Control of the chemostat model - Météo-FranceChemostat with inhibition The chemostat model ° °...
Transcript of Control of the chemostat model - Météo-FranceChemostat with inhibition The chemostat model ° °...
![Page 1: Control of the chemostat model - Météo-FranceChemostat with inhibition The chemostat model ° ° ¯ °° ® S D X dt dX S S D k S X dt dS in P P I S K S S K S S 2 P P 0 20 40 60](https://reader033.fdocuments.us/reader033/viewer/2022053109/607c644102351b35e3555354/html5/thumbnails/1.jpg)
Control of the chemostat model J. Harmand, SAMI research team, LBE-INRA & INRA-INRIA
MODEMIC
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2/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Le LBE-INRA et MODEMIC
Treating and valorize biomass within a bioreffinery context
• INRA • About 80 people
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CONTEXT
An « explosion » of –omic data : a problematic of « big
data »
High computation capacity
A (very) important deficit in modeling eduction within
education in biology
How available data and modeling may help in better
understanding and controling bioproceses?
Jérôme HARMAND / Bernoulli semester / Lausasse, Switzerland / October 13-17 2014
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4/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
CONTENT
Microbial ecosystems and the chemostat…
Bioprocess modeling
Observing and controling the chemostat : a robust approach
An example : control of the anaerobic digestion process
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Microbial ecosystems and the
chemostat
_01
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6/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Les écosystèmes microbiens
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7/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
The chemostat
V, S, X
Qout
Qin
Sin
S, X
V, S, X
Qout
Qin
Sin
S, X
« Chemostat »
S k1X+k2P m(.)
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8/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Le chemostat
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9/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
High diversity of scales
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10/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
How using microbial ecosystems
Studying the functional heart of any bioprocess: a natural « complex » ecosystem
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11/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
An immense world…
You, your cat and your red
fish…
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12/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Conclusions
Microbial ecosystems : complex systems;
Used in a very high number of production/treatment fields
The chemostat is only 60 years old;
Important research effort…
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Modeling
_02
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14/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Lots of model!
Deterministic continuous dynamical models vs stochastic IBM
Campillo, 2011
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15/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Which model : the viewpoint of
microbiologist…
Usually, they only know the two extreme cases : EDO-based
and IBM (used for describing space)!
Thenuse of a model instead of another depends essentially
of their collaboration and of their own modeling culture!
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16/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
One or several models?
Such nonlinear models may be usefull for my research to
be applied…
Which model : the viewpoint of
modelists/mathematicians…
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17/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Until recently…
How modling an ideal bioprocess?
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18/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Modern biological tools reveal rather…
How modeling an ideal bioprocess?
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19/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
The associated continuous deterministic model
( )S"... of massOuput S"-" of massInput "
dt
SVd
n"consumptio"-"production"...
( )( )
( )
( ) ( )( )
in in
S SdS Q QS S X S S D X
dt V V Y Y
dX QS X X S D X
dt V
m m
m m
The chemostat model
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20/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Kinetic modeling
The chemostat model
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21/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Matching data : identifying yields and kinetics coefficients
The chemostat model
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22/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Conclusions
Important research on chemostat modeling;
To study microorganism growth (ecological questions);
To optimize its functioning…
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Observing and controling the
chemostat…
_03
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24/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Chemostat with inhibition
The chemostat model
( ) ( )
( )( )
XDSdt
dX
XSkDSSdt
dSin
m
m
( )
I
SK
SKS
SS
2
m
m
0 20 40 60 80 100 1200
0.005
0.01
0.015
10,10,045.0 IS KKm
D
( )Sm
inS S
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25/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Qualitative propserties of the model
The chemostat model
1 equilibrium : washout
3 equilibria : bistability
2 equilibria : 1 stable and one unstable (washout)
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26/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
State space representation
The chemostat model
Washout X=0
Cas #2 : Under the condition
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27/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Closing the loop
Controling the chemostat
Chemostat D S
Control Sc
Controled chemostat Sc S
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28/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Solution : Output Feedback
Example #1 : Linearizing feedback control Cf. Bastin et Dochain 1986 Example #2 : PI Controller Cf. Alvarez Lopez-Arenas 2012 (and many others) Example #N : …
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29/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Solution : Output Feedback
Exemple #1 : Linearizing feedback control Drawback : We must know everything! (mu + sin, s and x…) Assuming we only know s and we have uncertainty on others input and parameters,
how stabilizing the system with guaranteed performances?
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30/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Solution : A robust observer scheme
( ) ( )( ) 0ˆlim
txtxt
( )
( )
xgy
yuxfx
obs
obs
ˆˆ
,,ˆ̂
( )
( )
xgy
uxfx ,u
y
x
x̂
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31/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Solution : An interesting change of variables
( )( )( ) ( )
( )
( ) ( ) ( )( )
tStZYtX
ZZ
tDtZSdt
tZdin
ˆˆ
ˆ0ˆ
ˆˆ
0( ) in
tStZ
lim
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32/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Robustifying the asymptotic observer with respect to uncertainty (inputs + measurements + parameters)
( )( )( ) ( )
( )
( ) ( ) ( )( )
tStZYtX
ZZ
tDtZSdt
tZdin
ˆˆ
ˆ0ˆ
ˆˆ
0
( )
in
tStZlim
( )( )( ) ( )
( )
( ) ( ) ( )( )
tStZYtX
ZZ
tDtZSdt
tZdin
ˆˆ
ˆ0ˆ
ˆˆ
0
( )
in
tStZlim
![Page 33: Control of the chemostat model - Météo-FranceChemostat with inhibition The chemostat model ° ° ¯ °° ® S D X dt dX S S D k S X dt dS in P P I S K S S K S S 2 P P 0 20 40 60](https://reader033.fdocuments.us/reader033/viewer/2022053109/607c644102351b35e3555354/html5/thumbnails/33.jpg)
An exemple : controling the
anaerobic digestion process
_04
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34/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Application
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35/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
The model
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36/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
The robust observer : the inputs
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37/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
The robust observer : the measurements
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38/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
The robust estimations
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39/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Coupling the robust observer with the robust control design : application to the anaerobic digestion
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40/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Stabilizing the chemostat
Results : control and controled variable
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Conclusions and perspectives
_04
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42/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
Conclusions and perspectives
• Model of the chemostat
• Stabilizing robustly the chemostat
• Towards biocontrol approaches…
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43/43 Jérôme HARMAND / Colloque National sur l’Assimilation de Données / Toulouse / 1-3 décembre 2014
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