1. 1 A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway Brazil, March 2010

2. 2 A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway NTU, Singapore / Petronas / Petrobras, March 2010

3. 3 Abstract Title: A systematic approach to plantwide control. Abstract: A chemical plant may have thousands of measurements and control loops. By the term plantwide control it is not meant the tuning and behavior of each of these loops, but rather the control philosophy of the overall plant with emphasis on the structural decisions. In practice, the control system is usually divided into several layers, separated by time scale: scheduling (weeks), site- wide optimization (day), local optimization (hour), supervisory (predictive, advanced) control (minutes) and regulatory control (seconds). Such a hiearchical (cascade) decomposition with layers operating on different time scale is used in the control of all real (complex) systems including biological systems and airplanes, so the issues in this section are not limited to process control. In the talk the most important issues are discussed, especially related to the choice of variables that provide the link the control layers.

4. 4 Trondheim, Norway Brasil

5. 5 Trondheim Oslo UK NORWAY DENMARK GERMANY North Sea SWEDEN Arctic circle

6. 6 NTNU, Trondheim

7. 7 Main references The following paper summarizes the procedure: –S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, 28 (1-2), 219-234 (2004). There are many approaches to plantwide control as discussed in the following review paper: –T. Larsson and S. Skogestad, ``Plantwide control: A review and a new design procedure'' Modeling, Identification and Control, 21, 209-240 (2000). Download papers: Google ”Skogestad”

8. 8 S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'', J. Proc. Control, 10, 487-507 (2000).``Plantwide control: the search for the self-optimizing control structure'', S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'', Comp.Chem.Engng., 24, 569- 575 (2000).``Self-optimizing control: the missing link between steady-state optimization and control'', I.J. Halvorsen, M. Serra and S. Skogestad, ``Evaluation of self-optimising control structures for an integrated Petlyuk distillation column'', Hung. J. of Ind.Chem., 28, 11-15 (2000).``Evaluation of self-optimising control structures for an integrated Petlyuk distillation column'', T. Larsson, K. Hestetun, E. Hovland, and S. Skogestad, ``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process'', Ind. Eng. Chem. Res., 40 (22), 4889-4901 (2001).``Self-Optimizing Control of a Large-Scale Plant: The Tennessee Eastman Process'', K.L. Wu, C.C. Yu, W.L. Luyben and S. Skogestad, ``Reactor/separator processes with recycles-2. Design for composition control'', Comp. Chem. Engng., 27 (3), 401-421 (2003).``Reactor/separator processes with recycles-2. Design for composition control'', T. Larsson, M.S. Govatsmark, S. Skogestad, and C.C. Yu, ``Control structure selection for reactor, separator and recycle processes'', Ind. Eng. Chem. Res., 42 (6), 1225-1234 (2003).``Control structure selection for reactor, separator and recycle processes'', A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), 2198-2208 (2003).``Buffer Tank Design for Acceptable Control Performance'', I.J. Halvorsen, S. Skogestad, J.C. Morud and V. Alstad, ``Optimal selection of controlled variables'', Ind. Eng. Chem. Res., 42 (14), 3273-3284 (2003).``Optimal selection of controlled variables'', A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8), 1475-1487 (2004).``pH-neutralization: integrated process and control design'', S. Skogestad, ``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'', Computers and Chemical Engineering, 29 (1), 127-137 (2004).``Near-optimal operation by self-optimizing control: From process control to marathon running and business systems'', E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), 863-867 (2005).``Perfect steady-state indirect control'', M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), 2207-2217 (2005).``Selection of controlled variables and robust setpoints'', V. Alstad and S. Skogestad, ``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'', Ind.Eng.Chem.Res, 46 (3), 846-853 (2007).``Null Space Method for Selecting Optimal Measurement Combinations as Controlled Variables'', S. Skogestad, ``The dos and don'ts of distillation columns control'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A1), 13-23 (2007).``The dos and don'ts of distillation columns control'', E.S. Hori and S. Skogestad, ``Selection of control structure and temperature location for two-product distillation columns'', Chemical Engineering Research and Design (Trans IChemE, Part A), 85 (A3), 293-306 (2007).``Selection of control structure and temperature location for two-product distillation columns'', A.C.B. Araujo, M. Govatsmark and S. Skogestad, ``Application of plantwide control to the HDA process. I Steady-state and self- optimizing control'', Control Engineering Practice, 15, 1222-1237 (2007).``Application of plantwide control to the HDA process. I Steady-state and self- optimizing control'', A.C.B. Araujo, E.S. Hori and S. Skogestad, ``Application of plantwide control to the HDA process. Part II Regulatory control'', Ind.Eng.Chem.Res, 46 (15), 5159-5174 (2007).``Application of plantwide control to the HDA process. Part II Regulatory control'', V. Kariwala, S. Skogestad and J.F. Forbes, ``Reply to ``Further Theoretical results on Relative Gain Array for Norn-Bounded Uncertain systems'''' Ind.Eng.Chem.Res, 46 (24), 8290 (2007).``Reply to ``Further Theoretical results on Relative Gain Array for Norn-Bounded Uncertain systems'''' V. Lersbamrungsuk, T. Srinophakun, S. Narasimhan and S. Skogestad, ``Control structure design for optimal operation of heat exchanger networks'', AIChE J., 54 (1), 150-162 (2008). DOI 10.1002/aic.11366``Control structure design for optimal operation of heat exchanger networks'', T. Lid and S. Skogestad, ``Scaled steady state models for effective on-line applications'', Computers and Chemical Engineering, 32, 990-999 (2008). T. Lid and S. Skogestad, ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', Journal of Process Control, 18, 320-331 (2008).``Scaled steady state models for effective on-line applications'', ``Data reconciliation and optimal operation of a catalytic naphtha reformer'', E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, 195-204 (2008).``Coordinator MPC for maximizing plant throughput'', A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32 (12), 2920-2932 (2008).``Control structure design for the ammonia synthesis process'', E.S. Hori and S. Skogestad, ``Selection of controlled variables: Maximum gain rule and combination of measurements'', Ind.Eng.Chem.Res, 47 (23), 9465-9471 (2008).``Selection of controlled variables: Maximum gain rule and combination of measurements'', V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, 138-148 (2009)``Optimal measurement combinations as controlled variables'', E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009).``Consistent inventory control'',

