Public PhD defence

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Esmaeil Jahanshahi | Control Solutions for Multiphase Flow

Public PhD defence

Control Solutions for Multiphase FlowLinear and nonlinear approaches to anti-slug control

PhD candidate: Esmaeil JahanshahiSupervisors: Professor Sigurd Skogestad Professor Ole Jørgen Nydal

PhD Defence – October 18th 2013, NTNU, Trondheim

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Outline

• Modeling

• Control structure design- Controlled variable selection

- Manipulated variable selection

• Linear control solutions- H∞ mixed-sensitivity design

- H∞ loop-shaping design

- IMC control (PIDF) based on identified model

- PI Control

• Nonlinear control solutions- State estimation & state feedback

- Feedback linearization

- Adaptive PI tuning

- Gain-scheduling IMC

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Introduction

* figure from Statoil

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Slug cycle (stable limit cycle)

Experiments performed by the Multiphase Laboratory, NTNU

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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

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Modeling

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Modeling: Pipeline-riser case study

OLGA sample case:4300 m pipeline300 m riser100 m horizontal pipe9 kg/s inflow rate

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Modeling: Simplified 4-state model

State equations (mass conservations law):

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

1 , ,G G in G lpm w w

1 , ,L L in L lpm w w

2 , ,G G lp G outm w w

2 , ,L L lp L outm w w

1 : mass of gas in the pipelineGm

1 : mass of liquid in the pipelineLm

2 : mass of gas in the riserGm

2 : mass of liquid in the riserLm

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Simple model compared to OLGA

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Experimental rig

Pump

BufferTank

WaterReservoir

Seperator

Air to atm.

Mixing Point

safety valveP1

Pipeline

Riser

Subsea Valve

Top-sideValve

Water Recycle

FT water

FT air

P3

P4

P2

3m

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Simple model compared to experiments

Top pressure Subsea pressure

Experiment

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Modeling: Well-pipeline-riser system

OLGA sample case:3000 m vertical well320 bar reservoir pressure4300 m pipeline300 m riser100 m horizontal pipe

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Modeling: 6-state simplified model

, ,Gp G in G lpm w w

, ,Lp L in L lpm w w

, ,Gr G lp G outm w w

, ,Lr L lp L outm w w

,1( )gor

Gw r G ingorm w w

1,1

( )Lw r L ingorm w w

Pwh

Pbh

Pin

Prt , m,rt , L,rt

win

wout

Qout

Prb

Z1

Z2

Two new states:mGw: mass of gas in wellmLw: mass of liquid in well

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Model fitting using bifurcation diagrams

simplified modelolga simulations

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Control Structure Design

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Control Structure What to control? using which valve?

Pin

P2

Prb

WQ

L

m

Pwh

Pbh

Win

• Candidate Manipulated Variables (MV): 1. Z1 : Wellhead choke valve2. Z2 : Riser-base choke valve3. Z3 : Topside choke valve

• Candidate Controlled Variables (CVs):1. Pbh: Pressure at bottom-hole2. Pwh: Pressure at well-head3. Win: Inlet flow rate to pipeline4. Pin: Pressure at inlet of the pipeline5. Pt: Pressure at top of the riser6. Prb: Pressure at base of the riser7. Pr: Pressure drop over the riser8. Q: Outlet Volumetric flow rate9. W: Outlet mass flow rate10. m: Density of two-phase mixture 11. L: Liquid volume fraction

• Disturbances (DVs):– WGin: Inlet gas flow (10% around nominal)– WLin: Inlet liquid flow (10% around nominal)

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Control Structure Design: Method

SimplifiedModel

ControllabilityAnalysis

Simulations withLinearized Model

Simulations withNonlinear Model

Input-output pairs

Experiment

Robust input-output pairing

ComparingResults

good

bad

bad

bad

good

good

ComparingResults

Experiment or detailed model

Model fitting

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Controllability Analysis

• The state controllability is not considered in this work. We use the input-output controllability concept as explained by Skogestad and Postlethwaite (2005)

• Chapter 5, Chapter 6

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Minimum achievable peaks of S and T

,min ,min1

p

i

Ni

S T zpi i

z pM M M

z p

�0.01 0 0.01 0.02 0.03 0.04 0.05�0.03

�0.02

�0.01

0

0.01

0.02

0.03

Real axis

Imag

inar

y ax

is

Z=1.5%

Z=2%

Z=3%

Z=3.33% Z=5%

Z=1.5%

Z=2%

Z=3%

Z=4%Z=30%

Z=5%

Z=10%Z=15%

Z=20%

Z=21.8% Z=24% Z=30%

Z=5%

Z=10%Z=15%

Z=20%

Z=24%Z=30%

RHP �ZerosRHP �poles

Top pressure:Fundamentallydifficult to controlWith large valve opening

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Control Structure: Suitable CVs

