1. 1 1 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 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. 2 2 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 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: 1.Gain scheduling 2.Adaptive tuning Experiments OLGA Simulations

3. 3 3 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU

4. 4 4 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Experimental mini-loop (2003) Ingvald Bårdsen, Espen Storkaas, Heidi Sivertsen

5. 5 5 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 100% SLUGGING

6. 6 6 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 25% SLUGGING

7. 7 7 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control p1p1 p2p2 z Experimental mini-loop Valve opening (z) = 15% NO SLUG

8. 8 8 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control p1p1 p2p2 z Experimental mini-loop: Bifurcation diagram Valve opening z % No slug Slugging

9. 9 9 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control How to avoid slugging?

10. 10 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control p1p1 p2p2 z Avoid slugging: 1. Close valve (but increases pressure) Valve opening z % No slugging when valve is closed Design change

11. 11 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Avoid slugging: 2. Design change to avoid slugging p1p1 p2p2 z Design change

12. 12 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Minimize effect of slugging: 3. Build large slug-catcher Most common strategy in practice p1p1 p2p2 z Design change

13. 13 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Avoid slugging: 4. ”Active” feedback control PT PC ref Simple PI-controller p1p1 z

14. 14 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Anti slug control: Mini-loop experiments Controller ONController OFF p 1 [bar] z [%]

15. 15 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Anti slug control: Full-scale offshore experiments at Hod-Vallhall field (Havre,1999)

16. 16 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Avoid slugging: 5. ”Active” feedback control with topside measurement? PC ref Control is difficult (Inverse reponse = Unstable zero dynamics) p2p2 z

17. 17 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 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

18. 18 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens 1 st step: New Experimental mini-rig 3m

19. 19 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 2 nd step: New Simplified 4-state model* State equations (mass conservations law): θ h L2L2 hchc w mix,out x 1, P 1,V G1, ρ G1, H L1 x 3, P 2,V G2, ρ G2, H LT P0P0 Choke valve with opening Z x4x4 h>h c w G,lp =0 w L,lp L3L3 w L,in w G,in w x2x2 L1L1 *Based on Storkaas model

20. 20 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control New 4-state model. Comparison with experiments: Top pressure Subsea pressure Experiment Nonlinear: Process gain = slope - approaches zero for large z

21. 21 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Fourth-order mechanistic model: Hankel Singular Values: Model reduction: 4 parameters need to be estimated 3 rd step: Experimental linear model (new approach) 7 parameters need to be estimated Stable part has little dynamic effect

22. 22 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Model Identification: Closed-loop step response using P-controller Experiment 1: Z=20% (valve opening)

23. 23 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Comparison with mechanistic model. Z=20% Identified model: Mechanistic model: Excellent agreement!

24. 24 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Identified model: Mechanistic model: Comparison with mechanistic model. Z=30%

25. 25 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control IMC Design for Unstable Process Bock diagram for Internal Model Control system IMC for unstable systems: y u e r + _ Plant Model: IMC controller:

26. 26 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Experiment IMC controller based on identified model z=30%

27. 27 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control PIDF and PI Tuning based on IMC IMC controller can be implemented as a PIDF controller PI tuning from asymptotes of IMC controller ---- IMC/PIDF ---- PI

28. 28 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control PIDF versus PI control. Experiment (z=30%) PI controller= PIDF controller (IMC)

29. 29 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Experiments on medium-scale S-riser Open-loop unstable: IMC controller (PIDF):

30. 30 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control PID-F controller: PI controller: Experiment Experiments on medium-scale S-riser

31. 31 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 1.Gain-scheduling 2.Adaptive controller gain Dealing with nonlinearity slope = gain

32. 32 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Solution 1: Gain-Scheduled PIDF Three identified model from step tests: Z=20%: Z=30%: Z=40%: Three IMC (PIDF) controllers:

33. 33 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Gain-Scheduled PIDF Experiment Experiment

34. 34 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Solution 2: Adaptive PI Tuning Static gain: Linear valve: PI Tuning: slope = gain

35. 35 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Experiment Adaptive PI Tuning. Experiment

36. 36 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control 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) “Direct” nonlinear approaches

37. 37 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Solution 4: Output-linearizing controller Stabilizing controller for riser subsystem System in normal form: Linearizing controller: Control signal to valve: dynamics bounded : riser-base pressure : top pressure

38. 38 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Experiment Gain: Solution 4: Output-linearizing controller Z=60%

39. 39 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control OLGA Simulations Solution 2: Adaptive PI Tuning OLGA Simulations Set-point Valve opening KcKc TiTi 67.36140.58400 67.1916.10.79600 67.0718.20.9410800 66.9920.11.2312000 66.9323.241.5613200 66.88--1.9314400

40. 40 Sigurd Skogestad | Closed-loop model identification and PID/PI tuning for robust anti-slug control Conclusions A 4-state mechanistic model verified by experiments Identify unstable slug-model from closed-loop step test Good agreement between identified and mechanistic models IMC design works well and gives PIDF controller Nonlinear “fixes” (adaptive gain or gain scheduling) work well Acknowledgement: SIEMENS: Funding of the project Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.