9. 9 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down (main new part) Step 1: Identify degrees of freedom Step 2: Identify operational objectives (optimal operation) Step 3: What to control ? (primary CV’s) (self-optimizing control) Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory control: What more to control? (secondary CV’s) Step 6: Supervisory control Step 7: Real-time optimization Case studies

10. 10 How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc.

11. 11 Idealized view of control (“Ph.D. control”)

12. 12 Practice: Tennessee Eastman challenge problem (Downs, 1991) (“PID control”)

13. 13 Alan Foss (“Critique of chemical process control theory”, AIChE Journal,1973): The central issue to be resolved... is the determination of control system structure. Which variables should be measured, which inputs should be manipulated and which links should be made between the two sets? There is more than a suspicion that the work of a genius is needed here, for without it the control configuration problem will likely remain in a primitive, hazily stated and wholly unmanageable form. The gap is present indeed, but contrary to the views of many, it is the theoretician who must close it. Carl Nett (1989): Minimize control system complexity subject to the achievement of accuracy specifications in the face of uncertainty.

14. 14 Control structure design Not the tuning and behavior of each control loop, But rather the control philosophy of the overall plant with emphasis on the structural decisions: –Selection of controlled variables (“outputs”) –Selection of manipulated variables (“inputs”) –Selection of (extra) measurements –Selection of control configuration (structure of overall controller that interconnects the controlled, manipulated and measured variables) –Selection of controller type (LQG, H-infinity, PID, decoupler, MPC etc.). That is: Control structure design includes all the decisions we need make to get from ``PID control’’ to “Ph.D” control

15. 15 Process control: “Plantwide control” = “Control structure design for complete chemical plant” Large systems Each plant usually different – modeling expensive Slow processes – no problem with computation time Structural issues important –What to control? Extra measurements, Pairing of loops Previous work on plantwide control: Page Buckley (1964) - Chapter on “Overall process control” (still industrial practice) Greg Shinskey (1967) – process control systems Alan Foss (1973) - control system structure Bill Luyben et al. (1975- ) – case studies ; “snowball effect” George Stephanopoulos and Manfred Morari (1980) – synthesis of control structures for chemical processes Ruel Shinnar (1981- ) - “dominant variables” Jim Downs (1991) - Tennessee Eastman challenge problem Larsson and Skogestad (2000): Review of plantwide control

16. 16 Control structure selection issues are identified as important also in other industries. Professor Gary Balas (Minnesota) at ECC’03 about flight control at Boeing: The most important control issue has always been to select the right controlled variables --- no systematic tools used!

