PLANTWIDE CONTROL Identifying and switching between active constraints regions

1. PLANTWIDE CONTROLIdentifying 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. 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. Ecomomic plantwide control The controlled variables (CVs) interconnect the layers OBJECTIVE Min J (economics) RTO cs = y1s Follow path (+ look after other variables) MPC y2s Stabilize + avoid drift PID u (valves)

4. 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=y1 (CVs) • Step 4: Where set the production rate? (Inventory control) II Bottom Up • Step 5: Regulatory / stabilizing control (PID layer) • What more to control (y2; local CVs)? • Pairing of inputs and outputs • Step 6: Supervisory control (MPC layer) • Step 7: Real-time optimization (Do we need it?) y1 y2 MVs Process

5. 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): 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

6. Step 2: Identify degrees of freedom and optimize for expected disturbances • Optimization: Identify regions of active constraints • Time consuming! 3+1 Control: 2 active constraints (xA, xB) + 2 “selfoptimizing” Example (Magnus G. Jacobsen): Two distillation columns in series. 4 degrees of freedom 5 3+1 4+0 1+3

7. Step 3: 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)?

8. 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

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

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

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

12. 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

13. 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)

14. Step 3. What should we control (c)?(primary controlled variables y1=c) Selection of controlled variables c • Control active constraints! • Unconstrained variables: Control self-optimizing variables! • The ideal self-optimizing variable c is the gradient (c =  J/ u = Ju) • In practice, control individual measurements or combinations, c = H y • We have developed a lot of theory for this

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

16. 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

17. 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.

18. 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.

19. ”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

20. Active constraint regions and implementation • Distillation examples

21. 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= pD D + pB B – pF F – pV V • Constraints Purity D: For example xD, impurity· max Purity B: For example, xB, impurity· max Flow constraints: min · D, B, L etc. · max Column capacity (flooding): V · Vmax, etc. Pressure: 1) p given (d) 2) p free: pmin· p · pmax Feed: 1) F given (d) 2) F free: F · Fmax • Optimal operation: Minimize J with respect to steady-state DOFs (u) cost energy (heating+ cooling) cost feed value products

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

23. Possible constraint combinations (= 23 = 8) • 0* • xD • xB* • V* • xD, V • xB, V* • xD, xB • xD, xB, V (infeasible, only 2 DOFs) *Not for this case because xB always optimally active (”Avoid product give away”)

24. Constraint regions as function of d1=F and d2=pV 3 regions

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

26. Control, pD independent of purity I: L – xD=0.95, V – xB? Self-optimizing?! xBs = f(pV) II: L – xD=0.95, V = Vmax III: As in I

27. 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

28. 2 Distillation columns in seriesWith given F (disturbance): 4 steady-state DOFs (e.g., L and V in each column) N=41 αAB=1.33 N=41 αBC=1.5 > 95% B pD2=2 $/mol > 95% A pD1=1 $/mol F ~ 1.2mol/s pF=1 $/mol < 4 mol/s < 2.4 mol/s > 95% C pB2=1 $/mol Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2 Energy price: pV=0-0.2 $/mol (varies) DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011) 25 = 32 possible combinations of the 5 constraints

29. 1. xB = 95% B Spec. valuable product (B): Always active! Why? “Avoid product give-away” 2. Cheap energy: V1=4 mol/s, V2=2.4 mol/s Max. column capacity constraints active! Why? Overpurify A & C to recover more B 2 Distillation columns in series. Active constraints? N=41 αAB=1.33 N=41 αBC=1.5 > 95% B pD2=2 $/mol > 95% A pD1=1 $/mol F ~ 1.2mol/s pF=1 $/mol < 4 mol/s < 2.4 mol/s > 95% C pB2=1 $/mol Cost (J) = - Profit = pF F + pV(V1+V2) – pD1D1 – pD2D2 – pB2B2 Energy price: pV=0-0.2 $/mol (varies) DOF = Degree Of Freedom Ref.: M.G. Jacobsen and S. Skogestad (2011)

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

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

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

33. Control of Distillation columns in series PC PC LC LC xB CC xBS=95% Given MAX V2 MAX V1 LC LC CONTROL ACTIVE CONSTRAINTS! Red: Basic regulatory loops

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

35. Active constraint regions for two distillation columns in series 0 1 Energy price 1 [$/mol] 2 0 2 3 1 [mol/s] 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”) CV = Controlled Variable

36. 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