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Energy management of a hybrid electric vehicle : anapproach based on type-2 fuzzy logic

Javier Enrique Solano Martinez

To cite this version:Javier Enrique Solano Martinez. Energy management of a hybrid electric vehicle : an approach basedon type-2 fuzzy logic. Other. Université de Franche-Comté, 2012. English. <NNT : 2012BESA2007>.<tel-00947626>

N° d'ordre : 2012006 Année 2012

THESE

présentée pour obtenir le grade de

Docteur de l'Université de Franche-Comté École Doctorale : Sciences pour l'Ingénieur et Microtechniques

Spécialité : Sciences pour l'Ingénieur

Par

Javier SOLANO MARTÍNEZ Ingénieur, Universidad Industrial de Santander, Bucaramanga, Colombie

M.Sc., Université de Franche-Comté Belfort, France ___________________

Modélisation et supervision des flux énergétiques à bord d'un véhicule hybride lourd : approche par logique floue de type-2

Energy management of a hybrid electric vehicle:

an approach based on type-2 fuzzy logic

Soutenue le 8 février 2012 devant le jury composé de :

M. Bernard DAVAT Président du jury Université de Lorraine

M. Hamid GUALOUS Rapporteur Université de Caen Basse-Normandie

M. Benoît ROBYNS Rapporteur Ecole des Hautes Etudes d'Ingénieur, Lille

M. Michel AMIET Examinateur Direction Générale de l'Armement, DGA

M. Bob JOHN Examinateur De Montfort University, Royaume-Uni

M. Joeri VAN MIERLO Examinateur Vrije Universiteit, Belgique

M. Daniel HISSEL Directeur de la thèse Université de Franche-Comté

Mme. Marie-Cécile PERA Co-directrice de la thèse Université de Franche-Comté

M. Samuel HIBON Membre invité ALSTOM Transport

Thèse européenne préparée en collaboration entre l'Institut FEMTO-ST (Département ENERGIE, UMR CNRS 6174, dans le cadre de l'Institut FCLAB) et le Centre for Computational Intelligence, De Montfort University,

