1. Comparison of nonlinear model-based controllers and gain-scheduled Internal Model Control based on identified model
Esmaeil Jahanshahi and Sigurd Skogestad
Department of Chemical Engineering
NTNU
Trondheim, Norway
Two-phase pipe flow
(liquid and vapor)
Slug (liquid) buildup
CDC, December 2013
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2. Slug cycle (stable limit cycle)
Experiments performed by the Multiphase Laboratory, NTNU

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

4. Experimental mini-loop Valve opening (z) = 100%
SLUGGING

5. Experimental mini-loop Valve opening (z) = 25%
SLUGGING

6. Experimental mini-loop Valve opening (z) = 15%
NO SLUG

7. Experimental mini-loop: Bifurcation diagramz
Experimental mini-loop: Bifurcation diagram
No slug
Valve opening z %
Slugging

8. How to avoid slugging?

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

10. Avoid slugging: 2. Design change to avoid sluggingp1 p2 z

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

12. Avoid slugging: 4. ”Active” feedback controlPT PC
ref
Simple PI-controller p1 z

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

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

15. Fundamental limitation – top pressure
Measuring topside pressure we can stabilize the system only in a limited range
Unstable (RHP) zero dynamics of top pressure
Z = 20%
Z = 40%
Ms,min
2.1
7.0

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. New Experimental mini-rig
: Esmaeil Jahanshahi, PhD-work supported by Siemens
New Experimental mini-rig 3m

18. 1st step: Developed new simple 4-state model*.θ h L2 hc
wmix,out
x1, P1,VG1, ρG1, HL1
x3, P2,VG2, ρG2 , HLT P0
Choke valve with opening Z x4
h>hc
wG,lp=0
wL,lp L3
wL,in
wG,in w x2 L1
State equations (mass conservations law):
*Based on Storkaas model

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

20. Linear Control Solutions

21. Experiment
Linear Solution 1: H∞ control by linearizing new model Experiment, mixed-sensitivity design

22. Experimental linear model (new approach)
Fourth-order mechanistic model:
Closed-loop step-response with P-control
Hankel Singular Values:
Model reduction:
4 parameters need to be estimated

23. Linear Solution 2: IMC based on identified model IMC design
Block diagram for Internal Model Control system
IMC for unstable systems:
Model: y u e r + _
Plant
IMC controller:

24. Linear Solution 2: IMC based on identified model Experiment

25. Linear Solution 3: «Robustified» IMC using H∞ loop shaping
Experiment
Linear Solution 3: «Robustified» IMC
using H∞ loop shaping

26. Comparing linear controllers (subsea pressure)*
*Controllers tuned at 30% valve opening

27. Nonlinear Control Solutions

28. Solution 1: observer & state feedbackPT
Nonlinear observer K
State
variables uc Pt

29. High-Gain Observer

30. State Feedback
Kc : linear optimal gain calculated by solving Riccati equation
Ki : small integral gain (e.g. Ki = 10−3)

31. High-gain observer – top pressure
Experiment
High-gain observer – top pressure
measurement: topside pressure valve opening: 20 %

32. High-gain observer – subsea pressure
Open-loop experiment
High-gain observer – subsea pressure
measurement: subsea pressure valve opening: 20 %
Closed-loop:
Not working !!?

33. Chain of Integrators
Fast nonlinear observer using subsea pressure: Not Working??!
Pipeline-riser system is a chain of integrator
Measuring top pressure and estimating subsea pressure is differentiating
Measuring subsea pressure and estimating top pressure is integrating x

34. Solution 2: feedback linearizationPT
Nonlinear controller uc
Prt
Jahanshahi, Skogestad and Grøtli, NOLCOS, 2013

35. Output-linearizing controller Stabilizing controller for riser subsystem
System in normal form:
: riser-base pressure
: top pressure
Linearizing controller:
dynamics bounded
Control signal to valve:

36. CV: riser-base pressure (y1), Z=60%
Experiment
CV: riser-base pressure (y1), Z=60%
Gain:

37. Solution 3: Gain-Scheduled IMC
Three identified model from step tests:
Z=20%:
Z=30%:
Z=40%:
Three IMC controllers:

38. Solution 3: Gain-Scheduled IMC Experiment

39. Comparison of Nonlinear Controllers
Gain-scheduling IMC is the most robust solution
Adaptive PI controller is the second-best
Controllability remarks:
Fundamental limitation control: gain of the system goes to zero for fully open valve
Additional limitation top-side pressure: Inverse response (non-minimum-phase)

40. Conclusions System is strongly nonlinear
Must increase controller gain for large valve openings (lower pressure)
Rank of nonlinear controllers for anti-slug control (using subsea pressure):
Gain-scheduled IMC
Feedback linearization
High-gain observer (doesn’t work)
More recently, even better:
Robustified gain-scheduled IMC using H-infinity loop shaping
Loop transfer recovery based on LQG-controller
Acknowledgements
Financial support from SIEMENS
Master students: Elisabeth Hyllestad, Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.