1
Closed-loop model identification and PID/PI
tuning for robust anti-slug control
Esmaeil Jahanshahi
Sigurd Skogestad
Department of Chemical Engineering,
NTNU, Trondheim, Norway
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Outline
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•
•
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•
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Introduction
New 4-state nonlinear model
New procedure to identify linear unstable slug-model
IMC Design for unstable slug process
PID(F) and PI tuning
Dealing with nonlinearity:
1.
2.
Gain scheduling
Adaptive tuning
• Experiments
• OLGA Simulations
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Slug cycle (stable limit cycle)
Experiments
performed by
the Multiphase
Laboratory,
NTNU
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Experimental mini-loop (2003)
Ingvald Bårdsen, Espen Storkaas,
Heidi Sivertsen
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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z
p2
Experimental mini-loop
Valve opening (z) = 100%
p1
SLUGGING
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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z
p2
Experimental mini-loop
Valve opening (z) = 25%
p1
SLUGGING
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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z
p2
Experimental mini-loop
Valve opening (z) = 15%
p1
NO SLUG
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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z
Experimental mini-loop:
Bifurcation diagram
p2
p1
No slug
Valve opening z %
Slugging
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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How to avoid slugging?
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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z
Design change
p2
Avoid slugging:
1. Close valve (but increases pressure)
No slugging when valve is closed
p1
Valve opening z %
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Design change
Avoid slugging:
2. Design change to avoid slugging
z
p2
p1
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Design change
Minimize effect of slugging:
3. Build large slug-catcher
z
p2
p1
• Most common strategy in practice
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Avoid slugging:
4. ”Active” feedback control
PC
ref
z
PT
p
1
Simple PI-controller
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Anti slug control: Mini-loop
experiments
p1
[bar]
z
[%]
Controller ON
Controller OFF
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Anti slug control: Full-scale offshore
experiments at Hod-Vallhall field (Havre,1999)
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Summary anti slug control (2008)*
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Stabilization of desired non-slug flow regime = $$$$!
Stabilization using downhole pressure simple
Stabilization using topside measurements difficult
Control can make a difference!
• “Only” problem: Not sufficiently robust
*Thanks to: Espen Storkaas + Heidi Sivertsen + Håkon Dahl-Olsen + Ingvald Bårdsen
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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2009-2013: Esmaeil Jahanshahi, PhD-work supported by Siemens
1st step:
New Experimental mini-rig
P2
Top-side Air to atm.
Valve
Seperator
3m
Riser
P1
safety valve
P3
FT water
Buffer
Tank
FT air
Mixing Point
Pipeline
P4
Subsea Valve
Water
Reservoir
Pump
Water Recycle
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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2nd step: New Simplified 4-state model*
Choke valve with opening Z
mG1 : mass of gas in the pipeline
mL1 : mass of liquid in the pipeline
mG 2 : mass of gas in the riser
mL 2 : mass of liquid in the riser
x3, P2,VG2, ρG2 , HLT
P0
wmix,out
L3
x1, P1,VG1, ρG1, HL1
x4
wL,in
wG,in
w
L2
h>hc
wG,lp=0
wL,lp
x2
h
L1
θ
hc
State equations (mass conservations law):
*Based on Storkaas model
mG1
mL1
mG 2
mL 2
 wG ,in  wG ,lp
 wL ,in  wL ,lp
 wG ,lp  wG , out
 wL ,lp  wL ,out
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
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New 4-state model. Comparison with
experiments:
Top pressure
Subsea pressure
Nonlinear: Process gain = slope - approaches zero for large z
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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3rd step:
Experimental linear model (new approach)
Fourth-order mechanistic model:
7 parameters need to be estimated
Hankel Singular Values:
Model reduction:
4 parameters need to be estimated
Stable part has little dynamic effect
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Model Identification: Closed-loop step
response using P-controller
Experiment 1: Z=20% (valve opening)
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Comparison with mechanistic model. Z=20%
1
10
0
10
Mag [-]
Identified model:
-1
10
-2
10
Mechanistic model
Identified model
-3
10
-2
Phase [deg]
10
100
Mechanistic model:
-1
0
10
1
10
10
0
-100
Mechanistic model
Identified model
-200
-2
10
-1
0
10
10
1
10
 [Rad/s]
29
Pin [kpa ]
28
Excellent agreement!