Leicester, Royaume-Uni

♥♦♠♥ts

♠ r② rt t r♥r t ♦r ♥ t r ♦ ♠② tss ♦♠♠tt

♥♦ît ♦②♥s ♥ ♠ ♦s ♦r tr r ♦ t ♠♥sr♣t ♥ t sst♦♥s

t② ♠ t♦ ♠♣r♦ t ♦r ❱♥ r♦ ♦rt ♦♥ ♠t ♥ ♠ ♦♥

①♠♥rs ♦ t P ♦r tr ♣rt♣t♦♥ ♥ tr ♥trst♥ qst♦♥s r♥ ♠②

tss ♥

♦ t♦ t♥ ♠② s♦rs ♥ ss ♥ ré Pér ♦r tr ♦♥st♥t

♣rs♦♥ ♥ ♣r♦ss♦♥ s♣♣♦rt ♥ ♥ tr♦♦t ts tss ♠ r② rt

t t♠ ♥♦t ♦♥② ♦r tr t s♦ ♦r trst♥ ♥ ♠② ♦r t s ♥ ♣sr

♥ ♣r ♦r♥ t t♠

♠st s♦ ♥♦ rst♦♣ s♣♥t ♣r♦ss♦r ♦ t ❯♥rst② ♦ r♥

♦♠té ♥ ♣r♥♣ s♦r r♥ ♠② s ♥♦t ♦♥② rt rsrr t s♦

s ♥ ①♣t♦♥ ♣rs♦♥ ♦ tr② ♠r

♥s ♦s t♦ t st ♦ ♠t♦ ♦rt♦r② ♥s t♦ ♥ r ♥ érô♠

♦t ♦ ♣ ♠ t♦ t ♥ t♦ ♠♣r♦ ♠② rsr ♥ s♦ ♠② ts ♥

②♦♦t ♥s t♦ r♥ ③ ♦ ♣ ♠ t t ①♣r♠♥t st♣ t

♥s t♦ s rst♥ ♥ r♥ r② ♦r tr ♣ ♥ t q♦t♥

♥s s♦ ♦s t♦ t ♣rt♥rs ♦ t ♣r♦t ♠t ♦ ♥♥r♥

t t r♥ r♠② ♦r ♥ ♠ t ♦♣♣♦rt♥t② t♦ ♦r ♥ ts ♥trst♥

♣r♦t ♥s t♦ ♥ ♦ ♥ t st ♦ P ♥ ♦r

tr ♥♥ss

♠ rt t ♦rt ♦♥ ♠♦♥ ♦♣♥ t♣♥ tts ③♦♥♦

♥ t ♠♠rs ♦ t r② ♥♦② ♦r♥ ♥ sr♥ t t♠

r♥ t s♠♠r ♠ rt t♦ t P ♦t♦r s♦♦ ♦ t ❯♥rst② ♦

r♥♦♠té ♦r t ♥♥ s♣♣♦rt t♦ rs ts ♣rt ♦ ♠② rsr t str ♥

❯♥t ♥♦♠

♠ rt t t ①♣rts ♦ ♥② ♣t t♦ ♣rt♣t ♥ t sr② t♦

s♥ t s②st♠ ③③② ♦ ♦♥tr♦r ♦ r ♥sttt

r♥ rst♦♣r ♦♠s ❯♥rst② ♦ Pr♦r♥ r♠♥② r♦ P♥t♦ ❯♥

rst② ♦ P♦rt♦ P♦rt ♥ ♥♠ ♥ ss ♥ ré Pér ❯♥

rsté r♥♦♠té ❱♥t ③♦ ♥ó♥ ♣r srr♦♦ ró♥♦

r♦♥ ♣♥ ❨♥ ♥ r♥ ❯♥rst② ♥ rr② q P P♦t t

rö♥ r♥ ♥ ♦ï ♦♦♥ ❯♥rsté à r♦sèrs ♥

s♦ ♥♦ ♠ ♦♥ ♦ s ♠ t ♦♣♣♦rt♥t② t♦ ♦♥t♥ ♠② rsr

s ♣♦st♦t♦r rsrr t st♦♠ r♥s♣♦rt ♥ s♦ ♦r t t♠ ♦s ♠ t♦

♣r♣r ♠② P ssrtt♦♥ ♠ ♦♥ tt ♦r♥ ♥ ♦♣t♠ ♦♥tr♦ s

r② ♥trst♥ ♦♥t♥t♦♥ ♦ ♠② rsr

♦ t♦ t♥s ♠② r♥s ♥ ♦s t ♦rt ♥ ♦s r♥ç♦s

r② ❱♥♥t érô♠ ss ♥ st♥② t r ② r♥s t str

t♣♥ ♥ ❩♦② ♦♥ ♥ s ♠② ♦s t ♦rt ♥rs ♥ ❱t♦r

