adaptive control of simulated moving bed plants using comsol’s … · 2009-01-29 · marco...
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Adaptive Control of Simulated Moving Bed Plants Using Comsol’s Simulink Interface
Speaker:Marco Fütterer
Institut für AutomatisierungstechnikOtto-von-Guericke Universität
Universitätsplatz 2, D-39106 MagdeburgGermany
e-mail: [email protected]
mailto:[email protected]
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Contents
Adaptive Control of Simulated Moving Bed Plants Using Comsol’s
Simulink InterfaceIntroductionModeling of SMB plants
Control of SMB plants
Conclusions
• Introduction
• Modeling of SMB plants
• Control of SMB plants
• Conclusions
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
How we can separate a mixture of two components?
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions One way is to make use of different adsorption affinities of components
BAA B+A+B
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Consider a simple pipe
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
which is filled up with adsorption materials
Consider a simple pipe
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
Now, a bucket with a mixture of two components dissolved in an eluent is pumped through this adsorption column.
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
The more retained component B takes more time to travel through the column as the less retained component A.
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to chromatography
Therefore, chromatography provides a simple method to separate components.
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to simulated moving bed
How one can achieve a continuous separation?
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Port-shifting A
,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeV
II
I
III
IV
FeU
ExU RaU
IU
B A
A B+
A+B
Several chromatographic columns are arranged in a circle, where the feedings and drains are shifted cyclically.
Source: D.B. Broughton, G. Gerhold, US Patent, 2 985 589 (1961)
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to simulated moving bed
Port-shifting A
,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeV
II
I
III
IV
FeU
ExU RaU
IU
B A
A B+
A+B
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
The four zones may be arranged in a plane to plot the associated concentration profile in cyclic-
steady-state above the columns.
I II III IV
ElV ExV FeV RaV
Bc Ac
,A Pc
,B Pc
zAcv
Bcv
I II III IV
,Ac sv
,Bc sv
B A B+A+B
A
The spatial coordinate is chosen so that this always begins with the first zone
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction to simulated moving bed
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
The four zones may be arranged in a plane to plot the associated concentration profile in cyclic-
steady-state above the columns.
Port-shifting A
,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeV
II
I
III
IV
FeU
ExU RaU
IU
B A
A B+
A+B
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Modeling
Modeling of a chromatographic columnG. Guiochon, B. Lin, Modeling for Preparative Chromatography, Academic Press, San Diego ( 2003)
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions ( ) ( ) ( ),0
,,0 ii in i
z
c t zD Ac t c tV zε
=
∂= −
∂i A B= ,
right boundary:
left boundary:
initial:( ), 0i
z L
c t zz =
∂=
∂i A B= , ( ) ( ),00,i ic z c z= i A B= ,
( ) 22
,,A A BA A Al
q c cc c cF v Dt t z z
∂∂ ∂ ∂+ =− +
∂ ∂ ∂ ∂
( ) 22
,,B A BB B Bl
q c cc c cF v Dt t z z
