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Polytech’ Paris SudJune 2014
«« IINVERSIONNVERSION--BBASED ASED CCONTROL ONTROL
DEDUCED FROM DEDUCED FROM EMREMR »»
Prof. B. Lemaire-Semail, Prof. A. Bouscayrol(Université Lille1, L2EP, France)
based on the course of Master“Electrical Engineering for Sustainable Development”
Université Lille1
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Objective: example of HEV control -
BAT
ICE
VSI EM
FuelParallel HEV Trans.
fast subsystemcontrols
EMcontrol
ICEcontrol
Transcontrol
Energy management(supervision/strategy)
driver request
slow systemsupervision
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Objective: example of HEV control -
BAT
ICE
VSI1 EM1
FuelParallel HEV Trans.
fast subsystemcontrols
EM1control
ICEcontrol
Transcontrol
Energy management(supervision/strategy)
driver request
slow systemsupervision
EMR
How to define controlscheme of complex systems?
(Structure? sensors?)
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EMR, Paris Sud, June 2014
- Outline -
1. Principle of model-based control• Open-loop and closed-loop controls• Inversion-based control methodology
2. Inversion of EMR elements• Inversion of accumulation elements• Inversion of conversion elements
3. Inversion-based control structures• Maximum control schemes• Practical control schemes
4. Example of a paper processing system
Polytech’ Paris SudJune 2014
1.1. «« Principle of Principle of modelmodel--based control based control »»
Prof. P. Sicard(Université du Québec à Trois-Rivières, Canada)
Prof. A. Bouscayrol(Université Lille1, L2EP, France)
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EMR, Paris Sud, June 2014
- Cybernetic systemic approach -
control
or “Black box” approach: no internal knowledge
in out identification test:observation of out(t) from selected in(t)
Behavior model: out(t) = f(t) in(t)
closed-loop control of out(t):for uncertainty compensationsoutref
Limitations: • limited validity range of the model• risk of physical “mistake”• non-optimal management of internal energy
multi-physical complex energetic systems?
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Cognitive systemic approach -
control
or “White box” approach: prior internal knowledge
in outKnowledge model:out(t) = f(t) in(t)
control = inversion of model:(closed loop = an inversion way)
in out
outref
Physical laws ofsystem components
Limitations: • physical knowledge of each subsystem• functions are not all reversible
multi-physical complexenergetic systems?
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
area xdt
knowledge of past evolution
OK inreal-time
Principle of causalityphysical causality is integral input output
cause effect
t1
t
x
knowledge of future evolution
slopedtdx
?
impossible inreal-time
- Causality principle and control -
CONTROL =real-time processmanagement
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
Systeminput output
u(t) y(t)System-1(.)
wishedoutput
- Open-loop control and inversion -
Controlling a system for output tracking can be interpreted as inverting the system
[Sicard 09]
yref(t)
control
… if we can implement a good approximation of the system’s inverse.
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
Systeminput output
u(t) y(t)controller
wishedoutput
- Principle of closed-loop control -
A closed-loop control is required when:• the model is not invertible, • the model is ill known or too complex, • and for robustness purpose.
[Sicard 09]
yref(t)
control
Controller objectives:• tracking of reference changes• rejection of disturbances and uncertainties
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
Systemcause effect
- Principle of Inversion-based methodology -
desired effectControl
right cause
measurements?
control = inversion of the causal path
1. Which algorithm? (how many controllers)2. Which variables to measure?3. How to tune controllers?4. How to implement the control?
Inversion-based methodology
automatic controlindustrial electronics
input output
[Hautier 96]
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- EMR and Inversion-based methodology -
desired effectright cause
measure?
SS1
causeeffect
inputoutputSS2 SSn
C1 C2 Cn
measure?measure?
EMR = system decomposition in basic energetic subsystems (SSs)
Remember,divide and conquer!
Inversion-based control: systematic inversion of each subsystems usingopen-loop or closed-loop control
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Mirror effect -
desired effectright cause
SS1
causeeffect
SS2 SSn
C1 C2 Cn
The control scheme is developed as a mirror of the model
[Hautier 96] [Bouscayrol 03]
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Mirror effect: example of cascaded control loops -
Well-known cascaded control loops can be described in the same may
SS1
y(t)C1
yref(t)SS2C2
SS1
y(t)SS2
yref(t)C2C1
u(t)
u(t)
Submodels
Functionalinverses
Polytech’ Paris SudJune 2014
2. 2. «« Inversion of Inversion of EMR elements EMR elements »»
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Inversion of I/O relationships -
Systemin(t) out(t)
outref(t)Algorithm?
in(t)
measurements?
