Anti-Slug Control Experiments Using Nonlinear Observers

1. 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. Pt,s PC uz PT 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. Nonlinear observer K State variables PT Solution?! uc 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 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):

10. Experiments 3m

11. Bifurcation diagrams Experiment 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: • - Scalingofstates and measurement in themodel

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

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

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

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

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

25. Experiment Summary of experiments Stabilizing Control * 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

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!