∂∂ ∂ ∂+ =− +
∂ ∂ ∂ ∂
1F εε−
=
lVvAε
=
0 L z
fluid concentration
adsorbed concentration
volumetric flow rate
void fraction
cross section area
diffusion
V
ε
A
D
q
c
( fast adsorption)
( ),i i A Bq q c c=adsorption behavior
i A B= ,
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Modeling
Comsol ImplementationComsol®
Multyphysics Users Guide, Comsol AB, Sweden, http://www.comsol.se ( 2005)
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
( ) ,TA Bc c=u
1,
1
A A
A B
B B
A B
q qF Fc cq qF Fc c
∂ ∂⎛ ⎞+ ⋅ ⋅⎜ ⎟∂ ∂⎜ ⎟=⎜ ⎟∂ ∂
⋅ + ⋅⎜ ⎟∂ ∂⎝ ⎠
ad
,T
A BA B
V c V cc D c DA z A zε ε
⎛ ⎞∂ ∂= ⋅ − ⋅ ⋅ − ⋅⎜ ⎟⋅ ∂ ⋅ ∂⎝ ⎠
Γ
( )0 0 .T=F
t∂⋅ + ∇ ⋅ =∂aud Γ F
,T∂⎛ ⎞− ⋅ = + ⋅⎜ ⎟∂⎝ ⎠
Rn Γ G μu
=R 0
, ,0 ,T
A in B inzV Vc cA Aε ε=
⎛ ⎞= ⋅ ⋅⎜ ⎟⋅ ⋅⎝ ⎠
G
,T
A Bz LV Vc cA Aε ε=
⎛ ⎞= − ⋅ − ⋅⎜ ⎟⋅ ⋅⎝ ⎠
G
( )0 0 0 .T
zz L==
=R
Comsol’s pde equation in general form:
boundary condition in general form:
M. Fütterer, Proc. of the European COMSOL Conf. 2007http://www.comsol.se/academic/papers/3309
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Modeling
Coupling of columns
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
External flow-
rates: 0 El Fe Ex RaV V V V= + − −
I IV ElV V V= + , , , ,i in I I i out IV IVc V c V⋅ = ⋅ ,i A B=
II I ExV V V= − , , , , ,i in II i out I i Exc c c= =
III II FeV V V= + , , , , ,i in III III i out II II i Fe Fec V c V c V⋅ = ⋅ + ⋅
IV III RaV V V= − , , , , ,i Ra i in IV i out IIIc c c= =
Eluent feed:
Extract-
drain:
Feed:
Raffinate-
drain:
,i A B=
,i A B=
Port-shifting A
,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeV
II
I
III
IV
FeU
ExU RaU
IU
-
On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
,01 B A
BB A B A
H HcK H H H
−= ⋅
⋅ + , ,0B Fe Bc c>
( ) ( )( ) ( )
2
,, 2 2
,
B A B B Fe B AB AB P
B A B A B B Fe B A
H H K c H HH HcK H H H K c H H
+ ⋅ ⋅ − −−= ⋅
⋅ + ⋅ ⋅ + −
( ) ( ) ( ) ( ) ( )( ) ( )( )
222, , , ,
, 2 2,
1 4
2
1B A A Fe A B A A Fe B Fe B A A FeB A
A P
A B A B Fe B A
A A B A
A B
H H c H H H c cK K K K
K
H H cH Hc
H H KH c H H
⋅ ⋅ + ⋅ ⋅ ⋅ ⋅ − ⋅
⋅
⎛ ⎞− + ⋅ ⋅ + − − ⋅⎜ ⎟− ⎝ ⎠
⋅⋅
⋅ + −⋅=
+
( ) ( )( )( )
( )( )
( )( )
2
,2
2
, ,
,
,
,
,
2
2
, ,
,
1
1
B I B I
FeB I
FeB I
A FeRa Fe
A IV A P
Fe
B A B A
I B B FeB A
B A
Ex B B FeB A
B AS
B A B B Fe
H H F H HV K c
F H H
H HV K c
H H
H HF A LTF H H K
V
V
cV V
c
cV
τ τ
τ
τ
τ
⎡ ⎤+ ⋅ ⋅ − ⋅ − +⎣ ⎦= ⋅ ⋅ ⋅⋅ −
+= ⋅ ⋅ ⋅
−
⋅
⋅
= ⋅⋅
−⋅= ⋅ ⋅
+ + ⋅ ⋅ I II III IVElV ExV FeV RaV
Bc Ac
,A Pc
,B Pc
zAcv
Bcv
I II III IV
,Ac sv
,Bc sv
M. Fütterer, Chem. Eng. Tech., 2009, 32http://dx.doi.org/10.1002/ceat.200800397
, , , ,I Ex Fe Ra SV V V V T ?Determining Operating points
Port-shifting A
,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeV
II
I
III
IV
FeU
ExU RaU
IU
ST
1i i
ii i
H cqK c⋅
=+ ⋅
adsorption behavior
,A Fec ,B Fec FeV ,0 1B Iτ ≤ ,0 1A IVτ ≤Given:
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Control of SMB Plants
Why control?
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
1. robust operation in presence of disturbances
2. minimize running costs e.g. reducing eluent consumption
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Control of SMB Plants for complete separation
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Model the essential dynamic
( ) ( ) ( ) ( ) [ ]0 1L Sz k v k k T kτ τΔ = , ∈ ,
( ) ( ) ( )( ) ( )1R Sz k v k k T kτΔ = −
( ) ( )1L Rz k L z kΔ + = −Δ
( ) ( ) ( ) ( ) ( )( ) ( )1 1 1 1S Sv k k T k L v k k T kτ τ+ + + = − −
•
UV-
sensor mounted between two columns of one zone
•
keep all controls fixed during one switching time
•
model only the foot point movement.