♦r r♦ ♥rés ❲♠ ♠t r♥ r♦s t ♥

♥② ♠ rt t ♠② ♠② ♥ t r ♦ s♣♣♦rt ♠ tr♦ t

♠② ♥r ♥ t ♥srs

♠② ♥r ♥rst♥ ②

♠② ♥r ♣r♦ t ♥♦ t♦ tr

t ♥♦ tt st t♦ tr②

♦♥ Ptr r♠ tr

és♠é

tr♥s♣♦rt s ♣rs♦♥♥s t s ♠r♥ss r♣rés♥t ♣s ♦♥s♦♠

♠t♦♥ é♥r t st ♥ s ♣r♥♣s s♦rs ♣♦t♦♥ ♥s ♠♦♥ Psrs

♦rts ♦♥t êtr ts ♣♦r rér é♣♥♥ ♣étr♦ ♦♥s♦♠♠t♦♥ é♥r

t ♠♣t ♥r♦♥♥♠♥t s s②stè♠s tr♥s♣♦rt ♥s tt ♣rs♣t rt♦♥

é♥ér r♠♠♥t s♦t♥ ♦♥♣t♦♥ t rést♦♥ ♥ t♦♥

♦♠♣♦s♥ts ♥ trq st ♥ ♦rt♦r ♠♦ q ♣r♠t

ér ♥s s ♦♥t♦♥s tst♦♥ rés s ér♥ts ♦♠♣♦s♥ts é♥rétqs

tsés ♥s s és étrqs

s tr① tt ès ♦t♦rt s♥sr♥t ♥s ♦♥t①t ♣r♦t

♣r♥♣ ♦t st ♦♥♦r ♠♣♥tr t r ①♣ér♠♥t♠♥t ♥

s②stè♠ t♠♣s ré st♦♥ é♥r ♣♦r é étrq ②r rttr

é♥rétq rt♥ ♣♦r tt ét ♦♠♣♦rt ♥ ♥ ttrs ♣♦♠ ♥ s②stè♠

♣ à ♦♠st t ♥ ♥ s♣r♦♥♥strs

♦s ♣r♦♣♦s♦♥s ♥ s②stè♠ st♦♥ é♥r q ♣r♠t ♣r♥r ♥ ♦♠♣t

①♣rts ♣srs s♣ésts sr s sts ♦♥♣t♦♥ s②stè♠ st♦♥

é♥r st ♥s résé ♥ ts♥t ♥ ♥qêt ♦♥ç ♣♦r ①trr ♦♥♥ss♥

s ①♣rts ♦♠♥ ①♣rts ér♥ts t♦♥s ♦q ♦ t②♣

♣r♠t ♥térr ♥rtt ♥s s ré♣♦♥ss t ♥s ♦♥sérr s♠t♥é♠♥t

s ér♥ts s s ①♣rts

tr ♣rés♥t ♥s ♥ ♣r♠èr ♣rt ét s ♠♦ès s s♦rs é♥rétqs

t strtr ♦♠♠♥ é tt strtr st sé sr ♣rés♥

tt♦♥ ♥rétq r♦s♦♣q s réstts s♠t♦♥ t t♦♥

①♣ér♠♥t ♥ ♠ét♦♦♦ ♣♦r ♣r♠étrr ♠♦è éq♥t s s♣r♦♥♥

strs s♦♥t é♠♥t ♣rés♥tés

①è♠ ♣rt st ♦♥sré à ét s s②stè♠s ♦q ♦ t②♣ s

s②stè♠s s♦♥t étés t ♣rés♥tés ♥ ts♥t ♥ ①♠♣ ♥♠érq ♥ ♦♠♣é♠♥t s

tr① ♠♥és sr ♠♣♥tt♦♥ ♦ ♦q ♦ t②♣ ♥ ♣♣t♦♥

été ♦♥ç ♠♣♥té t é ①♣ér♠♥t♠♥t st ♦♥trô t♥s♦♥

s♦rt ♥ r é♦tr ♦t ♣r♥♣ tt ♣♣t♦♥ étt ♣r♠ttr

♥ ♣rét♦♥ ♣♣t♦♥ ♦q ♦ t②♣ ♥s s ♣♣t♦♥s

♥strs

♥♠♥t s②stè♠ st♦♥ é♥r ♣r♦♣♦sé été é sss♠♥t ♣r s

s♠t♦♥s s sss sttqs ①♣ér♠♥t① s sss r♦ ♥ ♠♦ ♦♣ért♦♥

