« INVERSION-BASED CONTROL€¦ · • Inversion-based control methodology 2. Inversion of EMR...

EMR’18

Hanoi

June 2018

« INVERSION-BASED CONTROL

DEDUCED FROM EMR »

based on the course of Master

“Electrical Engineering for Sustainable Development”

Université Lille1

Prof. Alain BOUSCAYROL

L2EP, University of Lille, France

Prof. Pierre SICARD

GRÉI, Université du Québec à Trois Rivières, Canada

Prof. João P. TROVÃO

e-TESC, Université de Sherbrooke, Canada

Joint Summer School EMR’18

“Energetic Macroscopic Representation”

2

« Inversion-Based Control from EMR »

EMR’18, Hanoi, June 2018

- Objective: example of HEV control -

BAT

ICE

VSI EM

FuelParallel HEV Trans.

fast subsystem

controls

EM

control

ICE

control

Trans

control

Energy management

(supervision/strategy)

driver request

slow system

supervision

3



- Objective: example of HEV control -

BAT

ICE

VSI1 EM1

FuelParallel HEV Trans.

fast subsystem

controls

EM1

control

ICE

control

Trans

control

Energy management

(supervision/strategy)

driver request

slow system

supervision

EMR

How to define control

scheme 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

• Inversion of coupling elements

3. Inversion-based methodology structuring control

• Maximum control scheme

• Practical control schemes

4. Example of a paper processing system

EMR’18

Hanoi

June 2018

1. « Principle of

model-based control »

Prof. P. Sicard

(Université du Québec à Trois-Rivières, Canada)

6



Systeminput output

u(t) y(t)System-1(.)

wished

output

- 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.

7



Systeminput output

u(t) y(t)controller

wished

output

- Principle of closed-loop control -

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

8



Systemcause effect

- Principle of Inversion-based methodology -

desired effect

Control

right cause

measurements?

control = inversion of the causal path

1. Which structure? (how many controllers)

2. Which variables to measure?

3. How to tune controllers?

4. How to implement the control?

Inversion-based methodology

automatic control

industrial electronics

input output

[Hautier 96]

9



- 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 subsystem using

open-loop or closed-loop control

EMR’18

Hanoi

June 2018

2. « Inversion of

EMR elements »

11



?

Example:

- Inversion 1: single-input time-independant relationship -

output depends on a single input

without delay

Ku(t) y(t)

)( )( tuKty =

yref(t)uref (t)

1/K

direct

inversion

)(1

)( tyK

tu refref =

1. no measurement

2. no controller

(open-loop control) Assumption: K well-known and constant

Example: Resistance

1/R

R

vt) i(t)

)( 1

)( tvR

ti =

direct

inversion

)( )( tiRtv ref=

iref(t)v(t)

12



Manipulate u1

y2

u2

Objective: to control y2

y2-refu1-reg

u1

y1

y2 = f(u1 )

Ex : wheel

Wref = Vref / rwh

V= rwhW

T= rwh F

VrefWref

1rwh

- Inversion of a conversion element (1) -

13



?

Example:

- Inversion 2: multiple-input time-independant relationship -

Output depends on several inputs

without delay

u1(t) y(t)

)()( )( 21 tututy +=

yref(t)u1ref (t)

u2(t)+

+

1. measurement of the disturbance input

2. no controller

(open-loop control)

direct

inversion

)()()( 21 tutytu measrefref −=

+-

u1 is chosen to act on the output y

u2 becomes a disturbance input

Assumption: u2 can be measured

14



Manipulate u21 u1 is a disturbance

u1 y2

u2


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 )

- Inversion of a conversion element (2) -

Basic rule: as a first step, compensate all disturbances

assuming measurement is available.

15



?

