Anti-Slug Control Experiments Using Nonlinear Observers The thematic content of the series: 1 Facts Revenue from the last two years; Localization; History and surroundings 2 Research Six strategic areas; Three Centres of Excellence; Laboratories; Cooperation with SINTEF; 3 Education and student activities Study areas and programmes of study; Quality Reform; Further- and continuing education; Internationalization 4 Innovation and relationships with business and industry Innovative activities; Agreements with the public and private sectors 5 Dissemination Publications, events and the mass media Museum of Natural History and Archaeology, NTNU Library 6 Organization and strategy Board and organization; Vision, goal and strategies; For more on terminology, see www.uhr.no/informasjon/index.htm (“terminologiliste”) See also www.ntnu.no/intersek/english_matters/ (”Selected administrative terms with translations”) 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

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

Introduction * figure from Statoil

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

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

Motivation Objective: using topside pressure for control PT 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

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

Modeling

Modeling: Simplified 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):

Experiments 3m

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

Observer Design

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

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

2. High-Gain Observer

2. High-Gain Observer where

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

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

Experimental Results

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

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

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

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

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

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

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

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

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!