17. 17 Main objectives control system 1.Stabilization 2.Implementation of acceptable (near-optimal) operation ARE THESE OBJECTIVES CONFLICTING? Usually NOT –Different time scales Stabilization fast time scale –Stabilization doesn’t “use up” any degrees of freedom Reference value (setpoint) available for layer above But it “uses up” part of the time window (frequency range)

18. 18 c s = y 1s MPC PID y 2s RTO u (valves) Follow path (+ look after other variables) CV=y 1 (+ u) ; MV=y 2s Stabilize + avoid drift CV=y 2 ; MV=u Min J (economics); MV=y 1s OBJECTIVE Dealing with complexity Main simplification: Hierarchical decomposition Process control The controlled variables (CVs) interconnect the layers

19. 19 Example: Bicycle riding Note: design starts from the bottom Regulatory control: –First need to learn to stabilize the bicycle CV = y 2 = tilt of bike MV = body position Supervisory control: –Then need to follow the road. CV = y 1 = distance from right hand side MV=y 2s –Usually a constant setpoint policy is OK, e.g. y 1s =0.5 m Optimization: –Which road should you follow? –Temporary (discrete) changes in y 1s Hierarchical decomposition

20. 20 Summary: The three layers Optimization layer (RTO; steady-state nonlinear model): Identifies active constraints and computes optimal setpoints for primary controlled variables (y 1 ). Supervisory control (MPC; linear model with constraints): Follow setpoints for y 1 (usually constant) by adjusting setpoints for secondary variables (MV=y 2s ) Look after other variables (e.g., avoid saturation for MV’s used in regulatory layer) Regulatory control (PID): Stabilizes the plant and avoids drift, in addition to following setpoints for y 2. MV=valves (u). Problem definition and overall control objectives (y 1, y 2 ) starts from the top. Design starts from the bottom. A good example is bicycle riding: Regulatory control: First you need to learn how to stabilize the bicycle (y 2 ) Supervisory control: Then you need to follow the road. Usually a constant setpoint policy is OK, for example, stay y 1s =0.5 m from the right hand side of the road (in this case the "magic" self-optimizing variable self-optimizing variable is y1=distance to right hand side of road)self-optimizing variable Optimization: Which road (route) should you follow?

21. 21 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down (main new part) Step 1: Identify degrees of freedom Step 2: Identify operational objectives (cost function and constraints) Step 3: What to control ? (primary CV’s) –Active constraints –Self-optimizing variables Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory control strategy: What more to control? (secondary CV’s) Step 6: Supervisory control strategy: Decentralized or multivariable? Step 7: Real-time optimization: Do we need it? Case studies

22. 22 Step 1. Degrees of freedom (DOFs) for operation To find all operational (dynamic) degrees of freedom: Count valves! (N valves ) “Valves” also includes adjustable compressor power, etc. Anything we can manipulate!

23. 23 Steady-state degrees of freedom (DOFs) IMPORTANT! DETERMINES THE NUMBER OF VARIABLES TO CONTROL! No. of primary CVs = No. of steady-state DOFs CV = controlled variable (c) N ss = N valves – N 0ss – N specs N 0ss = variables with no steady-state effect

24. 24 N valves = 6, N 0y = 2, N specs = 2, N DOF,SS = 6 -2 -2 = 2 Distillation column with given feed and pressure N 0y : no. controlled variables (liquid levels) with no steady-state effect NEED TO IDENTIFY 2 CV’s - Typical: Top and btm composition 1 2 3 4 5 6

25. 25 Heat-integrated distillation process

26. 26 Heat-integrated distillation process

27. 27 Step 2. Define optimal operation (economics) What are we going to use our degrees of freedom u (MVs) for? Define scalar cost function J(u,x,d) –u: degrees of freedom (usually steady-state) –d: disturbances –x: states (internal variables) Typical cost function: Optimize operation with respect to u for given d (usually steady-state): min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 J = cost feed + cost energy – value products

28. 28 Optimal operation distillation column Distillation at steady state with given p and F: N=2 DOFs, e.g. L and V 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: min · D, B, L etc. · max Column capacity (flooding): V · V max, etc. Pressure: 1) p given, 2) p free: p min · p · p max Feed: 1) F given 2) F free: F · F max Optimal operation: Minimize J with respect to steady-state DOFs value products cost energy (heating+ cooling) cost feed