Example:

- Inversion 3: single-input causal relationship -

output depends on a single input

and time (delay)

u(t) y(t)

dt )()( = tuty

yref(t)uref (t)

causality principle

direct

inversion

)()( tydt

dtu refref =

not possible

in real-time

dt

1. measurement of output

2. a controller is required

(closed-loop control)

indirect

inversion

)()()()( tytytCtu measrefref −=

closed loop controller

C(t)+-

16



- Example: PM-DC machine -

i

u

Lm rm

u i e

ireudt

diL mm −−=

multi-input causal relationship

irudt

diL mm −=

decomposition

euu −=

U(s)

E(s)-

+K

1+ts

U(s) I(s)

+

Uref (s)

+

direct

inversion

Iref(s)Uref(s)C(s)

+-

closed-loop

control

17



Manipulate u1 u2 is a disturbance


u2

y2

y1

u1 y2=f(u1, u2 )

f is in integral form

Direct inversion is

in derivative form

Approximate inversion

by closed loop control

Ex : rotating shaft

loadT

emTf

dt

dJ −=W+W

+

Wref

C(t)Tem_ref

Wmeas

+-

Tload_meas

+

measloadT

measreftC

refemT

_

))((_

+

W−W=

- Inversion of an accumulation element -

u1-ref y2-ref

u2-meas

y2-meas

18



u1m

u11

- Inversion of coupling elements -

y2

u2

y2-ref

kD1…kD(m-1)

no measurement

no controller

(m - 1) distribution

variables

−=

=

=

−−

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

Fbog1ref

Fbog4ref

Fbog2ref

Fbog3ref

kD1 kD3

kD2

19



- Inversion of EMR elements -

coupling element distribution criteria

conversion elementdirect inversion +

disturbance rejection

accumulation element

controller +

disturbance rejection

Legend

Control = light blue

Parallelograms

with dark blue

contour

direct

inversion

indirect

inversion

sensor

mandatory link

facultative link

EMR’18

Hanoi

June 2018

3. « Inversion-based methodology

structuring control »

21



y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 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)

22



delay delay

2. Tuning path

y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 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

23



2. Tuning path

y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 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:

- 4 sensors

- 2 closed-loop controllers

24



2. Tuning path

y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 x2 x3 x4 x5 x6 x7


- Practical control schemes -

x7-refx4-refx3-ref


4. Simplification of control

Simplifications:

- non-consideration of disturbances

- merging control blocks…

impact on the tuning and on

the performances

25



2. Tuning path

y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 x2 x3 x4 x5 x6 x7



x7-refx4-refx3-ref



5. Estimation of non-measured variables

y4-est

x7-est

from measured variables

26



2. Tuning path

y3 y4 y5 y6y1

S1y2 y7

z23 z56

S2

x1 x2 x3 x4 x5 x6 x7



x7-refx4-refx3-ref



5. Estimation of non-measured variables

6. Tuning of controllers

y4-est

x7-est

PI / PID / fuzzy controller?

Calculation of parameters?

27



2. Tuning path


- Inversion-based control of a system -

3. Inversion step-by-step


5. Estimation of variables

6. Tuning of controllers

Maximal Control Scheme

• mirror of the EMR (systematic)

• unique and theoretical solution

Practical Control Schemes

• several solutions (expertise)

• reduced performances

EMR’18

Hanoi

June 2018

4. « Example of a

paper processing system »

based on common papers at IEEE ISIE’2004 and IEEE-IECON 2006

Prof. Pierre Sicard1, Prof. Alain Bouscayrol2, Prof. Betty Lemaire Semail2

1 GRÉI, Université du Québec à Trois Rivières, Canada2 L2EP, Université Lille1, MEGEVH network, France

29



IM1 IM2

IM2

IM1

Paper processing

using 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]

[Djani 06]

30



- Maximum control structure -

iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc

roll 2 induction machine 2 VSI 2

DC Bus

Vdc

ivsi1svsi1

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

31




iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc


DC Bus

Vdc

ivsi1svsi1

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 Wim1-ref Tband-refvroll1-ref