♥♦r♠ t ♥ ♠♦ ♦♣ért♦♥ éré ♦s ♦♥s ♠s ♥ é♥ q ♦q

♦ t②♣ st ♣rtèr♠♥t ♥ ♣té ♣♦r s ♣♣t♦♥s t♠♣s ré ♥s

♦♠♥ é♥ étrq

♦ts és

• ❱és étrqs ②rs

• st♦♥ é♥r

• ♦q ♦ t②♣

• rt♠♥t ♥rtt

• ♦ést♦♥ ①♣rts ♠♥

• Ps à ♦♠st s♣r♦♥♥strs ttrs

• ♠t♦♥ t♦♥ ①♣ér♠♥t

• ♣rés♥tt♦♥ é♥rétq ♠r♦s♦♣q strtr ♦♠♠♥

♦♥t♥ts

♥tr♦t♦♥

r♦♥ ♥ ♦tt♦♥

sr ♦r

♦rt♦r②

❨ rsr ♣rt♠♥t

P rsr r♦♣

♦r♠r rt rsr

♥tr ♦r ♦♠♣tt♦♥ ♥t♥

tst ②r tr

②r tr s

❱ sst♦♥

❱ ♥r② s♦rs

②rst♦♥ ♦ s♦rs

❱ ♥r② ♠♥♠♥t

♥ strts

②♥♠ ♣r♦r♠♠♥

rq♥②s ♥r② ♠♥♠♥t strts

♥♥ strts

♦t rt♦♥

Prt ♥r② ♠♥♠♥t

♦ ♣♦st♦♥ s ♥r② ♠♥♠♥t s②st♠s

t♦st ②♥♠ ♣r♦r♠♠♥

tt♦r rt♦♥

rt♦♥ s strt②

③③② ♦ s strts

③③② s②st♠ ♦t♣t s♦t ♦t♣t rr♥

③③② ♦t♣t rt♦♥ ♦♥ t s♦t ♦t♣t rr♥

③③② ♦ ♦♥tr♦rs s♥

♥rt r♦s♦♣ ♣rs♥tt♦♥ s ♦♥tr♦

♥rt r♦s♦♣ r♣rs♥tt♦♥

①♠ ♦♥tr♦ strtr

①

Prt ♦♥tr♦ strtr

♦♥tr♦ trt②

t ♦rs

♦t ♦♠♣t♥ ♥ t②♣ ③③② ♦

③③② ♦

②♣ ③③② ♦

♣tr ♦♥s♦♥

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

ttrs ♥ s

♦♥ ♥ ♣r♠tr ♥tt♦♥

tt♦r

♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

❯tr♣t♦r s②st♠

♦♥

Pr♠tr ♥tt♦♥

①♣r♠♥t ♠sr♠♥ts

♥♠st♦♥ ♥t♦♥ ♦♥str♥ts ♥ ♣r♠trs

♥♠st♦♥ ♥t♦♥ trt ♣r♦r

①♣r♠♥t t♦♥

tt♦r

♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

s②st♠

♦t♦r♦♠♣rss♦r r♦♣

s s♣♣②

st

P♦r tr♦♥s

s②st♠

①♠ ♦♥tr♦ strtr

Prt ♦♥tr♦ strtr

♠♣t♦♥s

st♠t ❱rs

♦t♦r♦♠♣rss♦r r♦♣

♦♠♣t P

② s②st♠

♣rs♥tt♦♥

♥ ♣rt

tr ♣rt

② s②st♠

rt♦♥ ♥ ♥ ♥rs

♦♥ ♦ t trt♦♥ ♥

①

r♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

♣tr ♦♥s♦♥

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

③③② ♦ ♦♥tr♦ ♥ ♥rt♥t②

❯♥rt♥t②

s

♠rs♣ ♥t♦♥s

♥tr t②♣ ♠♠rs♣ ♥t♦♥s