29. 29 Optimal operation 1.Given feed Amount of products is then usually indirectly given and J = cost energy. Optimal operation is then usually unconstrained: 2.Feed free Products usually much more valuable than feed + energy costs small. Optimal operation is then usually constrained: minimize J = cost feed + cost energy – value products “maximize efficiency (energy)” “maximize production” Two main cases (modes) depending on marked conditions: Control: Operate at bottleneck (“obvious what to control”) Control: Operate at optimal trade-off (not obvious what to control to achieve this)

30. 30 Comments optimal operation Do not forget to include feedrate as a potential degree of freedom!! “Good times (good prices)”: Identify bottleneck –see later: “Where to set the production rate”

31. 31 Implementation of optimal operation Optimal operation for given d * : min u J(u,x,d) subject to: Model equations: f(u,x,d) = 0 Operational constraints: g(u,x,d) < 0 → u opt (d * ) Problem: Usally cannot keep u opt constant because disturbances d change How should we adjust the degrees of freedom (u)?

32. 32 Implementation (in practice): Local feedback control! “Self-optimizing control:” Constant setpoints for c gives acceptable loss y FeedforwardOptimizing controlLocal feedback: Control c (CV) d

33. 33 Remarks “self-optimizing control” Old idea (Morari et al., 1980): “We want to find a function c of the process variables which when held constant, leads automatically to the optimal adjustments of the manipulated variables, and with it, the optimal operating conditions.” “Self-optimizing control” = acceptable steady-state behavior (loss) with constant CVs. is similar to “Self-regulation” = acceptable dynamic behavior with constant MVs.

34. 34 Step 3. What should we control (c)? (primary controlled variables y 1 =c) Introductory example: Runner Issue: What should we control?

35. 35 –Cost to be minimized, J=T –One degree of freedom (u=power) –What should we control? Optimal operation - Runner Optimal operation of runner

36. 36 Sprinter (100m) 1. Optimal operation of Sprinter, J=T –Active constraint control: Maximum speed (”no thinking required”) Optimal operation - Runner

37. 37 2. Optimal operation of Marathon runner, J=T Unconstrained optimum! Any ”self-optimizing” variable c (to control at constant setpoint)? c 1 = distance to leader of race c 2 = speed c 3 = heart rate c 4 = level of lactate in muscles Optimal operation - Runner Marathon (40 km)

38. 38 Conclusion Marathon runner c = heart rate select one measurement Simple and robust implementation Disturbances are indirectly handled by keeping a constant heart rate May have infrequent adjustment of setpoint (heart rate) Optimal operation - Runner

39. 39 Example: Driving a car Two degrees of freedom 1.Gas pedal 2.Choice of gear Objective: Minimize time (J=T) Highway driving: What should we control? Obvious: 1.Active constraint: Speed limit 2.Active constraint: Highest gair

40. 40 Example: Driving a car Two degrees of freedom 1.Gas pedal 2.Choice of gear Objective: Minimize time (J=T) Windy road: What should we control? Not so obvious: 1.? Speed proportional to distance to turn? 2. Constant engine speed (”self- optimizing”)

41. 41 Step 3. What should we control (c)? (primary controlled variables y 1 =c) 1.Control active constraints! 2.Unconstrained variables: Look for “magic” self-optimizing variables! Issue: What should we control?

42. 42 1. CONTROL ACTIVE CONSTRAINTS!

43. 43 Active constraints can vary! Example: Optimal operation distillation Cost to be minimized J = - P where P= p D D + p B B – p F F – p V V 2 Steady-state DOFs (must find 2 CVs) Product purity constraints distillation: –Purity spec. valuable product (y1): Always active “avoid give-away of valuable product”. –Purity spec. “cheap” product (y2): May not be active may want to overpurify to avoid loss of valuable product Many possibilities for active constraint sets (may vary from day to day!) 1.Two active purity constraints (CV1 = y1 & CV2=y2) Happens when energy is relatively expensive 2.One active purity constraint. CV1 = y1 Energy quite cheap: Unconstrained. Overpurify cheap product. CV2=? (self-optimizing, e.g. y2) Energy really cheap: Overpurify until reach MAX load (active input constraint) CV2= max input (max. energy)

