Fremtidige trender innen prosessoptimalisering

1. Fremtidige trender innen prosessoptimalisering Sigurd Skogestad Institutt for kjemisk prosessteknologi NTNU, Trondheim Effective Implementation of optimal operation using Off-Line Computations

2. Research Sigurd Skogestad Graduated PhDs since 2000 • Truls Larsson, Studies on plantwide control, Aug. 2000. (Aker Kværner, Stavanger) • Eva-Katrine Hilmen, Separation of azeotropic mixtures, Des. 2000. (ABB, Oslo) • Ivar J. Halvorsen; Minimum energy requirements in distillation ,May 2001. (SINTEF) • Marius S. Govatsmark, Integrated optimization and control, Sept. 2003. (Statoil, Haugesund) • Audun Faanes, Controllability analysis and control structures, Sept. 2003. (Statoil, Trondheim) • Hilde K. Engelien, Process integration for distillation columns, March 2004. (Aker Kværner) • Stathis Skouras, Heteroazeotropic batch distillation, May 2004. (StatoilHydro, Haugesund) • Vidar Alstad, Studies on selection of controlled variables, June 2005. (Statoil, Porsgrunn) • Espen Storkaas, Control solutions to avoid slug flow in pipeline-riser systems, June 2005. (ABB) • Antonio C.B. Araujo, Studies on plantwide control, Jan. 2007. (Un. Campina Grande, Brazil) • Tore Lid, Data reconciliation and optimal operation of refinery processes , June 2007 (Statoil) • Federico Zenith, Control of fuel cells, June 2007 (Max Planck Institute, Magdeburg) • Jørgen B. Jensen, Optimal operation of refrigeration cycles, May 2008 (ABB, Oslo) • Heidi Sivertsen, Stabilization of desired flow regimes (no slug), Dec. 2008 (Statoil, Stjørdal) • Elvira M.B. Aske, Plantwide control systems with focus on max throughput, Mar 2009 (Statoil) • Andreas Linhart An aggregation model reduction method for one-dimensional distributed systems, Oct. 2009. • Current research: • Restricted-complexity control (self-optimizing control): • off-line and analytical solutions to optimal control (incl. explicit MPC & explicit RTO) • Henrik Manum, Johannes Jäschke, Håkon Dahl-Olsen, Ramprasad Yelshuru • Plantwide control. Applications: LNG, GTL • Magnus G. Jacobsen, Mehdi Panahi,

3. Outline • Implementation of optimal operation • Paradigm 1: On-line optimizing control (including RTO) • Paradigm 2: "Self-optimizing" control schemes • Precomputed (off-line) solution • Examples • Control of optimal measurement combinations • Nullspace method • Exact local method • Summary/Conclusions

4. RTO y1s MPC y2s PID u (valves) Process control: Implementation of optimal operation

5. Optimal operation • A typical dynamic optimization problem • Implementation: “Open-loop” solutions not robust to disturbances or model errors • Want to introduce feedback

6. Implementation of optimal operation • Paradigm 1:On-line optimizing control where measurements are used to update model and states • Process control: Steady-state “real-time optimization” (RTO) • Update model and states: “data reconciliation” • Paradigm 2: “Self-optimizing” control scheme found by exploiting properties of the solution • Most common in practice, but ad hoc

7. Implementation: Paradigm 1 • Paradigm 1: Online optimizing control • Measurements are primarily used to update the model • The optimization problem is resolved online to compute new inputs. • Example: Conventional MPC, RTO (real-time optimization) • This is the “obvious” approach (for someone who does not know control)

8. Example paradigm 1: On-line optimizing control of Marathon runner • Even getting a reasonable model requires > 10 PhD’s  … and the model has to be fitted to each individual…. • Clearly impractical!

9. Implementation: Paradigm 2 • Paradigm 2: Precomputed solutions based on off-line optimization • Find properties of the solution suited for simple and robust on-line implementation • Most common in practice, but ad hoc • Proposed method: Do this is in a systematic manner. • Turn optimization into feedback problem. • Find regions of active constraints and in each region: • Control active constraints • Control “self-optimizing ” variables for the remaining unconstrained degrees of freedom • “inherent optimal operation”

10. Example: Runner • One degree of freedom (u): Power • Cost to be minimized J = T • Constraints • u ≤ umax • Follow track • Fitness (body model) • Optimal operation: Minimize J with respect to u(t) • ISSUE: How implement optimal operation?

11. Optimal operation - Runner Solution 2 – Feedback(Self-optimizing control) • What should we control?

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

13. Optimal operation - Runner Self-optimizing control: Marathon (40 km) • Optimal operation of Marathon runner, J=T • 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

14. Implementation paradigm 2: Feedback control of Marathon runner Simplest case: select one measurement c = heart rate measurements • Simple and robust implementation • Disturbances are indirectly handled by keeping a constant heart rate • May have infrequent adjustment of setpoint (heart rate)

15. Example paradigm 2: Optimal operation of chemical plant • Hierarchial decomposition based on time scale separation Self-optimizing control: Acceptable operation (=acceptable loss) achieved using constant set points (cs) for the controlled variables c cs • Controlled variables c • Active constraints • “Self-optimizing” variables c • for remaining unconstrained degrees of freedom (u) • No or infrequent online optimization needed. • Controlled variables c are found based on off-line analysis.