2. PWM: Pulse Width Modulation

Tim1-ref

Fim1-ref

iim1-ref

1. FOC: Field Oriented Control

12

uvsi2-ref

Fim2-ref

iim2-refTim2-refWim2-refvroll2-ref

1 2

32




iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc


DC Bus

Vdc

ivsi1svsi1

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 Wim1-ref Tband-refvroll1-ref

2. PWM: Pulse Width Modulation

Tim1-ref

Fim1-ref

iim1-ref

1. FOC: Field Oriented Control

12

uvsi2-ref

Fim2-ref


1 2

33



- Practical control structures -

iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc


DC Bus

Vdc

ivsi1svsi1

uvsi1

VSI 1

DC Bus

uvsi1-ref Wim1-ref Tband-refvroll1-refTim1-ref

Fim1-ref

iim1-ref

12

uvsi2-ref

Fim2-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.

34




iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc


DC Bus

Vdc

ivsi1svsi1

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


Fim1-ref

iim1-ref

12

uvsi2-ref

Fim2-ref


1 2

Troll2_est

Wim2_est

Wim2_est

Tim2_est iim2

Wim2

closed-loop observer

35




iim1

iim1 eim1

Tim1

Wim1

Wim1

induction machine 1

Troll1

vroll1

roll 1

Tband

Tband

band

vroll2

Troll2

Wim2

Wim2

Tim2 iim2

iim2eim2

uvsi2svsi2

ivsi2

Vdc


DC Bus

Vdc

ivsi1svsi1

uvsi1

VSI 1

DC Bus


Fim1-ref

iim1-ref

12

uvsi2-ref

Fim2-ref


1 2

Step 6: choose and tune all controllers

(dynamic decoupling), and estimatorsPI controllers OK

except

EMR’18

Hanoi

June 2018

« Conclusion»

Inversion based control = inversion of EMR

based on the cognitive systemic

and the causality principle (energy)

Inversion rule for control scheme

closed-loop control to invert accumulation, direct inversion for

conversion element, degrees of freedom for coupling element

Different steps on the control scheme

From Maximum Control Scheme….

… to Practical Control Schemes

EMR’18

Hanoi

June 2018

« BIOGRAPHIES AND REFERENCES »

38



- Speaker & contributors -

Prof. Alain BOUSCAYROL

University of Lille 1, L2EP, MEGEVH, France

Coordinator of MEGEVH, French network on HEVs

PhD in Electrical Engineering at University of Toulouse (1995)

Research topics: EMR, HIL simulation, traction systems, EVs and HEVs

Prof. Pierre SICARD

Université du Québec à Trois-Rivières, GRÉI, Canada

Professor in electrical engineering

PhD in Electrical Engineering at Rensselaer Polytechnic Institute, USA (1993)

Research topics: EMR, nonlinear control, AI, traction systems, EVs and HEVs

Prof. João P. TROVÃO

Université de Sherbrooke, e-TESC Lab., Qc, Canada

PhD in Electrical Engineering at University of Coimbra (2012)

Research topics: Electric Vehicles, Multiple Energy Storages, Energy Management

39



- References -

[Barre 2006] 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.

[Bouscayrol 2000] 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).

[Bouscayrol 2006] 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, 53(6), pp. 1799-1806 (common paper of L2EP Lille and LEEI Toulouse).

[Bouscayrol 2012] 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

[Delarue 2003] 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, 28(8), pp. 1159-1324 (common paper L2EP and

Jeumont SA).

[Leclercq 2004] 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.

[Djani 2006] Djani Wankam, Y., P. Sicard, A. Bouscayrol "Maximum control structure of a five-drive paper system using

Energetic Macroscopic Representation," IEEE IECON’2006, Special Session Graphical Description for Modeling and

Control Power Systems, Paris, France, November 2006, 5332-5337.

[Sicard 2009] P. Sicard, A. Bouscayrol, “Inversion-based control of electromechanical systems”, EMR’09 summer school,

Trois-Rivières, Canada, September 2009

« INVERSION-BASED CONTROL€¦ · • Inversion-based control methodology 2. Inversion of EMR...

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