44. 44 a)If constraint can be violated dynamically (only average matters) Required Back-off = “bias” (steady-state measurement error for c) b)If constraint cannot be violated dynamically (“hard constraint”) Required Back-off = “bias” + maximum dynamic control error J opt Back-off Loss c ≥ c constraint c J 1. CONTROL ACTIVE CONSTRAINTS! Active input constraints: Just set at MAX or MIN Active output constraints: Need back-off Want tight control of hard output constraints to reduce the back-off “Squeeze and shift”

45. 45 Example. Optimal operation = max. throughput. Want tight bottleneck control to reduce backoff! Time Back-off = Lost production Rule for control of hard output constraints: “Squeeze and shift”! Reduce variance (“Squeeze”) and “shift” setpoint c s to reduce backoff

46. 46 Hard Constraints: «SQUEEZE AND SHIFT» © Richalet SHIFT SQUEEZE

47. 47 2. UNCONSTRAINED VARIABLES: - WHAT MORE SHOULD WE CONTROL? - WHAT ARE GOOD “SELF-OPTIMIZING” VARIABLES? Intuition: “Dominant variables” (Shinnar) Is there any systematic procedure? A. Sensitive variables: “Max. gain rule” (Gain= Minimum singular value) B. “Brute force” loss evaluation C. Optimal linear combination of measurements, c = Hy

48. 48 Optimal operation Cost J Controlled variable c c opt J opt Unconstrained optimum

49. 49 Optimal operation Cost J Controlled variable c c opt J opt Two problems: 1. Optimum moves because of disturbances d: c opt (d) 2. Implementation error, c = c opt + n d n Unconstrained optimum

50. 50 Candidate controlled variables c for self-optimizing control Intuitive 1.The optimal value of c should be insensitive to disturbances (avoid problem 1) 2.Optimum should be flat (avoid problem 2 – implementation error). Equivalently: Value of c should be sensitive to degrees of freedom u. “Want large gain”, |G| Or more generally: Maximize minimum singular value, Unconstrained optimum BADGood

51. 51 EXAMPLE: Recycle plant (Luyben, Yu, etc.) 1 2 3 4 5 Given feedrate F 0 and column pressure: Dynamic DOFs: N m = 5 Column levels: N 0y = 2 Steady-state DOFs:N 0 = 5 - 2 = 3 Feed of A Recycle of unreacted A (+ some B) Product (98.5% B)

52. 52 Recycle plant: Optimal operation mTmT 1 remaining unconstrained degree of freedom

53. 53 Control of recycle plant: Conventional structure (“Two-point”: x D ) LC XC LC XC LC xBxB xDxD Control active constraints (M r =max and x B =0.015) + x D

54. 54 Luyben rule Luyben rule (to avoid snowballing): “Fix a stream in the recycle loop” (F or D)

55. 55 Luyben rule: D constant Luyben rule (to avoid snowballing): “Fix a stream in the recycle loop” (F or D) LC XC

56. 56 A. Maximum gain rule: Steady-state gain Luyben rule: Not promising economically Conventional: Looks good

57. 57 How did we find the gains in the Table? 1.Find nominal optimum 2.Find (unscaled) gain G 0 from input to candidate outputs:  c = G 0  u. In this case only a single unconstrained input (DOF). Choose at u=L Obtain gain G 0 numerically by making a small perturbation in u=L while adjusting the other inputs such that the active constraints are constant (bottom composition fixed in this case) 3.Find the span for each candidate variable For each disturbance d i make a typical change and reoptimize to obtain the optimal ranges  c opt (d i ) For each candidate output obtain (estimate) the control error (noise) n The expected variation for c is then: span(c) =  i |  c opt (d i )| + |n| 4.Obtain the scaled gain, G = |G 0 | / span(c) 5.Note: The absolute value (the vector 1-norm) is used here to "sum up" and get the overall span. Alternatively, the 2-norm could be used, which could be viewed as putting less emphasis on the worst case. As an example, assume that the only contribution to the span is the implementation/measurement error, and that the variable we are controlling (c) is the average of 5 measurements of the same y, i.e. c=sum yi/5, and that each yi has a measurement error of 1, i.e. nyi=1. Then with the absolute value (1-norm), the contribution to the span from the implementation (meas.) error is span=sum abs(nyi)/5 = 5*1/5=1, whereas with the two-norn, span = sqrt(5*(1/5^2) = 0.447. The latter is more reasonable since we expect that the overall measurement error is reduced when taking the average of many measurements. In any case, the choice of norm is an engineering decision so there is not really one that is "right" and one that is "wrong". We often use the 2-norm for mathematical convenience, but there are also physical justifications (as just given!). IMPORTANT!

