Adaptive Control of Simulated Moving Bed Plants Using Comsol’s … · 2009-01-29 · Marco...

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]


Contents

Adaptive Control of Simulated Moving Bed Plants Using Comsol’s

Simulink InterfaceIntroductionModeling of SMB plants


Conclusions

• Introduction

• Modeling of SMB plants

• Control of SMB plants

• Conclusions


Introduction to chromatography

How we can separate a mixture of two components?

Introduction



Conclusions One way is to make use of different adsorption affinities of components

BAA B+A+B



Introduction



Conclusions

Consider a simple pipe



Introduction



Conclusions

which is filled up with adsorption materials

Consider a simple pipe



Now, a bucket with a mixture of two components dissolved in an eluent is pumped through this adsorption column.

Introduction



Conclusions



Introduction



Conclusions

The more retained component B takes more time to travel through the column as the less retained component A.



Therefore, chromatography provides a simple method to separate components.

Introduction



Conclusions


Introduction to simulated moving bed

How one can achieve a continuous separation?

Introduction



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)



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



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



Introduction



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


Modeling

Modeling of a chromatographic columnG. Guiochon, B. Lin, Modeling for Preparative Chromatography, Academic Press, San Diego ( 2003)

Introduction



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= ,


Modeling

Comsol ImplementationComsol®

Multyphysics Users Guide, Comsol AB, Sweden, http://www.comsol.se ( 2005)

Introduction



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


Modeling

Coupling of columns

Introduction



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


Introduction



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:


Control of SMB Plants

Why control?

Introduction



Conclusions

1. robust operation in presence of disturbances

2. minimize running costs e.g. reducing eluent consumption


Control of SMB Plants for complete separation

Introduction



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



Introduction



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 = , , ,



Introduction



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



Introduction



Conclusions

ÎVÊxVˆFeVˆRaV ŜT

,Â 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


Conclusions

Introduction



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.


End of Presentation

Introduction



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

Adaptive Control of Simulated Moving Bed Plants Using Comsol’s … · 2009-01-29 · Marco...

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