1 AntiSlug Control Experiments Using Nonlinear Observers Esmaeil

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

2 Outline § § Introduction Motivation Modeling Observer design • Unscented Kalman Filter (UKF) • High-Gain observe • Fast UKF § State-feedback § Experimental results § Controllability limitation 2 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

3 Introduction * figure from Statoil 3 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

4 Slug cycle (stable limit cycle) Experiments performed by the Multiphase Laboratory, NTNU 4 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

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 5 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

6 Pt, s Motivation PC uz PT Objective: using topside pressure for control Problem 1: Nonlinearity Additional Problem 2: Unstable zero dynamics (RHP-zero) MS=5. 87, MT=6. 46 6 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

7 Solution? ! uc K State variables Nonlinear observer uc Pt PT Questions: 1. Is this solution applicable for anti-slug control? 2. Can observer bypass fundamental limitations? 3. Which kind of observer is suitable? • Experiments 7 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

8 Modeling 8 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

9 Modeling: Simplified 4 -state model Choke valve with opening Z x 3, P 2, VG 2, ρG 2 , HLT P 0 wmix, out L 3 x 1, P 1, VG 1, ρG 1, HL 1 x 4 w. L, in w. G, in w L 2 h>hc w. G, lp=0 w. L, lp x 2 L 1 h θ hc State equations (mass conservations law): 9 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

10 Experiments 3 m 10 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

11 Experiment Bifurcation diagrams Top pressure Subsea pressure Gain = slope 11 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

12 Observer Design 12 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

13 1. Unscented Kalman Filter Nonlinear plant: (1) Prediction step: 13 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

14 1. Unscented Kalman Filter (UKF) (2) Update step: (3) Correction step: 14 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

15 2. High-Gain Observer 15 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

16 2. High-Gain Observer where 16 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

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: - Scaling of states and measurement in the model 17 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

18 State Feedback Kc : a linear optimal controller calculated by solving Riccati equation Ki : a small integral gain (e. g. Ki = 10− 3) 18 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

19 Experimental Results 19 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

20 Experiment High-gain observer – top pressure measurement: topside pressure valve opening: 20 % 20 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

21 Experiment Fast UKF – top pressure measurement: topside pressure valve opening: 20 % 21 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

22 Experiment High-gain observer – subsea pressure measurement: topside pressure valve opening: 20 % 22 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

23 Experiment PI Controller – subsea pressure measurement: subsea pressure valve opening: 40 % 23 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

24 Experiment Linear observer (KF) – subsea pressure measurement: subsea pressure valve opening: 40 % 24 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

25 Experiment Summary of experiments Stabilizing Control Method CV Subsea pressure Top Pressure Linear Controllers (PI, H∞) Working Not Working Fast Linear Observer Working Not Working Fast Nonlinear Observer Not Working? ? !* Working Slow Nonlinear Observer Not Robust* Max. Valve 40% 20% * Estimation works (open-loop), but slow * Estimation also not working 25 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

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 26 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

27 Controllability limitation – top pressure Measuring topside pressure we can stabilize the system only in a limited range RHP-zero dynamics of top pressure Ms, min Z = 20% Z = 40% 2. 1 7. 0 27 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,

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! 28 E. I. Grøtli | Anti-Slug Control Experiments Using Nonlinear Observers E. Jahanshahi, S. Skogestad,