58. 58 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down Step 1: Degrees of freedom Step 2: Operational objectives (optimal operation) Step 3: What to control ? (self-optimzing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

59. 59 Step 4. Where set production rate? Very important! Determines structure of remaining inventory (level) control system Set production rate at (dynamic) bottleneck Link between Top-down and Bottom-up parts

60. 60 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 each unit the local inventory control loops by themselves are sufficient to achieve steady-state mass balance consistency for that unit.

61. 61 Local-consistency rule (also called self-consistency) 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

62. 62 CONSISTENT?

63. 63 Production rate set at inlet : Inventory control in direction of flow* * Required to get “local-consistent” inventory control

64. 64 Production rate set at outlet: Inventory control opposite flow

65. 65 Production rate set inside process

66. 66 QUIZ. Consistent? Local-consistent? Note: Local-consistent is more strict as it implies consistent

67. 67 Closed system: Must leave one inventory uncontrolled

68. 68 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

69. 69 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.

70. 70 Reactor-recycle process: Want to maximize feedrate: reach bottleneck in column Bottleneck: max. vapor rate in column

71. 71 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

72. 72 MAX Reactor-recycle process with max. feedrate: Alt. 2 Optimal: Set production rate at bottleneck (MAX) Feedrate used for lost task (xb) Get “long loop”: May need back-off in xB instead… Bottleneck: max. vapor rate in column

73. 73 Reactor-recycle process with max. feedrate: Alt. 3: Optimal: Set production rate at bottleneck (MAX) Reconfigure upstream loops MAX OK, but reconfiguration undesirable…

74. 74 Reactor-recycle process: Alt.3: reconfigure (permanently) F 0s For cases with given feedrate: Get “long loop” but no associated loss

75. 75 Conclusion production rate manipulator Think carefully about where to place it! Difficult to undo later One approach: Put MPC 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).

76. 76 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down Step 1: Degrees of freedom Step 2: Operational objectives (optimal operation) Step 3: What to control ? (self-optimizing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

77. 77 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 issues: What more should we control? y 2 =? (secondary cv’s, y 2, use of extra measurements) Pairing with manipulated variables (mv’s u 2 ) y 1 = c y 2 = ?

78. 78 Example: Distillation Primary controlled variable: y 1 = c = x D, x B (compositions top, bottom) BUT: Delay in measurement of x + unreliable Regulatory control: For “stabilization” need control of (y 2 ): –Liquid level condenser (M D ) –Liquid level reboiler (M B ) –Pressure (p) –Holdup of light component in column (temperature profile) Unstable (Integrating) + No steady-state effect Variations in p disturb other loops Almost unstable (integrating) TC TsTs T-loop in bottom

79. 79 XCXC TC FC ysys y LsLs TsTs L T z XCXC Cascade control distillation With flow loop + T-loop in top

80. 80 Note Cascade/Hierarchical control: Number of 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

81. 81 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

82. 82 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 Implications for selection of y 2 : 1.Control of y 2 “stabilizes the plant” 2.y 2 is easy to control (favorable dynamics)

83. 83 Selection of extra measuments: 1. “Control of y 2 stabilizes the plant” 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 ). B. “Practical extended stabilization” (avoid “drift” due to disturbance sensitivity): Intuitive: y 2 located close to important disturbance Maximum gain rule (again!): Avoid drift by controlling a “sensitive” y 2 (large gain from u to y2)

84. 84 2. “y 2 is easy to control” (controllability) 1.Statics: Want large gain (from u 2 to y 2 ) 2.Main rule: y 2 is easy to measure and located close to available manipulated variable u 2 (“pairing”) 3.Dynamics: Want small effective delay (from u 2 to y 2 ) “effective delay” includes inverse response (RHP-zeros) + high-order lags

85. 85 3. Rules for selecting u 2 (to be paired with y 2 ) 1.Avoid using variable u 2 that may saturate (especially in loops at the bottom of the control hieararchy) Alternatively: Need to use “input resetting” in higher layer (“mid- ranging”) Example: Stabilize reactor with bypass flow (e.g. if bypass may saturate, then reset in higher layer using cooling flow) 2.“Pair close”: The controllability, for example in terms a small effective delay from u 2 to y 2, should be good.