16. “Magic” self-optimizing variables: How do we find them? • Intuition: “Dominant variables” (Shinnar) • Is there any systematic procedure?

17. Systematic procedure for selecting controlled variables for optimal operation • Define economics (cost J) and operational constraints • Identify degrees of freedom and important disturbances • Optimize for various disturbances • Identify active constraints regions (off-line calculations) For each active constraint region do step 5-6: • Identify “self-optimizing” controlled variables for remaining unconstrained degrees of freedom A. “Brute force” loss evaluation B. Sensitive variables: “Max. gain rule” (Gain= Minimum singular value) C. Optimal linear combination of measurements, c = Hy 6. Identify switching policies between regions

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

19. 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

20. 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,

21. Unconstrained optimum Quantitative steady-state: Maximum gain rule G c u Maximum gain rule (Skogestad and Postlethwaite, 1996): Look for variables that maximize the scaled gain (Gs) (minimum singular value of the appropriately scaled steady-state gain matrix Gsfrom u to c)

22. Why is Large Gain Good? J(u) J, c Loss Δc = GΔu Jopt copt Variation of u c-copt uopt u Controlled variable Δc = G Δu Want large gain G: Large implementation error n (in c) translates into small deviation of u from uopt(d) - leading to lower loss

23. Unconstrained degrees of freedom: Ideal “Self-optimizing” variables • Operational objective: Minimize cost function J(u,d) • The ideal “self-optimizing” variable is the gradient (first-order optimality condition (ref: Bonvin and coworkers)): • Optimal setpoint = 0 • BUT: Gradient can not be measured in practice • Possible approach: Estimate gradient Ju based on measurements y • Approach here: Look directly for c without going via gradient

24. Unconstrained degrees of freedom: Optimal measurement combination • Candidate measurements (y): Include also inputs u H So far: H is a ”selection matrix” [0 0 1 0 0] Now: H is a full ”combination matrix”

25. Unconstrained degrees of freedom: Optimal measurement combination 1. Nullspace method for n = 0 (Alstad and Skogestad, 2007) Basis: Want optimal value of c to be independent of disturbances • Find optimal solution as a function of d: uopt(d), yopt(d) • Linearize this relationship: yopt= F d • Want: • To achieve this for all values of  d: • Always possible to find H that satisfies HF=0 provided • Optimal when we disregard implementation error (n) Amazingly simple! Sigurd is told by Vidar Alstad how easy it is to find H 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).

26. Unconstrained degrees of freedom: Optimal measurement combination 2. “Exact local method” (Combined disturbances and implementation errors) Theorem 1. Worst-case loss for given H(Halvorsen et al, 2003): Applies to any H (selection/combination) Theorem 2 (Alstad et al. ,2009): Optimization problem to find optimal combination is convex. • V. Alstad, S. Skogestad and E.S. Hori, ``Optimal measurement combinations as controlled variables'', Journal of Process Control, 19, 138-148 (2009).

27. Example: CO2 refrigeration cycle Unconstrained DOF (u) Control what? c=? pH

28. CO2 refrigeration cycle Step 1. One (remaining) degree of freedom (u=z) Step 2. Objective function. J = Ws (compressor work) Step 3. Optimize operation for disturbances (d1=TC, d2=TH, d3=UA) • Optimum always unconstrained Step 4. Implementation of optimal operation • No good single measurements (all give large losses): • ph, Th, z, … • Nullspace method: Need to combine nu+nd=1+3=4 measurements to have zero disturbance loss • Simpler: Try combining two measurements. Exact local method: • c = h1 ph + h2 Th = ph + k Th; k = -8.53 bar/K • Nonlinear evaluation of loss: OK!

29. Refrigeration cycle: Proposed control structure Control c= “temperature-corrected high pressure”

30. Summary feedback approach: Turn optimization into setpoint tracking Issue: What should we control to achieve indirect optimal operation ? Primary controlled variables (CVs): • Control active constraints! • Unconstrained CVs: Look for “magic” self-optimizing variables! Need to identify CVs for each region of active constraints

31. RTO y1s MPC y2s PID u (valves) Fremtidige trender innen prosessoptimalisering • RTO (real-time optimization) • requires detailed steady-state model • Expensive to develop and maintain • Use only when necessary! • Try first simpler methods • Control the right CVs!!! .

32. Depending on marked conditions: Two main modes of optimal operation Mode I. Given throughput (“nominal case”) Given feed or product rate “Maximize efficiency”: Unconstrained optimum (“trade-off”) • key is to select right “self-optimizing variable”. • May use RTO in some cases Mode II. Max/Optimum throughput Throughput is a degree of freedom + good product prices Maximum throughput Increase throughput until constraints give infeasible operation Do not need RTO if we can identify active constraints (bottleneck!) • Operation/control: • Traditionally: Focus on mode I • But: Mode II is where we really can make “extra” money!

33. Conclusion optimal operation ALWAYS: 1. Control active constraints and control them tightly!! • Good times: Maximize throughput -> tight control of bottleneck 2. Identify “self-optimizing” CVs for remaining unconstrained degrees of freedom • Use offline analysis to find expected operating regions and prepare control system for this! • One control policy when prices are low (nominal, unconstrained optimum) • Another when prices are high (constrained optimum = bottleneck) ONLY if necessary: consider RTO on top of this