1. 1 PLANTWIDE CONTROL Identifying and switching between active constraints regions Sigurd Skogestad and Magnus G. Jacobsen Department of Chemical Engineering Norwegian University of Science and Tecnology (NTNU) Trondheim, Norway EFCE conference, Berlin 29 Sep. 2011

2. 2 Outline Overview of economic plantwide control Distillation case studies –Finding and plotting active constraints regions as a function of disturbances –Control implications –Switching –Unconstrained ”self-optimizing variables” S. Skogestad, ``Control structure design for complete chemical plants'', Computers and Chemical Engineering, vol. 28, 219-234 (2004). See also: http://www.nt.ntnu.no/users/skoge/plantwide/

3. 3 c s = y 1s MPC PID y 2s RTO u (valves) Follow path (+ look after other variables) Stabilize + avoid drift Min J (economics) OBJECTIVE Ecomomic plantwide control The controlled variables (CVs) interconnect the layers

4. 4 How we design a control system for a complete chemical plant? Where do we start? What should we control? and why? etc.

5. 5 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. 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

6. 6 Control structure design procedure I Top Down Step 1: Define operational objectives (optimal operation) –Cost function J (to be minimized) –Operational constraints Step 2: Identify degrees of freedom (MVs) and optimize for expected disturbances Step 3: Select primary controlled variables c=y 1 (CVs) Step 4: Where set the production rate? (Inventory control) II Bottom Up Step 5: Regulatory / stabilizing control (PID layer) –What more to control (y 2 ; local CVs)? –Pairing of inputs and outputs Step 6: Supervisory control (MPC layer) Step 7: Real-time optimization (Do we need it?) y1y1 y2y2 Process MVs

7. 7 Step 1. 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

8. 8 Step 2: Identify degrees of freedom and optimize for expected disturbances Optimization: Identify regions of active constraints Time consuming! Control: 2 active constraints (x A, x B ) + 2 “selfoptimizing” 3+13+1 1+31+3 Example (Magnus G. Jacobsen): Two distillation columns in series. 4 degrees of freedom 3+13+1 4+04+0 5

9. 9 Step 3: 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)?

10. 10 Implementation (in practice): Local feedback control! “Self-optimizing control:” Constant setpoints for c gives acceptable loss y FeedforwardOptimizing controlLocal feedback: Control c (CV) d

11. 11 Question: What should we control (c)? (primary controlled variables y 1 =c) Introductory example: Runner Issue: What should we control?

12. 12 –Cost to be minimized, J=T –One degree of freedom (u=power) –What should we control? Optimal operation - Runner Optimal operation of runner

13. 13 Sprinter (100m) 1. Optimal operation of Sprinter, J=T –Active constraint control: Maximum speed (”no thinking required”) Optimal operation - Runner

14. 14 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)

15. 15 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

16. 16 Step 3. What should we control (c)? (primary controlled variables y 1 =c) Selection of controlled variables c 1.Control active constraints! 2.Unconstrained variables: Control self-optimizing variables! –The ideal self-optimizing variable c is the gradient (c =  J/  u = J u ) –In practice, control individual measurements or combinations, c = H y –We have developed a lot of theory for this

17. 17 Example active constraint Optimal operation = max. throughput (active constraint) 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 Want tight bottleneck control to reduce backoff!

18. 18 Step 4. Where set production rate? Where locale the TPM (throughput manipulator)? Very important! Determines structure of remaining inventory (level) control system Link between Top-down and Bottom-up parts

19. 19 LOCATE TPM? Default choice: place the TPM at the feed Consider moving if there is an important active constraint that could otherwise not be well controlled.

20. 20 Step 5: Regulatory control layer Step 5. Choose structure of regulatory (stabilizing) layer: (a) Identify “stabilizing” CV2s (levels, pressures, reactor temperature,one temperature in each column, etc.). In addition, control active constraints (CV1) that require tight control (small backoff) (b) Identify pairings (MVs to be used to control CV2), taking into account Preferably, the same regulatory layer should be used for all operating regions without the need for reassigning inputs or outputs.

21. 21 ”Advanced control” STEP 6. SUPERVISORY LAYER Objectives of supervisory layer: 1. Switch control structures (CV1) depending on operating region Active constraints self-optimizing variables 2. Perform “advanced” economic/coordination control tasks. –Control primary variables CV1 at setpoint using as degrees of freedom Setpoints to the regulatory layer (CV2s) –Keep an eye on stabilizing layer Avoid saturation in stabilizing layer –Feedforward from disturbances –Make use of extra inputs –Make use of extra measurements Implementation: Alternative 1: Advanced control based on ”simple elements” Alternative 2: MPC

22. 22 Summary. Systematic procedure for plantwide control 1.Start “top-down” with economics: –Step 1: Define operational objectives and identify degrees of freeedom –Step 2: 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 (level) control structure. 3.Regulatory control II: “Bottom-up” stabilization of the plant Step 5B: Control variables to stop “drift” (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

