A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL

1. A SYSTEMATIC APPROACH TO PLANTWIDE CONTROL Sigurd Skogestad Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway NTU, TU Petronas, 09 March 2010

2. Abstract • The talks gives a systematic procedure for plantwide control. An important part is the selection of controlled variables based on self-optimizing control. These are the controlled variables for the "supervisory" control layer. In addition, we need a regulatory control system to stabilize the plant and avoid drift. • 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).

3. Trondheim, Norway Malaysia

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

5. NTNU, Trondheim

6. 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”

7. S. Skogestad ``Plantwide control: the search for the self-optimizing control structure'',J. Proc. Control, 10, 487-507 (2000). • S. Skogestad, ``Self-optimizing control: the missing link between steady-state optimization and control'',Comp.Chem.Engng., 24, 569-575 (2000). • 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). • 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). • 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). • 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). • A. Faanes and S. Skogestad, ``Buffer Tank Design for Acceptable Control Performance'', Ind. Eng. Chem. Res., 42 (10), 2198-2208 (2003). • 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). • A. Faanes and S. Skogestad, ``pH-neutralization: integrated process and control design'', Computers and Chemical Engineering, 28 (8), 1475-1487 (2004). • 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). • E.S. Hori, S. Skogestad and V. Alstad, ``Perfect steady-state indirect control'', Ind.Eng.Chem.Res, 44 (4), 863-867 (2005). • M.S. Govatsmark and S. Skogestad, ``Selection of controlled variables and robust setpoints'', Ind.Eng.Chem.Res, 44 (7), 2207-2217 (2005). • 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). • 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). • 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). • 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). • 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). • 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). • 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 • 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). • E.M.B. Aske, S. Strand and S. Skogestad, ``Coordinator MPC for maximizing plant throughput'', Computers and Chemical Engineering, 32, 195-204 (2008). • A. Araujo and S. Skogestad, ``Control structure design for the ammonia synthesis process'', Computers and Chemical Engineering, 32 (12), 2920-2932 (2008). • 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). • V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, 138-148 (2009) • E.M.B. Aske and S. Skogestad, ``Consistent inventory control'', Ind.Eng.Chem.Res, 48 (44), 10892-10902 (2009).

8. 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

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

10. 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.

11. 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

12. 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!

13. Dealing with complexity Main simplification: Hierarchical decomposition The controlled variables (CVs) interconnect the layers Process control OBJECTIVE Min J (economics); MV=y1s RTO cs = y1s Follow path (+ look after other variables) CV=y1 (+ u); MV=y2s MPC y2s Stabilize + avoid drift CV=y2; MV=u PID u (valves)

14. 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

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

16. Steady-state degrees of freedom (DOFs) IMPORTANT! DETERMINES THE NUMBER OF VARIABLES TO CONTROL! • No. of primary CVs = No. of steady-state DOFs Nss =Nvalves – N0ss– Nspecs • N0ss= variables with no steady-state effect CV = controlled variable (c)

17. Distillation column with given feed and pressure 4 5 3 1 NEED TO IDENTIFY 2 CV’s - Typical: Top and btm composition 6 2 Nvalves = 6 , N0y = 2 , Nspecs = 2, NDOF,SS = 6 -2 -2 = 2 N0y: no. controlled variables (liquid levels) with no steady-state effect

18. Heat-integrated distillation process

19. Heat-integrated distillation process

20. 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): minu 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

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

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

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

24. Issue: What should we control? Step 3. What should we control (c)?(primary controlled variables y1=c) • Introductory example: Runner

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

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

27. Optimal operation - Runner Marathon (40 km) • 2. Optimal operation of Marathon runner, J=T • Unconstrained optimum! • Any ”self-optimizing” variable c (to control at constant setpoint)? • c1 = distance to leader of race • c2 = speed • c3 = heart rate • c4 = level of lactate in muscles

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

29. Active constraints can vary!Example: Optimal operation distillation • Cost to be minimized J = - P where P= pD D + pB B – pF F – pV 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!) • Two active purity constraints(CV1 = y1 & CV2=y2) • Happens when energy is relatively expensive • 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)

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

31. 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

32. Unconstrained optimum Optimal operation Cost J Jopt copt Controlled variable c

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

34. Good Good BAD Unconstrained optimum Candidate controlled variables c for self-optimizing control Intuitive • 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,

35. Recycle plant: Optimal operation mT 1 remaining unconstrained degree of freedom

36. Control of recycle plant:Conventional structure (“Two-point”: xD) LC LC xD XC XC xB LC Control active constraints (Mr=max and xB=0.015) + xD

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

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

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

40. 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

41. 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

42. 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. • Local-consistency (desired property): A consistent inventory control system is said to be local-consistent if for each unit thelocalinventory control loops by themselves are sufficient to achieve steady-state mass balance consistency for that unit.

43. CONSISTENT?

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

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

46. Production rate set inside process

47. 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

48. 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.

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

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