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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

2

«« 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

3



- Objective: example of HEV control -

BAT

ICE

VSI1 EM1



EM1control

ICEcontrol

Transcontrol


driver request


EMR

How to define controlscheme of complex systems?

(Structure? sensors?)

4



- 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


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)

6



- 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?

7



- 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?

8



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

9



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.

10



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

11



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]

12



- 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

13



- 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]

14



- 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


2. 2. «« Inversion of Inversion of EMR elements EMR elements »»

16



- 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]

17



?

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)

18



?

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

19



?

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)+-

20



- 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

21



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) -

22



2. Manipulate u1 u21 is a disturbance

y2

u2u21


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 )


u1-reg y2-ref

23



3. Manipulate u1

y2

u2


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


24



Manipulate u1 u2 is a disturbance


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

25



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

26



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!

27



- 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


3. 3. «« InversionInversion--based methodology based methodology for control structures for control structures »»

29



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)

30



delay delay

2. Tuning path

y3 y4 y5 y6y1S1

y2 y7z23 z67

S2x1 x2 x3 x4 x5 x6 x7



The tuning path is:- dependant on the technical requirements (chosen tuning input / output to control)- independent of the power flow direction

31



2. Tuning path

y3 y4 y5 y6y1S1

y2 y7z23 z67

S2x1 x2 x3 x4 x5 x6 x7



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

32



2. Tuning path

y3 y4 y5 y6y1S1

y2 y7z23 z67

S2x1 x2 x3 x4 x5 x6 x7


- Practical control schemes -

x7-refx4-refx3-ref


4. Simplification of controlSimplifications:- non-consideration of disturbances- merging control blocks…

impact on the tuning and/onthe performances

33



2. Tuning path

y3 y4 y5 y6y1S1

y2 y7z23 z67

S2x1 x2 x3 x4 x5 x6 x7



x7-refx4-refx3-ref


4. Simplification of control

5. Estimation of non-measured variables

y4-est

x7-est

from measured variables

34



2. Tuning path

y3 y4 y5 y6y1S1

y2 y7z23 z67

S2x1 x2 x3 x4 x5 x6 x7



x7-refx4-refx3-ref


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?

35



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


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

37



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]

38



- 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

39




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


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

40




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


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


1 2

41



- 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


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


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

42




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


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


im1-ref

iim1-ref

12

uvsi2-ref

im2-ref


1 2

Troll2_est

im2_est

im2_est

Tim2_est iim2

im2

closed-loop observer

43




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


DC Bus

Vdc

ivsi1 svsi1

uvsi1

VSI 1

DC Bus


im1-ref

iim1-ref

12

uvsi2-ref

im2-ref


1 2

Step 6: choose and tune all controllers(dynamic decoupling), and estimators PI controllers OK

except

44



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]

45



- 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

47



- Different control levels -

BAT

ICE

VSI1 EM1



EM1control

ICEcontrol

Transcontrol


driver request


EMR

Inversion-based control

NextStepStrategy (supervision)

48



- 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

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