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Experimental data
Identified model
Mechanistic model
26
25
0
20
40
60
80
100
120
140
t [sec]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Comparison with mechanistic model. Z=30%
0
10
-1
10
Mag [-]
Identified model:
-2
10
-3
10
-4
Phase [deg]
10
-2
10
100
Mechanistic model:
-1
0
10
1
10
10
0
-100
Mechanistic model
Identified model
-200
-2
10
-1
0
10
10
1
10
 [Rad/s]
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Pin [kpa ]
Mechanistic model
Identified model
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Experimental data
Identified model
Mechanistic model
25
24
0
20
40
60
80
100
120
140
t [sec]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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IMC Design for Unstable Process
Bock diagram for Internal Model Control system
IMC for unstable systems:
r
e
+ _
C (s)
u
Plant
Model:
y
IMC controller:
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
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IMC controller based on identified model
z=30%
inlet pressure (controlled variable)
40
open-loop stable
Pin [kpa ]
35
30
25
20
15
open-loop unstable
0
2
4
6
8
10
12
14
16
18
20
t [min]
actual valve position (manipulated variable)
80
open-loop unstable
Zm [%]
60
Controller On
Controller Off
Controller Off
40
20
0
open-loop stable
0
2
4
6
8
10
12
14
16
18
20
t [min]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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PIDF and PI Tuning based on IMC
IMC controller can be implemented as a PIDF controller
Bode Diagram
80
---- IMC/PIDF
---- PI
Magnitude (dB)
60
40
20
Phase (deg)
0
225
PI tuning from asymptotes of IMC controller
180
135
90
-4
10
-3
10
-2
10
-1
10
0
10
1
10
Frequency (rad/s)
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
28
PIDF versus PI control. Experiment (z=30%)
(IMC)
= PIDF controller
PI controller
inlet pressure (controlled variable)
inlet pressure (controlled variable)
40
open-loop stable
30
25
20
15
open-loop unstable
0
2
4
6
8
10
12
14
open-loop stable
35
Pin [kpa ]
35
Pin [kpa ]
40
30
25
20
16
18
15
20
t [min]
open-loop unstable
0
2
Controller On
Controller Off
Controller Off
40
20
0
8
10
12
14
16
18
20
open-loop unstable
60
Zm [%]
Zm [%]
80
open-loop unstable
60
6
t [min]
actual valve position (manipulated variable)
actual valve position (manipulated variable)
80
4
Controller On
Controller Off
Controller Off
40
20
open-loop stable
0
2
4
6
8
10
t [min]
12
14
16
18
20
0
open-loop stable
0
2
4
6
8
10
12
14
16
18
20
t [min]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Experiments on medium-scale S-riser
Open-loop unstable:
IMC controller (PIDF):
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
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Experiments on medium-scale S-riser
PID-F controller:
PI controller:
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Dealing with nonlinearity
1. Gain-scheduling
2. Adaptive controller gain
50
min & max
steady-state
Pin [kpa ]
40
30
slope = gain
20
10
0
10
20
30
40
50
60
70
80
90
100
Z [%]
1
30
Prt [kpa ]
25
min & max
steady-state
20
15
10
5
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
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Solution 1: Gain-Scheduled PIDF
Three identified model from step tests:
Z=20%:
Z=30%:
Z=40%:
Three IMC (PIDF) controllers:
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
33
Gain-Scheduled PIDF
Experiment
inlet pressure (controlled variable)
40
open-loop stable
Pin [kPa]
35
30
25
open-loop unstable
20
15
0
5
10
15
20
t [min]
topside pressure
open-loop stable
Prt [kPa]
