loop + T-loop in top

19. 19 Summary step 5: Rules for selecting y 2 (and u 2 ) Selection of y 2 1.Control of y 2 “stabilizes” the plant Control variables that “drift” The (scaled) gain for y 2 should be large 2.Measurement of y 2 should be simple and reliable For example, temperature or pressure 3.y 2 should have good controllability small effective delay favorable dynamics for control y 2 should be located “close” to a manipulated input (u 2 ) Selection of u 2 (to be paired with y 2 ): 1.Avoid using inputs u 2 that may saturate (at steady state) When u 2 saturates we loose control of the associated y 2. 2.Avoid variables u 2 where (frequent) changes are undesirable For example, they may disturb other parts of the process. 3.The effective delay from u 2 to y 2 should be small (“pair close”!)

20. 20 QUIZ: What are the benefits of adding a flow controller (inner cascade)? q z qsqs 1.Counteracts nonlinearity in valve, f(z) With fast flow control we can assume q = q s 2.Eliminates effect of disturbances in p1 and p2 Extra measurement y 2 = q

21. 21 Example regulatory control: Distillation Assume given feed 5 dynamic DOFs (L,V,D,B,V T ) Overall objective: Control compositions (x D and x B ) “Obvious” stabilizing loops: 1.Condenser level (M 1 ) 2.Reboiler level (M 2 ) 3.Pressure E.A. Wolff and S. Skogestad, ``Temperature cascade control of distillation columns'', Ind.Eng.Chem.Res., 35, 475-484, 1996.

22. 22 The dos and don’ts of distillation column control Sigurd Skogestad Norwegian University of Science and Technology – NTNU N-7491 Trondheim, Norway From: Plenary lecture Distillation’06, London, 05 Sep 2006 Will mainly consider (indirect) composition control

23. 23 Studied in hundreds of research and industrial papers over the last 60 years

24. 24 Issues distillation control The “configuration” problem (level and pressure control) –Which are the two remaining degrees of freedom? e.g. LV-, DV-, DB- and L/D V/B- configurations The temperature control problem –Which temperature (if any) should be controlled? Composition control problem –Control two, one or no compositions? TC TsTs L V

25. 25 Objectives of this work Apply general plantwide control procedure (Skogestad, 2004) to distillation From this derive (if possible) simple recommendations for distillation control Is the latter possible? Luyben (2006) has his doubts: –“ There are many different types of distillation columns and many different types of control structures. The selection of the ``best'' control structure is not as simple as some papers* claim. Factors that influence the selection include volatilities, product purities, reflux ratio, column pressure, cost of energy, column size and composition of the feed ” + prices products * He may be referring to my work...

26. 26 2. General procedure plantwide control y 1s y 2s Control of primary variables: compositions (MPC) “Stabilizing” control: p, levels, T (PID) Step I. “Top-down” steady-state approach to identify primary controlled variables (y 1 ) –Active constraints –Self-optimizing control Step II. Bottom-up identification of regulatory (“stabilizing”) control layer. –Identify secondary controlled variables (y 2 )

27. 27 Cost to be minimized (economics) J = - P where P= p D D + p B B – p F F – p V V Constraints Purity D: For example x D, impurity · max Purity B: For example, x B, impurity · max Flow constraints: 0 · D, B, L etc. · max Column capacity (flooding): V · V max, etc. value products cost energy (heating+ cooling) cost feed 3. Primary controlled variables distillation (y 1 ) Selection of primary CVs (y 1 )

28. 28 Expected active constraints distillation Valueable product: Purity spec. always active –Reason: Amount of valuable product (D or B) should always be maximized 1.Avoid product “give-away” (“Sell water as methanol”) 2.Also saves energy Control implications: ALWAYS Control valueable purity at spec. valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% methanol + water Selection of primary CVs (y 1 )

29. 29 Cheap product Over-fractionate cheap product? Trade-off: –Yes, increased recovery of valuable product (less loss) –No, costs energy Control implications cheap product: 1.Energy expensive: Purity spec. active → Control purity at spec. 2.Energy “cheap”: Overpurify (a)Unconstrained optimum given by trade-off between energy and recovery. In this case it is likely that composition is self-optimizing variable → Possibly control purity at optimum value (overpurify) (b) Constrained optimum given by column reaching capacity constraint → Control active capacity constraint (e.g. V=V max ) –Methanol + water example: Since methanol loss anyhow is low (0.1% of water), there is not much to gain by overpurifying. Nevertheless, with energy very cheap, it is probably optimal to operate at V=V max. valuable product methanol + max. 0.5% water cheap product (byproduct) water + max. 0.1% methanol + water Selection of primary CVs (y 1 )