( ) ( ) ( )( ) ( )( ) ( )1
11 1
S
S
L v k k T kk
v k T kτ
τ− −
+ =+ +
L
UV- sensor
( )v k ( )v k
( ),c t z ( ),Sc t T z+
( )Lz kΔ ( )Rz kΔ( )1Lz kΔ +
L L( ), UVc t z
tSTSTτ
M. Fütterer, Chem. Eng. Tech., 2008, 31 ( 10), 1438.http://dx.doi.org/10.1002/ceat.200800277
A,A Rac ,B Rac
RaV
ElV
B,A Exc ,B Exc
ExV
,A Fec ,B FecFeVzone II
zone I
zone III
zone IV
FeU
ExU RaU
IU
1UV 4UV
2UV 3UV
1
2
3
4 5
6
7
8
SMB with 8 columns
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Control of SMB Plants for complete separation
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Use a P- controller with ideal open loop control:
( ) ( )( )ˆ ˆ0.25i i i ref i iu k y y kθ θ,= − ⋅ − ⋅ 1 2 3 4i = , , ,
M. Fütterer, Chem. Eng. Tech., 2008, 31 ( 10), 1438.http://dx.doi.org/10.1002/ceat.200800277
( ) ( ) ( ) ( ) ( ) ( )( )ˆ ˆ ˆ1 1 1i i i i ik k a u k y k y kθθ θ= − + − ⋅ − ⋅ −Use a parameter estimator for model parameters:
1aθ < 1 2 3 4i = , , ,
( ) ( )i iu k V k= 1 2 3 4i = , , , ( ) ( )5 Su k T k=( ) ( ) ( )5i iu k u k u k= ( ) ( )1i iy k kτ= −
( ) ( ) ( )( )( )1 1
1 i i iii
u k y ky k
u kθ − − −
+ =
Rename the variables to make it nice for control peoples.
model equations:
( ) ( )i ii
Lv k V kθ
= ⋅ * * *i i i Su V Tθ = = ⋅
1 2 3 4i = , , ,
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Control of SMB Plants for complete separation
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
Simulation Results
0 10 20 30 40 50 60 70 806.5
7
7.5
8
8.5
9
9.5
10
10.5
11x 10
-5
tstept / [ min]
θ 1, θ
2, θ
3, θ
4 / [
m3 ]
0 10 20 30 40 50 60 70 800
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8
0.9
1
tstept / [ min]
τ I, τ
II, τ I
II, τ I
V
t
, ,ˆ2A Fe A Fec c= ⋅
, ,ˆ0.5B Fe B Fec c= ⋅,ˆB Fec,ˆA Fec
( ),A Fec t( ),B Fec t
stept
0 10 20 30 40 50 60 70 800
50
100
150
200
250
300
tstept / [ min]
T S /
[ s]
c A, c
B / [
mol
/ m3 ]
ElV ExV FeV RaV
1 2 3 4 5 6 7 8
1UV 2UV 3UV 4UV
zone I zone II zone III zone IV
ElV ExV FeV RaV
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.90
0.2
0.4
0.6
0.8
1
1.2
extract
feed
raffinatez / [m]
c A, c
B / [
mol
/ m3 ]
cAcB
1 2 3 4 5 6 7 8
1UV 2UV 3UV 4UV
zone I zone II zone III zone IV
a counter stepdisturbance
( )1
i ii i
i i
H cq cK c
=+ ,i A B=
M. Fütterer, Proc. of the European COMSOL Conf. 2008http://www.comsol.se/academic/papers
t
, ,ˆ2A Fe A Fec c= ⋅
, ,ˆ0,5B Fe B Fec c= ⋅,ˆB Fec,ˆA Fec
stept
( ),A Fec t( ),B Fec t
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Control of SMB Plants for complete separation
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
ˆIVˆExVˆFeVˆRaV ŜT
,ˆA Fec ,ˆB Fec
adaptive controller
,A Fec ,B Fec
SMBprocess
IV
ExV
FeV
RaV
ST
1,Refτ,A Exc,B Exc
,B Rac,A Rac
controllerparameter
disturbance
references
2,Refτ3,Refτ4,Refτ
Control concept with minor a-priori knowledge.
More knowledge is not necessary than for operation in open loop!
Plug and Play solution
positions of foot points
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
Conclusions
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
An adaptive control concept of SMB plants was successfully implemented and tested using Comsol®
Multiphysics
and Matlab®
Simulink®.
Comsol
is a powerful tool to model complex dynamic systems described by partial differential equations.
Comsol’s
interface to Matlab
Simulink
provides control designers a simple way to design and test control loop’s in familiar Simulink
environment.
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On Adaptive Control of Simulated Moving Bed PlantsMarco Fütterer, 6. Nov. 2008
End of Presentation
Introduction
Modeling of SMB plants
Control of SMB plants
Conclusions
•
Details can be found at Comsol’s
conference CD.
•
The full simulation example will be made public for everyone.
Thank You
Adaptive Control of Simulated Moving Bed Plants Using Comsol’s Simulink InterfaceContentsIntroduction to chromatographyIntroduction to chromatographyIntroduction to chromatographyIntroduction to chromatographyIntroduction to chromatographyIntroduction to chromatographyIntroduction to simulated moving bedIntroduction to simulated moving bedIntroduction to simulated moving bedModelingModelingModelingDetermining Operating pointsControl of SMB PlantsControl of SMB Plants�for complete separationControl of SMB Plants�for complete separationControl of SMB Plants�for complete separationControl of SMB Plants�for complete separationConclusionsEnd of Presentation