Control
There are 3 basic inversion categories:1. Single-input time independent relationships (incl. conversion elements)2. Multiple-input time independent relationships (incl. coupled conversion
elements)3. Single-input causal relationships (accumulation elements)
Other inversion schemes can be deduced from these basic inversions.[Barre 06]
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EMR, Paris Sud, June 2014
?
Example:
- Inversion 1: single-input time-independant relationship -
output depends on a single inputwithout delay
Ku(t) y(t)
)( )( tuKty
yref(t)u (t)1/K
directinversion
)(1)( tyK
tu ref
1. no measurement2. no controller(open-loop control) Assumption: K well-known and constant
Example: Resistance
1/R
R
vt) i(t)
)( 1)( tvR
ti
directinversion
)( )( tiRtv refiref(t)v(t)
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
?
Example:
- Inversion 2: multiple-input time-independant relationship -
Output depends on several inputswithout delay
u1(t) y(t))()( )( 21 tututy
yref(t)u1 (t)
u2(t)+
+
1. measurement of the disturbance input2. no controller(open-loop control)
directinversion
)()()( 21 tutytu measref
+-
u1 is chosen to act on the output y
u2 becomes a disturbance input
Assumption: u2 well-known and can be measured
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
?
Example:
- Inversion 3: single-input causal relationship -
output depends on a single input and time (delay)
u(t) y(t)
dt )()( tuty
yref(t)u (t)
causality principle
directinversion
)()( tydtdtu ref
not possible in real-time
dt
1. measurement of output2. a controller is required(closed-loop control)
indirectinversion
)()()()( tytytCtu measref
closed loop controller
C(t)+-
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Example: PM-DC machine -
i
u
Lm rm
u i e
ireudtdiL mm
multi-input causal relationship
irudtdiL mm
decomposition
euu
U(s)
E(s)-
+ K1+s
U(s) I(s)
+
U (s)
+direct
inversion
Iref(s)Uref(s)C(s)
+-closed-loop
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
Manipulate u21 u1 is a disturbance
u1 y2
u2
Objective: to control y2
y2-refu1-meas
uHb= mHb VDC
iHb= mHb idcm
Ex : H-bridge chopper
mHb = uHb_ref / VDC_meas
uHb_ref⁄ ×
mHbVDC_meas
y1 u21
y2 = f(u1, u21 )
Basic rule: at first, compensate all disturbances assuming measurement is available.
- Inversion of a conversion element (1) -
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
2. Manipulate u1 u21 is a disturbance
y2
u2u21
Objective: to control y2
u1
y1
gear= kgear1
Tgear = kgear Tload
Ex : speed gearbox
1_ref = gear_ref / kgear_meas
kgear_meas
gear_ref×1_ref
⁄
y2 = f(u1, u21 )
- Inversion of a conversion element (2) -
u1-reg y2-ref
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
3. Manipulate u1
y2
u2
Objective: to control y2
y2-refu1-reg
u1
y1
Ex : pulley or roller
y2 = f(u1 )
1_ref = trans_ref / rtpull
Vtrans= rpull1
Ttrans = rtpull Fload
Vtrans_ref1_ref
1rtpull
- Inversion of a conversion element (3) -
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
Manipulate u1 u2 is a disturbance
Objective: to control y2
u2
y2
y1
u1 y2=f(u1, u2 )
f is in integral form
Direct inversion isin derivative form
Approximate inversionby closed loop control
Ex : rotating shaft
loadTemTfdtdJ
+
ref
C(t)Tem_ref
meas
+-
Tload_meas
+
measloadTmeasreftCrefemT
_
))((_
Basic rule: compensate disturbances or linearize dynamics, then design a controller to obtain the desired dynamics.
- Inversion of an accumulation element -
u1-reg y2-ref
u2-meas
y2-meas
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
i
u
U(s)
E(s)-
+ K1+s
U(s) I(s)
+
U (s)
+
Iref(s)Uref(s)C(s)
+-
iu
Lm rm
u i e
ireudtdiL mm
- Example: PM-DC machine -
iref
emeas
imeas
u
ei
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
u1m
u11
- Inversion of coupling elements -
y2
u2
y2-ref
kD1…kD(m-1)
no measurement no controller
(m - 1) distributionvariables
refDim
refmDm
refD
yku
yku
yku
21
2)1()1(1
2111
)1(
...
y11
u11
y1m
u1m
Fbog4
Fbog2
Fbog3
vtrain
vtrain
vtrain
vtrain
Example: chassis of a train
Fbog1
vtrain
Ftot
Ftot-ref
Fbog1
Fbog4
Fbog2
Fbog3
kD1 kD3kD2
next lecture!