30. 30 Conclusion primary controlled variables Product purities are very often the primary controlled variables (y 1 ) for distillation columns Assume in the following “two-point” composition control: y 1 = x D, x B (impurity key component) Selection of primary CVs (y 1 )

31. 31 4. Stabilizing control distillation Secondary controlled variables (y 2 ) 5 dynamic degrees of freedom with given feed: L, V, D, B, V T To “stabilize”: Control levels and pressure: y 2 = M D, M B, p Choice of input u 2 (to be paired with y 2 ): –V T is usually used to control p –Levels (M D and M B ): Many possible configurations Additional y 2 : Temperature is usually controlled to “stabilize” composition profile:

32. 32 5. Control “configurations” (pairing u 2 -y 2 for level control) “XY-configuration” X: remaining input in top after controlling top level (M D ): X= L (reflux), D, L/D,… Y: remaining input in bottom after controlling M B : Y = V (boilup, energy input), B, V/B,... Configurations

33. 33 Top of Column “Standard” : LY-configuration (“energy balance”) LC LSLS VTVT L+D D L “Reversed”: DY-configuration (“material balance”) LC L VTVT D DSDS cooling Set manually or from upper-layer controller (temperature or composition) Set manually or from upper-layer controller Configurations

34. 34 L VTVT D LC x D (L/D) s Set manually or from upper-layer controller Similar in bottom... XV, XB, X V/B LsLs Top of Column Configurations

35. 35 LV-configuration (most common) “LV-configuration”: D and B for levels (“local consistent”) L and V remain as degrees of freedom after level loops are closed Other possibilities: DB, L/D V/B, etc….

36. 36 How do the configurations differ? 1.Level control by itself (emphasized by Buckley et al., 1985) 2.Interaction of level control with composition control Related to “local consistency” (Do not want inventory control to depend on composition loops being closed) 3.“Self-regulation” in terms of disturbance rejection (emphasized by Skogestad and Morari, 1987) 4.Remaining two-point composition control problem (steady-state RGA - emphasized by Shinskey, 1984) Has been a lot of discussion in the literature (Shinskey, Buckley, Skogestad, Luyben, etc.). Probably over-emphasized Configurations BUT: These comparisons are mostly without temperature control…..

37. 37 LIGHT HEAVY F D B TC To stabilize the column we must use feedback (feedforward will give drift) Simplest: “Profile feedback” using sensitive temperature Even with the level and pressure loops closed the column is practically unstable - either close to integrating or even truly unstable ( e.g. with mass reflux: Jacobsen and Skogestad, 1991) feedback using e.g. D,L,V or B BUT: To avoid strong sensitivity to disturbances: Temperature profile must also be “stabilized”

38. 38 Stabilizing the column profile Should close one “fast” loop (usually temperature) in order to “stabilize” the column profile –Makes column behave more linearly –Strongly reduces disturbance sensitivity –Keeps disturbances within column –Reduces the need for level control –Makes it possible to have good dual composition control P-control usually OK (no integral action) –Similar to control of liquid level

39. 39 Stabilizing the column profile Which fast loop should be closed (“pairing”)? –Which end? Close loop in end with “most important” product –Which output (temperature)? Choose “sensitive” stage –Which input (flow)? Want fast control ) “pair close” “Use same end” (reduces interactions for composition control): –Use V (or indirect by B) for temperature control in bottom section –Use L (or indirect by D) for temperature control in top section Dynamics –L: Some delay for liquid to go down the column –V: Vapor flow moves quickly up the column, but may take some time before it starts changing (heat transfer dynamics) In general, for stabilizing loops: Avoid using an input (flow) that can saturate –Do not use boilup (V) if column is close to max. capacity TC Top loop using L TCTSTS Top loop using L LV TC T s Btm. loop using V LV TC T s LV TC T s Btm. loop using V

40. 40 Bonus 1 of temp. control: Indirect level control TC Disturbance in V, q F : Detected by TC and counteracted by L -> Smaller changes in D required to keep M d constant!