15
10
open-loop unstable
5
0
0
5
10
15
20
t [min]
actual valve position (manipulated variable)
100
Zm [%]
open-loop unstable
50
0
open-loop stable
0
5
10
15
20
t [min]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
34
Solution 2: Adaptive PI Tuning
50
min & max
steady-state
Static gain:
Pin [kpa ]
40
slope = gain
30
20
10
0
10
20
30
40
50
60
70
80
90
100
Z [%]
1
30
Linear valve:
Prt [kpa ]
PI Tuning:
min & max
25
steady-state
20
15
10
5
0
0
10
20
30
40
50
60
70
80
90
100
Z [%]
1
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
35
Adaptive PI Tuning. Experiment
inlet pressure (controlled variable)
40
open-loop stable
30
25
open-loop unstable
20
15
proportional
gain
open-loop
stable
0
0
5
10
15
20
25
30
t [min]
Kc [-]
Pin [kpa ]
35
-50
actual valve position (manipulated variable)
80
open-loop unstable
-100
0
5
10
20
0
15
20
25
30
20
25
30
t [min]
integral time
40
600
open-loop stable
0
5
10
15
t [min]
20
25
30
I [sec]
Zm [%]
60
400
200
0
5
10
15
t [min]
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
36
“Direct” nonlinear approaches
Solution 3: High-gain observer + state
feedback: Did NOT work with bottom
pressure (CDC, Dec. 2013)
Solution 4: Output linearizing controller + Pcontrol: Worked well, but gain-scheduled IMC
more robust with respect to time delay (CDC,
Dec. 2013)
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
37
Solution 4: Output-linearizing controller
Stabilizing controller for riser subsystem
System in normal form:
: riser-base pressure
: top pressure
Linearizing controller:
dynamics bounded
Control signal to valve:
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
Experiment
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Solution 4: Output-linearizing controller
Z=60%
riser-base pressure (controlled variable)
Prb [kPa]
40
open-loop stable
30
open-loop unstable
set-point
measurement
20
10
0
5
10
15
20
t [min]
Prt [kPa]
topside pressure (measurement used by controller)
open-loop stable
15
10
open-loop unstable
5
0
0
5
10
15
Gain:
20
t [min]
actual valve position (manipulated variable)
50
min & max
100
Controller On
Controller Off
50
0
open-loop unstable
open-loop stable
0
5
10
15
Pin [kpa ]
Zm [%]
Controller Off
steady-state
40
30
20
20
10
t [min]
0
10
20
30
40
50
60
70
80
90
100
Z [%]
1
30
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust
anti-slug
control
min & max
steady-state
25
OLGA Simulations
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Solution 2: Adaptive PI Tuning
OLGA Simulations
bottom pressure, P 1
68
measurement
set-point
1
P [bara]
67.5
67
66.5
0
1
2
3
time [h]
4
5
6
valve opening, Z
0.5
Set-point
Z [%]
0.4
0.3
0.2
X: 5.289
Y: 0.2324
0.1
0
0
1
2
3
time [h]
4
5
67.36
67.19
67.07
66.99
66.93
66.88
Valve
opening
14
16.1
18.2
20.1
23.24
--
Kc
Ti
0.5
0.7
0.94
1.23
1.56
1.93
8400
9600
10800
12000
13200
14400
6
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control
40
Conclusions
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•
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•
•
A 4-state mechanistic model verified by experiments
Identify unstable slug-model from closed-loop step test
Good agreement between identified and mechanistic models
IMC design works well and gives PIDF controller
Nonlinear “fixes” (adaptive gain or gain scheduling) work well
Acknowledgement:
• SIEMENS: Funding of the project
• Master students: Anette Helgesen, Knut Åge Meland, Mats Lieungh, Henrik
Hansen, Terese Syre, Mahnaz Esmaeilpour and Anne Sofie Nilsen.
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Sigurd Skogestad | Closed-loop
model identification and PID/PI tuning for robust anti-slug control