86. 86 Summary: Rules for selecting y 2 (and u 2 ) Selection of y 2 1.Control of y 2 “stabilizes” the plant 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 Should generally avoid failures, including saturation, in lower layers 2.“Pair close”! The effective delay from u 2 to y 2 should be small

87. 87 Use of extra inputs Two different cases 1.Have extra dynamic inputs (degrees of freedom) Cascade implementation: “Input resetting to ideal resting value” Example: Heat exchanger with extra bypass 2.Need several inputs to cover whole range (because primary input may saturate) (steady-state) Split-range control Example 1: Control of room temperature using AC (summer), heater (winter), fireplace (winter cold) Example 2: Pressure control using purge and inert feed (distillation)

88. 88 qBqB T hot TC Example HEX: Use both inputs (with input resetting of dynamic input) closed FC q Bs TC: Gives fast control of T hot using the “dynamic” input q B FC: Resets q B to its setpoint (IRV) (e.g. 5%) using the “primary” input CW IRV = ideal resting value

89. 89 Too few inputs Must decide which output (CV) has the highest priority –Selectors

90. 90 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down Step 1: Degrees of freedom Step 2: Operational objectives (optimal operation) Step 3: What to control ? (primary CV’s) (self-optimizing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control (secondary CV’s) ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

91. 91 Step 6. Supervisory control layer Purpose: Keep primary controlled outputs c=y 1 at optimal setpoints c s Degrees of freedom: Setpoints y 2s in reg.control layer Main structural issue: Decentralized or multivariable?

92. 92 Decentralized control (single-loop controllers) Use for: Noninteracting process and no change in active constraints +Tuning may be done on-line +No or minimal model requirements +Easy to fix and change -Need to determine pairing -Performance loss compared to multivariable control - Complicated logic required for reconfiguration when active constraints move

93. 93 Multivariable control (with explicit constraint handling = MPC) Use for: Interacting process and changes in active constraints +Easy handling of feedforward control +Easy handling of changing constraints no need for logic smooth transition -Requires multivariable dynamic model -Tuning may be difficult -Less transparent -“Everything goes down at the same time”

94. 94 Outline Control structure design (plantwide control) A procedure for control structure design I Top Down Step 1: Degrees of freedom Step 2: Operational objectives (optimal operation) Step 3: What to control ? (self-optimizing control) Step 4: Where set production rate? II Bottom Up Step 5: Regulatory control: What more to control ? Step 6: Supervisory control Step 7: Real-time optimization Case studies

95. 95 Step 7. Optimization layer (RTO) Purpose: Identify active constraints and compute optimal setpoints (to be implemented by supervisory control layer) Main structural issue: Do we need RTO? (or is process self- optimizing) RTO not needed when –Can “easily” identify change in active constraints (operating region) –For each operating region there exists self-optimizing variables

96. 96 Conclusion I: Focus on “what to control” 1. Control for economics (Top-down steady-state arguments) –Primary CVs, c = y 1 : Control active constraints For remaining unconstrained degrees of freedom: Look for “self-optimizing” variables 2. Control for stabilization (Bottom-up; regulatory PID control) –Secondary CVs, y 2 : Control “drifting” variables Identify pairings with MVs (u –Pair close and avoid MVs that saturate Both cases: Control “sensitive” variables (large gain)! cscs y 2s u MV = manipulated variable (u) CV = controlled variable (c)

97. 97 Conclusion II. Systematic procedure for plantwide control 1.Start “top-down” with economics: –Step 1: Identify degrees of freeedom –Step 2: Define operational objectives and optimize steady-state operation. –Step 3A: Identify active constraints = primary CVs c. Should controlled to maximize profit) –Step 3B: For remaining unconstrained degrees of freedom: Select CVs c based on self-optimizing control. –Step 4: Where to set the throughput (usually: feed) 2.Regulatory control I: Decide on how to move mass through the plant: Step 5A: Propose “local-consistent” inventory control structure (y 2 = levels,…). 3.Regulatory control II: “Bottom-up” stabilization of the plant Step 5B: Control variables to stop “drift” (y 2 = sensitive temperatures, pressures,....) –Pair variables to avoid interaction and saturation 4.Finally: make link between “top-down” and “bottom up”. Step 6: “Advanced control” system (MPC): CVs: Active constraints and self-optimizing economic variables + look after variables in layer below (e.g., avoid saturation) MVs: Setpoints to regulatory control layer. Coordinates within units and possibly between units cscs y 2s u