41. 41 Bonus 2 of temp. control: Less interactive TC TsTs Setpoint T: New “handle” instead of L

42. 42 Less interactive: RGA with temperature loop closed

43. 43 Less interactive: Closed-loop response with decentralized PID-composition control Interactions much smaller with “stabilizing” temperature loop closed … and also disturbance sensitivity is expected smaller %

44. 44 Integral action in inner temperature loop has little effect %

45. 45 Note: No need to close two inner temperature loops % Would be even better with V/F

46. 46 Would be even better with V/F: TC x (V/F) s F V TsTs

47. 47 A “winner”: L/F-T-conguration Only caution: V should not saturate TC x TsTs (L/F) s

48. 48 Temperature control: Which stage? TC

49. 49 Which temperature? Rule: Maximize the scaled gain Scalar case. Minimum singular value = gain |G| Maximize scaled gain: |G| = |G 0 | / span –|G 0 |: gain from independent variable (u) to candidate controlled variable (c) –span (of c) = variation (of c) = optimal variation in c + control error for c

50. 50 Binary distillation: Unscaled steady-state gain G 0 = ΔT/ΔL for small change in L BTM  T /  L TOP

51. 51 Procedure scaling 1.Nominal simulation 2.Unscaled gains (“steady-state sensitivity”) –Make small change in input (L) with the other inputs (V) constant. Find gain =  T i /  L –Do the same for change in V 3.Obtain scalings (“optimal variation for various disturbances”) Find  T i,opt for the following disturbances 1.F (from 1 to 1.2)yoptf 2.z F from 0.5 to 0.6yoptz “Optimal” variation yopt to disturbances: Keep constant x D and x B by changing both L and V (disturbance in F has no effect in this case, so yoptf=0) 4.Control (implementation) error. Assume=0.5 K on all stages 5.Find scaled-gain = gain/span where span = abs(yoptf)+abs(yoptz)+0.5 “Maximize gain rule”: Prefer stage where scaled-gain is large

52. 52 Implementation error used, n = 0.5C BTMTOP Conclusion: Control in middle of section (not at column ends or around feed) Scalings not so important here Scaling 2: Not used

53. 53 8. Indirect composition control Which temperature to control? Evaluate relative steady-state composition deviation (”exact local method”): e c includes: - disturbances (F, z F, q F ) - implementation measurement error (0.5 for T)

54. 54 Have looked at 15 binary columns and 5 multicomponent (Hori, Skogestad, 2007) Main focus on “column A” –40 theoretical stages –Feed in middle –1% impurity in each product –Relative volatility: 1.5 –Boiling point difference: 10K

55. 55 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. BAD

56. 56 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. BEST

57. 57 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. Good

58. 58 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. Simple

59. 59 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. Simple

60. 60 Table: Binary mixture - Steady-state relative composition deviations ( )for binary column A Fixed variables T b,55% – T t,55% *0.530 T b,70% – L/F*0.916 T b,50% – L/F0.975 T b,75% - V/F*1.148 T b,90% – L*1.223 T b,70% – L/D*1.321 T b,50% – L1.386 T t,95% – V*1.470 L/D – V/B15.84 L/F – V/B18.59 L – B21.06 D – V21.22 L – V63.42 D – Binfeasible * Temperature optimally located ** Optimal temperature in opposite section. Bad Conclusion: Fix L and a temperature

61. 61 Composition deviation: 1- L/F and one temperature 2- V/F and one temperature 3- Two temperatures symmetrically located Avoid controlling temperature at column ends column A

62. 62 Rule 1. Avoid temperatures close to column ends (especially at end where impurity is small) Rule 2. Control temperature at important end (expensive product) Rule 3. To achieve indirect composition control: Control temperature where the steady-state sensitivity is large ( “ maximum gain rule ” ). Rule 4. For dynamic reasons, control temperature where the temperature change is large (avoid “ flat ” temperature profile). (Binary column: same as Rule 3) Rule 5. Use an input (flow) in the same end as the temperature sensor. Rule 6. Avoid using an input (flow) that may saturate. Which temperature should we control?

63. 63 Conclusion stabilizing control: Remaining supervisory control problem TC TsTs LsLs + may adjust setpoints for p, M 1 and M 2 (MPC) With V for T-control Would be even better with L/F

64. 64 Summary step 5: Rules for selecting y 2 (and u 2 ) Selection of y 2 1.Control of y 2 “stabilizes” the plant Control variables that “drift” The (scaled) gain for y 2 should be large 2.Measurement of y 2 should be simple and reliable For example, temperature or pressure 3.y 2 should have good controllability small effective delay favorable dynamics for control y 2 should be located “close” to a manipulated input (u 2 ) Selection of u 2 (to be paired with y 2 ): 1.Avoid using inputs u 2 that may saturate (at steady state) When u 2 saturates we loose control of the associated y 2. 2.Avoid variables u 2 where (frequent) changes are undesirable For example, they may disturb other parts of the process. 3.The effective delay from u 2 to y 2 should be small (“pair close”!)