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Inversion of EMR elements -
coupling element distribution criteria
conversion element direct inversion +disturbance rejection
accumulation elementcontroller +
disturbance rejection
Legend
Control = light blue Parallelogramswith dark bluecontour
directinversion
indirectinversion
sensor
mandatory link
facultative link
Polytech’ Paris SudJune 2014
3. 3. «« InversionInversion--based methodology based methodology for control structures for control structures »»
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Maximum control scheme -
EMR depends on:- the study objective (limits between system and sources)- the physical laws of subsystems (physical causality)- the association of subsystems (systemic approach)
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
delay delay
2. Tuning path
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Maximum control scheme -
The tuning path is:- dependant on the technical requirements (chosen tuning input / output to control)- independent of the power flow direction
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EMR, Paris Sud, June 2014
2. Tuning path
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Maximum control scheme -
x7-refx6-refx5-refx4-refx3-ref
3. Inversion step-by-step Strong assumption: all variables can be measured!
Maximal Control Structure (or scheme):- maximum of sensors- maximum of operations
Example:- 6 sensors- 2 closed-loop controls
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
2. Tuning path
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Practical control schemes -
x7-refx4-refx3-ref
3. Inversion step-by-step Strong assumption: all variables can be measured!
4. Simplification of controlSimplifications:- non-consideration of disturbances- merging control blocks…
impact on the tuning and/onthe performances
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
2. Tuning path
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Practical control schemes -
x7-refx4-refx3-ref
3. Inversion step-by-step Strong assumption: all variables can be measured!
4. Simplification of control
5. Estimation of non-measured variables
y4-est
x7-est
from measured variables
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
2. Tuning path
y3 y4 y5 y6y1S1
y2 y7z23 z67
S2x1 x2 x3 x4 x5 x6 x7
1. EMR of the system
- Practical control schemes -
x7-refx4-refx3-ref
3. Inversion step-by-step Strong assumption: all variables can be measured!
4. Simplification of control
5. Estimation of non-measured variables
6. Tuning of controllers
y4-est
x7-est
PI / PID / fuzzy controller?Calculation of parameters?
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
2. Tuning path1. EMR of the system
- Inversion-based control of a system -
3. Inversion step-by-step
4. Simplification of control5. Estimation of variables6. Tuning of controllers
Maximal Control Scheme• mirror of the EMR (systematic)• unique and theoretical solution
Practical Control Schemes• several solutions (expertise) • reduced performances
Polytech’ Paris SudJune 2014
4. 4. «« Example of a Example of a paper processing system paper processing system »»
Prof. A. Bouscayrol, Prof. B. Lemaire-Semail(Université Lille1, L2EP, France)
Prof. P. Sicard(Université du Québec à Trois-Rivières, Canada)
based on common paper at IEEE-IECON 2006
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
IM1 IM2
IM2
IM1
Paper processingusing 2 induction machines
Technical requirements:- paper tension control for high quality of paper roll- winding velocity control for high quality of processing
- Paper processing system as an example -
[Leclerc 04][Barre 06]
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Maximum control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
Step 2a: identify all variables to be controlled (outputs) and control inputs
Step 2b: identify tuning paths from inputs to outputs, avoiding crossing the paths
Step 1: develop the EMR of the system
DC Bus
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Maximum control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
DC Bus
Step 3: invert each element of the tuning paths by applying inversion rules• assume that all the signals are measurable;• compensate for all disturbances.