23. 23 Active constraint regions and implementation Distillation examples

24. 24 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 (d)2) p free: p min · p · p max Feed: 1) F given (d) 2) F free: F · F max Optimal operation: Minimize J with respect to steady-state DOFs (u) value products cost energy (heating+ cooling) cost feed

25. 25 Example column with 41 stages u = [L V] for expected disturbances d = (F, p V )

26. 26 Possible constraint combinations (= 2 3 = 8) 1.0* 2.x D 3.x B * 4.V* 5.x D, V 6.x B, V* 7.x D, x B 8.x D, x B, V (infeasible, only 2 DOFs) * Not for this case because x B always optimally active (”Avoid product give away”)

27. 27 Constraint regions as function of d 1 =F and d 2 =p V 3 regions

28. 28 5 regions Only get paid for main component (”gold”)

29. 29 I: L – x D =0.95, V – x B ?Self-optimizing?! xBs = f(p V ) II: L – x D =0.95, V = Vmax III: As in I Control, p D independent of purity

30. 30 I: L – xD?, V – xB?Self-optimizing? II: L – xD?, V = Vmax III:L – xB=0.99, V = Vmax ”active constraints” No simple decentralized structure. OK with MPC

31. 31 2 Distillation columns in series With given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column) DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011) Energy price: p V =0-0.2 $/mol (varies) Cost (J) = - Profit = p F F + p V (V 1 +V 2 ) – p D1 D 1 – p D2 D 2 – p B2 B 2 > 95% B p D2 =2 $/mol F ~ 1.2mol/s p F =1 $/mol < 4 mol/s < 2.4 mol/s > 95% C p B2 =1 $/mol N=41 α AB =1.33 N=41 α BC =1. 5 > 95% A p D1 =1 $/mol 2 5 = 32 possible combinations of the 5 constraints

32. 32 DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011) Energy price: p V =0-0.2 $/mol (varies) Cost (J) = - Profit = p F F + p V (V 1 +V 2 ) – p D1 D 1 – p D2 D 2 – p B2 B 2 > 95% B p D2 =2 $/mol F ~ 1.2mol/s p F =1 $/mol < 4 mol/s < 2.4 mol/s > 95% C p B2 =1 $/mol 1. x B = 95% B Spec. valuable product (B): Always active! Why? “Avoid product give-away” N=41 α AB =1.33 N=41 α BC =1. 5 > 95% A p D1 =1 $/mol 2. Cheap energy: V 1 =4 mol/s, V 2 =2.4 mol/s Max. column capacity constraints active! Why? Overpurify A & C to recover more B 2 Distillation columns in series. Active constraints?

33. 33 Active constraint regions for two distillation columns in series [mol/s] [$/mol] CV = Controlled Variable Energy price BOTTLENECK Higher F infeasible because all 5 constraints reached 8 regions

34. 34 Active constraint regions for two distillation columns in series [mol/s] [$/mol] CV = Controlled Variable Assume low energy prices (pV=0.01 $/mol). How should we control the columns? Energy price

35. 35 Control of Distillation columns in series Given LC PC Assume low energy prices (pV=0.01 $/mol). How should we control the columns? Red: Basic regulatory loops

36. 36 Control of Distillation columns in series Given LC PC Comment: Should normally stabilize column profiles with temperature control, Should use reflux (L) in this case because boilup (V) may saturate. T1 S and T2 S would then replace L1 and L2 as DOFs…… but leave this out for now.. Red: Basic regulatory loops TC T1 s T2 s T1 T2 Comment

37. 37 Control of Distillation columns in series Given LC PC Red: Basic regulatory loops CC xBxB x BS =95% MAX V1 MAX V2 CONTROL ACTIVE CONSTRAINTS!

38. 38 Control of Distillation columns in series Given LC PC Red: Basic regulatory loops CC xBxB x BS =95% MAX V1 MAX V2 Remains: 1 unconstrained DOF (L1): Use for what? CV=x A ? No!! Optimal x A varies with F Maybe: constant L1? (CV=L1) Better: CV= x A in B1? Self-optimizing? CONTROL ACTIVE CONSTRAINTS!

39. 39 Active constraint regions for two distillation columns in series CV = Controlled Variable 3 2 0 1 1 0 2 [mol/s] [$/mol] 1 Cheap energy: 1 remaining unconstrained DOF (L1) -> Need to find 1 additional CVs (“self-optimizing”) More expensive energy: 3 remaining unconstrained DOFs -> Need to find 3 additional CVs (“self-optimizing”) Energy price

40. 40 Conclusion Generate constraint regions by offline simulation for expected important disturbances –Time consuming - so focus on important disturbance range Implementation / control –Control active constraints! –Switching between these usually easy –Less obvious what to select as ”self-optimizing” CVs for remaining unconstrained degrees of freedom