1. Anti-Slug Control Experiments Using Nonlinear Observers
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Anti-Slug Control Experiments Using Nonlinear Observers
Esmaeil Jahanshahi, Sigurd Skogestad, Esten I. Grøtli
Norwegian University of Science & Technology (NTNU)
American Control Conference - June 17th 2013, Washington, DC

2. Outline Introduction Motivation Modeling Observer design
Unscented Kalman Filter (UKF)
High-Gain observe
Fast UKF
State-feedback
Experimental results
Controllability limitation

3. Introduction
* figure from Statoil

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

5. Introduction Anti-slug solutions Conventional Solutions:
Choking (reduces the production)
Design change (costly) : Full separation, Slug catcher
Automatic control: The aim is non-oscillatory flow regime together with the maximum possible choke opening to have the maximum production

6. Motivation Objective: using topside pressure for controlPT PC uz
Pt,s
Motivation
Objective: using topside pressure for control
Problem 1: Nonlinearity
Additional Problem 2: Unstable zero dynamics (RHP-zero)
MS=5.87, MT=6.46

7. Solution?! PT
Nonlinear observer K
State
variables uc Pt
Questions:
Is this solution applicable for anti-slug control?
Can observer bypass fundamental limitations?
Which kind of observer is suitable?
Experiments

8. Modeling

9. Modeling: Simplified 4-state modelθ 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):

10. Experiments 3m

11. Bifurcation diagrams Top pressure Subsea pressure Gain = slope
Experiment
Bifurcation diagrams
Top pressure
Subsea pressure
Gain = slope

12. Observer Design

13. 1. Unscented Kalman Filter
Nonlinear plant:
(1) Prediction step:

14. 1. Unscented Kalman Filter (UKF)
(2) Update step:
(3) Correction step:

15. 2. High-Gain Observer

16. 2. High-Gain Observer
where

17. 3. Fast UKF Nonlinear model with transformed states:
This is the high-gain observer without the observer term, therefore we do not need to specify the observer gain manually.
High-gain Strategy:
Large Qk and small Rk increase the UKF gain
UKF gain:
- Scaling of states and measurement in the model

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

19. Experimental Results

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

21. Experiment
Fast UKF – top pressure
measurement: topside pressure valve opening: 20 %

22. High-gain observer – subsea pressure
Experiment
High-gain observer – subsea pressure
measurement: topside pressure valve opening: 20 %

23. PI Controller – subsea pressure
Experiment
PI Controller – subsea pressure
measurement: subsea pressure valve opening: 40 %

24. Linear observer (KF) – subsea pressure
Experiment
Linear observer (KF) – subsea pressure
measurement: subsea pressure valve opening: 40 %

25. Summary of experiments
Stabilizing Control
Method \ CV
Subsea pressure
Top Pressure
Linear Controllers (PI, H∞)
Working
Not Working
Fast Linear Observer
Fast Nonlinear Observer
Not Working??!*
Slow Nonlinear Observer
Not Robust*
Max. Valve
40%
20%
* Estimation works (open-loop), but slow
* Estimation also not working

26. Chain of Integrators
Fast nonlinear observer using subsea pressure: Not Working??!
Fast nonlinear observer (High-gain) acts like a differentiator
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

27. Controllability limitation – top pressure
Measuring topside pressure we can stabilize the system only in a limited range
RHP-zero dynamics of top pressure
Z = 20%
Z = 40%
Ms,min
2.1
7.0

28. Conclusions
Nonlinear observers work only when measuring topside pressure
This works in a limited range (valve opening)
A fast observer is needed for stabilizing control
Fast nonlinear observers fail when measuring subsea pressure
Observer can counteract nonlinearity
But cannot bypass fundamental limitation (non-minimum-phase system)
Thank you!