uvsi1-ref im1-ref Tband-refvroll1-ref
2. PWM: Pulse Width Modulation
Tim1-ref
im1-ref
iim1-ref
1. FOC: Field Oriented Control
12
uvsi2-ref
im2-ref
iim2-refTim2-refim2-refvroll2-ref
1 2
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Maximum control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
DC Bus
Maximal Control Structure• 16 sensors (including 2 ac components for currents and voltages)• 5 closed-loop controls (including 2 controllers of dimension 2 for currents)
uvsi1-ref im1-ref Tband-refvroll1-ref
2. PWM: Pulse Width Modulation
Tim1-ref
im1-ref
iim1-ref
1. FOC: Field Oriented Control
12
uvsi2-ref
im2-ref
iim2-refTim2-refim2-refvroll2-ref
1 2
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Practical control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
DC Bus
uvsi1-ref im1-ref Tband-refvroll1-refTim1-ref
im1-ref
iim1-ref
12
uvsi2-ref
im2-ref
iim2-refTim2-refim2-refvroll2-ref
1 2
Step 4: Simplify the MCS: group operations, do not reject disturbances explicitly. — Impact will be on cost, on processing time and on performance
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Practical control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
DC Bus
Step 5: Estimate non-measured variables, e.g. disturbances that cannot be neglected, and estimate unknown or time varying parameters
uvsi1-ref im1-ref Tband-refvroll1-refTim1-ref
im1-ref
iim1-ref
12
uvsi2-ref
im2-ref
iim2-refTim2-refim2-refvroll2-ref
1 2
Troll2_est
im2_est
im2_est
Tim2_est iim2
im2
closed-loop observer
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Practical control structure -
iim1
iim1 eim1
Tim1
im1
im1
induction machine 1
Troll1
vroll1
roll 1
Tband
Tband
band
vroll2
Troll2
im2
im2
Tim2 iim2
iim2eim2
uvsi2 svsi2
ivsi2
Vdc
roll 2 induction machine 2 VSI 2
DC Bus
Vdc
ivsi1 svsi1
uvsi1
VSI 1
DC Bus
uvsi1-ref im1-ref Tband-refvroll1-refTim1-ref
im1-ref
iim1-ref
12
uvsi2-ref
im2-ref
iim2-refTim2-refim2-refvroll2-ref
1 2
Step 6: choose and tune all controllers(dynamic decoupling), and estimators PI controllers OK
except
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
vroll2_mes
urefvroll1_ref
west
Tband-refyref
Tband_mes
- Band controller -
Tband vroll2
vroll1 Tband
band
Tband-refvroll1-ref
vroll1
w
Tbandy
vroll2
u
Details using Causal Ordering Graph (COG) [Hautier 96]
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Simulation results -
Velocity of roll 2 (m/s) vs time (s)
0
2
Tension of band (pu) vs time (s)0 2 4 6
1
-10 2 4 6
1
4
3
2
0
00 2 4 6
1
2
without compensation
of west
Tension of band (pu) vs time (s)
with compensation
of west
reference
Simulation results
Polytech’ Paris SudJune 2014 «« Conclusion Conclusion »»
Inversion based control = inversion of EMRbased on the cognitive systemicand the causality principle (energy)
Inversion rule for control schemeclosed-loop control to invert accumulation, direct inversion forconversion element, degree of freedom for coupling element
Different steps on the control schemeFrom Maximum Control Scheme….
… to Practical Control Schemes….… to the strategy level
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- Different control levels -
BAT
ICE
VSI1 EM1
FuelParallel HEV Trans.
fast subsystemcontrols
EM1control
ICEcontrol
Transcontrol
Energy management(supervision/strategy)
driver request
slow systemsupervision
EMR
Inversion-based control
NextStepStrategy (supervision)
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«« InversionInversion--Based Control from EMR Based Control from EMR »»
EMR, Paris Sud, June 2014
- References -
P. J. Barre, A. Bouscayrol, P. Delarue, E. Dumetz, F. Giraud, J. P. Hautier, X. Kestelyn, B. Lemaire-Semail, E. Semail, "Inversion-based control of electromechanical systems using causal graphical descriptions", IEEE-IECON'06, Paris, November 2006.
A. Bouscayrol, B. Davat, B. de Fornel, B. François, J. P. Hautier, F. Meibody-Tabar, M. Pietrzak-David, “Multimachine multiconverter system: application for electromechanical drives”, European Physics Journal - Applied Physics, vol. 10, no. 2, May 2000, p. 131-147 (common paper GREEN Nancy, L2EP Lille and LEEI Toulouse, according to the SMM project of the GDR-SDSE).
A. Bouscayrol, M. Pietrzak-David, P. Delarue, R. Peña-Eguiluz, P. E. Vidal, X. Kestelyn, “Weighted control of traction drives with parallel-connected AC machines”, IEEE Transactions on Industrial Electronics, December 2006, vol. 53, no. 6, p. 1799-1806 (common paper of L2EP Lille and LEEI Toulouse).
A. Bouscayrol, J. P. Hautier, B. Lemaire-Semail, "Graphic Formalisms for the Control of Multi-Physical Energetic Systems", Systemic Design Methodologies for Electrical Energy, tome 1, Analysis, Synthesis and Management, Chapter 3, ISTE Willey editions, October 2012, ISBN: 9781848213883
P. Delarue, A. Bouscayrol, A. Tounzi, X. Guillaud, G. Lancigu, “Modelling, control and simulation of an overall wind energy conversion system”, Renewable Energy, July 2003, vol. 28, no. 8, p. 1159-1324 (common paper L2EP and Jeumont SA).
A. Leclercq, P. Sicard, A. Bouscayrol, B. Lemaire-Semail,"Control of a triple drive paper system based on the Energetic Macroscopic Representation", IEEE-ISIE'04, Ajaccio (France), May 2004, pp. 889-893.
P. Sicard, A. Bouscayrol, “Inversion-based control of electromechanical systesm”, EMR’09 summer school, Trois-Rivières, Canad,a, September 2009