• Good CVs – Bottom-hole pressure or subsea pressures

– Outlet flow rate

– Top-side pressure combined with flow-rate or density (Cascade)

• Bad CVs– Top-side pressure

– Liquid volume fraction

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Control Structure: Suitable MVsUsing top-side valveUsing riser-base valve

Wellhead valvecannot stabilizethe system

Experiment

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Nonlinearity of system

Process gain = slope

Experiment

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Linear Control Solutions

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y1

y2

K (s)

G (s)

W P

W u

W Ty

GENERALIZED PLANT P (s)

eu1

u2

+_

CONTROLLER

u

min ( ) ,u

TK

P

W KS

N K N W T

W S

1

1

1

( ( )) ( ( ))

( ( )) ( ( ))

( ( )) ( ( ))

u

T

P

KS j W j

T j W j

S j W j

Small γ means a better controller, but it depends on design specifications Wu, WT and WP

WP: PerformanceWT: RobustnessWu: Input usage

Solution 1: H∞ control based on mechanistic modelmixed-sensitivity design

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Solution 1: H∞ control based on mechanistic modelmixed-sensitivity design

10-2

10-1

100

101

0

20

40

60

80

Mag

[-]

10-2

10-1

100

101

100

150

200

250

Phas

e [d

eg]

[Rad/s]

10-2

10-1

100

101

10-2

100

102

|S|

Sensitivity transfer function

|S| |/WP|

10-2

10-1

100

101

10-2

100

102

|T|

Complementary sensitivity transfer function

|T| |/WT|

10-2

10-1

100

101

100

101

102

103

Input usage

[Rad/s]

|KS |

|KS| |/Wu|

Controller:

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0 2 4 6 8 10 12 14 16 18 2015

20

25

30

35

40

open-loop stable

open-loop unstable

inlet pressure (controlled variable)P

in [k

pa]

t [min]

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80

Controller Off Controller On Controller Off

open-loop stable

open-loop unstable

Zm

[%]

t [min]

actual valve position (manipulated variable)

Experiment

Solution 1: H∞ control based on mechanistic modelExperiment, mixed-sensitivity design

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Controller:

10-2

10-1

100

101

0

20

40

60

80

Mag

[-]

IMC H Mixed-sensitivity H Loop-shaping

10-2

10-1

100

101

50

100

150

200

250

Phas

e [d

eg]

[Rad/s]


10-2

10-1

100

101

10-2

10-1

100

101

102

|S|

Sensitivity transfer function


10-2

10-1

100

101

10-2

10-1

100

101

102

|T|

Complementary sensitivity transfer function


10-2

10-1

100

101

10-2

100

102

104

Input usage

[Rad/s]

|KS |


Solution 2: H∞ control based on mechanistic modelloop-shaping design

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0 5 10 15 20

15

20

25

30

35 open-loop stable

open-loop unstable

inlet pressure (controlled variable)P

in [k

pa]

t [min]

0 5 10 15 200

20

40

60

80

Controller OffController On

Controller Off

open-loop stable

open-loop unstable

Zm

[%]

t [min]


Experiment

Solution 2: H∞ control based on mechanistic modelExperiment - loop-shaping design

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Solution 3: IMC based on identified modelModel identification

First-order model is not a good choice

First-order unstable with time delay:

Closed-loop stability:

Steady-state gain:

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Solution 3: IMC based on identified modelModel identification

Fourth-order mechanistic model:

Hankel Singular Values:

Model reduction:

4 parameters need to be estimated

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Solution 3: IMC based on identified modelIMC design

Bock diagram for Internal Model Control system

IMC for unstable systems:

y u e r + _ Plant( )C s

Model:

IMC controller:

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Solution 3: IMC based on identified modelPID and PI tuning based on IMC

IMC controller can be implemented as a PID-F controller

PI tuning from asymptotes of IMC controller

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20

40

60

80

Mag

nitu

de (

dB)

10-4

10-3

10-2

10-1

100

101

90

135

180

225

Pha

se (

deg)

Bode Diagram

Frequency (rad/s)

---- IMC/PID-F

---- PI

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Solution 3: IMC based on identified modelExperiment

0 20 40 60 80 100 120 14023

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25

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27

Pin

[kpa

]

t [sec]

data set-point filtered identified

Closed-loop stable:

Open-loop unstable:

IMC controller:

Experiment

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Solution 3: IMC based on identified modelExperiment

PID-F controller:

PI controller:

0 2 4 6 8 10 12 14 16 18 2015

20

25

30

35

40

open-loop stable

open-loop unstable

inlet pressure (controlled variable)

Pin

[kpa

]

t [min]

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80


Controller Off

open-loop stable

open-loop unstable

Zm

[%]

t [min]


0 2 4 6 8 10 12 14 16 18 2015

20

25

30

35

40

open-loop stable

open-loop unstable


Pin

[kpa

]

t [min]

0 2 4 6 8 10 12 14 16 18 200

20

40

60

80


Controller Off

open-loop stable

open-loop unstable

Zm

[%]

t [min]


Experiment

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Comparing linear controllers

• IMC controller does not need any mechanistic model• IMC controller is easier to tune using the filter time constant

• H ∞ loop-shaping controller results in a faster controller that stabilizes the system up to a larger valve opening

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Experiments on medium-scale S-riser

Open-loop unstable:

IMC controller:

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PID-F controller:

PI controller:

Experiment

Experiments on medium-scale S-riser

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Nonlinear Control Solutions

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PTNonlinear observer K

Statevariables

uc

uc

Pt

Solution 1: observer & state feedback

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High-Gain Observer

1 1

2 2

3 3

4 4

ˆ ˆ( )

ˆ ˆ( )

1ˆ ˆˆ( ) ( )

ˆ ˆ( )

m

z f z

z f z

z f z y y

z f z

1 : mass of gas in the pipeline ( )gpz m

2 : mass of liquid in the pipeline ( )lpz m

3 ,: pressure at top of the riser ( )r tz P

4 : mass of liquid in the riser ( )lrz m

,

( )

g r

LrG r

rr t

l

RT

mM

m

VP

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State Feedback

0

ˆˆ( ) ( ( ) ) ( ( ) )t

c ss i inu t K x t x K P r d

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

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0 50 100 150 200 250 3002.75

2.8

2.85

x 104

Pbh

[kPa]

0 50 100 150 200 250 3006600

680070007200

740076007800

Pwh

[kPa]

0 50 100 150 200 250 300

9

10

11

12

win [kg/s]

0 50 100 150 200 250 3005000

5200

5400

5600

Pr,t

[kPa]

0 50 100 150 200 250 3000

10

20

30

time [min]

wout

[kg/s]

0 50 100 150 200 250 3000

0.05

0.1

0.15

0.2

Z (valve opening)

0 50 100 150 200 250 300-0.5

0

0.5

1

time [min]

K1

K2

K3

K4

K5

Control signal

Nonlinear observer and state feedbackOLGA Simulation

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High-gain observer – top pressure

measurement: topside pressurevalve opening: 20 %

Experiment

0 5 10 15 20 25 30 35

20

30

40

time [min]

P1 [k

pa g

auge

]

subsea pressure (estimated by observer)

Open-Loop Stable

Open-Loop Unstable

actualobserverset-point

0 5 10 15 20 25 30 350

5

10

15

time [min]

P2 [k

pa g

auge

]

top-side pressure (measurement used by observer)

Open-Loop Stable

Open-Loop Unstable

actualobserver

0 5 10 15 20 25 30 350

20

40

60

ControllerOff

Controller On Controller Off

Open-Loop Stable

Open-Loop Unstable

time [min]

Zm

[%]

top-side valve actual position

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Fundamental limitation – top pressure

,min1

pNi

Si i

z pM

z p

Z = 20% Z = 40%

Ms,min 2.1 7.0

Measuring topside pressure we can stabilize the system only in a limited range

RHP-zero dynamics of top pressure

-0.1 0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9-0.2

-0.15

-0.1

-0.05

0

0.05

0.1

0.15

Real axis

Imag

inar

y ax

is

Z=5% Z=95%Z=5% Z=95%

Z=15%

Z=20%

Z=30%

Z=45%

Z=60% Z=95%

Z=15%

Z=20%

Z=30%

Z=45%

Z=60%Z=95%

RHP-Zeros

RHP-poles

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High-gain observer – subsea pressure

measurement: subsea pressurevalve opening: 20 %

Experiment

0 2 4 6 8 10

20

30

40 Open-Loop Stable

Open-Loop Unstable

time [min]

P1 [k

pa g

auge

]

subsea pressure (measurement used by observer)

actualobserver

0 2 4 6 8 100

5

10

15 Open-Loop Stable

Open-Loop Unstable

time [min]

P2 [k

pa g

auge

]

top-side pressure (estimated by observer)

actualobserver

0 2 4 6 8 100

20

40

60

Controller Off

Open-Loop Stable

Open-Loop Unstable

time [min]

Zm

[%]

top-side valve actual position Not working ??!

