Closed-loop model identification and PID/PI tuning for robust anti-slug control

1. Closed-loop model identification and PID/PI tuning for robust anti-slug control Esmaeil Jahanshahi Sigurd Skogestad Department of Chemical Engineering, NTNU, Trondheim, Norway

2. Outline • Introduction • New 4-state nonlinear model • New procedure to identify linear unstable slug-model • IMC Design for unstable slug process • PID(F) and PI tuning • Dealing with nonlinearity: • Gain scheduling • Adaptive tuning • Experiments • OLGA Simulations

3. Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

4. Experimental mini-loop (2003) Ingvald Bårdsen, Espen Storkaas, Heidi Sivertsen

5. z p2 p1 Experimental mini-loopValve opening (z) = 100% SLUGGING

6. z p2 p1 Experimental mini-loopValve opening (z) = 25% SLUGGING

7. z p2 p1 Experimental mini-loopValve opening (z) = 15% NO SLUG

8. z p2 p1 Experimental mini-loop:Bifurcation diagram No slug Valve opening z % Slugging

9. How to avoid slugging?

10. z p2 p1 Design change Avoid slugging:1. Close valve (but increases pressure) No slugging when valve is closed Valve opening z %

11. z p2 p1 Design change Avoid slugging:2. Design change to avoid slugging

12. z p2 p1 Design change Minimize effect of slugging:3. Build large slug-catcher • Most common strategy in practice

13. ref PC PT Avoid slugging:4. ”Active” feedback control z p1 Simple PI-controller

14. Anti slug control: Mini-loop experiments p1 [bar] z [%] Controller ON Controller OFF

15. Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

16. Summary anti slug control (2008)* • Stabilization of desired non-slug flow regime = $$$$! • Stabilization using downhole pressure simple • Stabilization using topside measurements difficult • Control can make a difference! • “Only” problem: Not sufficiently robust *Thanks to: Espen Storkaas + Heidi Sivertsen + Håkon Dahl-Olsen + Ingvald Bårdsen

17. 2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens 1st step: New Experimental mini-rig 3m

18. 2nd step: New Simplified 4-state model* Choke valve with opening Z x3, P2,VG2, ρG2 , HLT P0 wmix,out L3 x1, P1,VG1, ρG1, HL1 x4 L2 h>hc wG,lp=0 wL,in wG,in w x2 wL,lp h L1 hc θ State equations (mass conservations law): *Based on Storkaas model

19. New 4-state model. Comparison with experiments: Experiment Top pressure Subsea pressure Nonlinear: Process gain = slope - approaches zero for large z

20. 3rd step: Experimental linear model (new approach) Fourth-order mechanistic model: Model reduction: 7 parameters need to be estimated Hankel Singular Values: 4 parameters need to be estimated Stable part has little dynamic effect

21. Model Identification: Closed-loop step response using P-controller Experiment 1: Z=20% (valve opening)

22. Comparison with mechanistic model. Z=20% Identified model: Mechanistic model: Excellent agreement!

23. Comparison with mechanistic model. Z=30% Identified model: Mechanistic model:

24. y r u e Plant + _ IMC Design for UnstableProcess Bock diagram for Internal Model Control system IMC for unstable systems: Model: IMC controller:

25. Experiment IMC controller based on identifiedmodel z=30%

26. PIDF and PI Tuning basedon IMC IMC controller can be implemented as a PIDF controller ---- IMC/PIDF ---- PI PI tuning from asymptotes of IMC controller

27. PIDF versus PI control. Experiment (z=30%) (IMC) = PIDF controller PI controller

28. Experimentsonmedium-scale S-riser Open-loop unstable: IMC controller (PIDF):

29. Experiment Experimentsonmedium-scale S-riser PID-F controller: PI controller:

30. Dealing with nonlinearity • Gain-scheduling • Adaptive controller gain slope = gain

31. Solution 1: Gain-Scheduled PIDF Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC (PIDF) controllers:

32. Experiment Gain-Scheduled PIDFExperiment

33. Solution 2: Adaptive PI Tuning Static gain: slope = gain Linear valve: PI Tuning:

34. Experiment Adaptive PI Tuning. Experiment

35. “Direct” nonlinear approaches Solution 3: High-gain observer + state feedback: Did NOT work with bottom pressure (CDC, Dec. 2013) Solution 4: Output linearizing controller + P-control: Worked well, but gain-scheduled IMC more robust with respect to time delay (CDC, Dec. 2013)

36. Solution 4: Output-linearizing controllerStabilizing controller for riser subsystem System in normal form: : top pressure : riser-base pressure Linearizingcontroller: dynamics bounded Control signal to valve:

37. Experiment Solution 4: Output-linearizing controllerZ=60% Gain:

38. OLGA Simulations Solution 2: Adaptive PI TuningOLGA Simulations

39. Conclusions • A 4-state mechanisticmodelverified by experiments • Identify unstable slug-model from closed-loop step test • Good agreement betweenidentified and mechanisticmodels • IMC design works well and gives PIDF controller • Nonlinear “fixes” (adaptive gain or gain scheduling) work well Acknowledgement: • SIEMENS: Fundingoftheproject • Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, MahnazEsmaeilpour and Anne Sofie Nilsen.