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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

2 ( )f x1( )f xrtP

inP

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• Anti-slug control with top-pressure is possible using fast nonlinear observers

• The operating range of top pressure is still less than subsea pressure• Surprisingly, nonlinear observer is not working with subsea pressure,

but a (simpler) linear observer works very fine.

Method \ CV Subsea pressure Top Pressure

Nonlinear Observer Not Working !? Working

Linear Observer Working Not Working

PI Control Working Not Working

Max. Valve 60% 20%

Nonlinear observer and state feedbackSummary

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Solution 2: feedback linearization

PT

PT

Nonlinear controller

ucPrt

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Solution 2: feedback linearizationCascade system

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Output-linearizing controllerStabilizing controller for riser subsystem

System in normal form:

Linearizing controller:

Control signal to valve:

dynamics bounded

: riser-base pressure : top pressure

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0 5 10 15 2010

20

30

40

t [min]

Prb

[kP

a]

riser-base pressure (controlled variable)

open-loop stable

open-loop unstable

set-point

measurement

0 5 10 15 200

5

10

15 open-loop stable

open-loop unstable

topside pressure (measurement used by controller)

t [min]

Prt [

kPa]

0 5 10 15 200

50

100Controller Off Controller On Controller Off

open-loop stableopen-loop unstable

t [min]

Zm

[%

]


Experiment

0 10 20 30 40 50 60 70 80 90 10010

20

30

40

50

Z1 [%]

Pin

[kpa

]

min & max steady-state

0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

Z1 [%]

Prt [k

pa]


Gain:

CV: riser-base pressure (y1), Z=60%

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0 5 10 15 20

20

30

40

open-loop stable

open-loop unstable

riser-base pressure (measurement used by controller)

t [min]

Prb

[kP

a]

0 5 10 15 200

5

10

15

t [min]

Prt [

kPa]

topside pressure (controlled variable)

open-loop stable

open-loop unstable

set-point

measurement

0 5 10 15 200

50

100

Controller Off Controller On Controller Off

open-loop stable

open-loop unstable

t [min]

Zm

[%

]


Experiment

CV: topside pressure (y2), Z=20%

y2 is non-minimum phase

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Solution 3: Adaptive PI Tuning

0 10 20 30 40 50 60 70 80 90 10010

20

30

40

50

Z1 [%]

Pin

[kpa

]


0 10 20 30 40 50 60 70 80 90 1000

5

10

15

20

25

30

Z1 [%]

Prt [k

pa]


Static gain:

Linear valve:

PI Tuning:

slope = gain

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Experiment

Solution 3: Adaptive PI TuningExperiment

0 5 10 15 20 25 3015

20

25

30

35

40

open-loop stable

open-loop unstable


Pin

[kpa

]

t [min]

0 5 10 15 20 25 300

20

40

60

80

open-loop stable

open-loop unstable

Zm

[%]

t [min]


0 5 10 15 20 25 30-100

-50

0 open-loop stable

Kc [-

]

t [min]

proportional gain

0 5 10 15 20 25 30

200

400

600

I [se

c]

t [min]

integral time

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Solution 4: Gain-Scheduling IMC

Three identified model from step tests:

Z=20%:

Z=30%:

Z=40%:

Three IMC controllers:

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Solution 4: Gain-Scheduling IMCExperiment

0 5 10 15 2015

20

25

30

35

40

open-loop stable

open-loop unstable


t [min]

Pin

[kP

a]

0 5 10 15 200

5

10

15 open-loop stable

open-loop unstable

topside pressure

t [min]

Prt [

kPa]

0 5 10 15 200

50

100

open-loop stable

open-loop unstable

t [min]

Zm

[%

]


Experiment

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Comparison of Nonlinear Controllers

• Gain-scheduling IMC is the most robust solution• Gain-scheduling IMC does not need any mechanistic model• Adaptive PI controller is the second controller, and it is based on a

simple model for static gain• 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)

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Conclusions

• A new simplified model verified by OLGA simulations and experiments• Suitable CVs and MVs for stabilizing control were identified• Anti-slug control using a subsea valve close to riser-base• Online PID and PI tuning rules for anti-slug control• New linear and nonlinear control solutions were developed and tested

experimentally• We showed that …

– Simple methods work better for process control

– Fundamental controllability limitations are idependant from control design

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Acknowledgements

Thank you!

• SIEMENS: Funding of the project• Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh,

Henrik Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.

Documents

Public PhD defence