♠rs♣ ♥t♦♥s rt♦♥

♥tr♦ ♦ ♥ ♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥

r♥♥ ♦rt♠

③③r

③③r ①♠♣

♥r♥ ♥♥

♥r♥ ♥♥ ①♠♣

t♣t Pr♦ss♦r

②♣rr

③③t♦r

t♣t Pr♦ss♦r ①♠♣

♦♥rtr ♦t ♦♥tr♦r

r

♥♣t

♥♣t ♥♦r♠st♦♥

③③② ♦ ♦♥tr♦r

③③② ♦ ♦♥tr♦r ♦t♣t ♥♦r♠st♦♥

♦♥tr♦r t♣t t② ②

③③② ♦ ♦♥tr♦r

③③② ♦ s②st♠ s♥

s s♥

♥♣t ♠♠rs♣ ♥t♦♥s s♥

Pr♠trs

t♣t ♠♠rs♣ ♥t♦♥s s♥

③③② ♦ ♦♥tr♦ srs

③③② ♦♥tr♦r t♦♥ ♥ t♦♥

t♦♥ ♦ t ♦♥tr♦r

❱t♦♥ rsts

♣tr ♦♥s♦♥

①

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦ ♥r② ♠♥♠♥t strt②

♦ ♥r② ♠♥♠♥t strt② ♦ts

♦ ♥r② ♠♥♠♥t strt② ♥♣ts

♦ ♥r② ♠♥♠♥t strt② ♦t♣ts

♦ ♥r② ♠♥♠♥t strts ♦r

ttrs ♥r② ♠♥♠♥t strt②

ttrs ♦ ♣r♠trs

ttrs t♦♥ ♣♦r stt♦r ♦♥tr♦

ttrs t♦♥ ♣♦r ♦rrt♦♥ ♦t ♠tt♦♥s

❯ ♥r② ♠♥♠♥t strt②

❯ ♠♥♠♥t strt② ♣r♠trs

❯ rr♥ ♣♦r

❯ ♣♦r rr♥ ②♥♠ ♠tt♦♥

❯ rr♥ ♣♦r stt ♠tt♦♥

♥r② ♠♥♠♥t strt②

s②st♠ ♥r② ♠♥♠♥t ♣r♠trs

③③② ♦ ♦♥tr♦r ♥♣ts

♥♣t ♥♦r♠st♦♥

❯ ②♥♠ rr♥ ❯ ♦♥tr♦

③③② ♦ ♦♥tr♦r s♥

③③② rs

③③② ♠♠rs♣ ♥t♦♥s

③③② ♦ ♦♥tr♦r ①♠♣

③③② ♦ ♦♥tr♦r ♦t♣t

♥trt♦♥ ♦ t ♦ ♥t♦ t ♦ strt②

r ♦♣rt♦♥ strts

r ♦♣rt♦♥ t♦t

r ♦♣rt♦♥ t♦t ❯

♠t♦♥ t♦♥

♠t♦♥ ♣r♠trs

♠t♦♥ rsts

①♣r♠♥t t♦♥

tt t♦♥

①♣r♠♥t st♣

tt t♦♥ ♣r♠trs

tt t♦♥ rsts ♦

tt t♦♥ rsts ❯ ♦

tt t♦♥ rsts ♦

r♥ t♦♥

r♥ t♦♥ ♣r♠trs

①

♦♠♥ ♦♣rt♦♥ ♦♥t♦♥s rsts

r ♦♣rt♦♥ t♦t ❯

r ♦♣rt♦♥ t♦t

♣tr ♦♥s♦♥

♦♥s♦♥

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

♠rs♣ ♥t♦♥s rt♦♥

③③② sts rt♦♥

③③② sts ♠♣♠♥tt♦♥ s♥ t

♥tr♦ ♦ t②♣ ③③②

♥tr♦ ♦♠♣tt♦♥ s♥ t

t ♣♦♥t ♦ t ♥tr♦

♥tr♦ ①♠♣

③③r

③③r ♠♣♠♥tt♦♥ s♥ t

♥r♥ ♥♥

♥r♥ ♥♥ ♠♣♠♥tt♦♥ s♥ t

t♣t ♣r♦ss♦r

t♣t ♣r♦ss♦r ♠♣♠♥tt♦♥ s♥ t

t ♣♦♥t ♦ t t②♣rt♦r

③③② ♦ ♦♥tr♦ s♦tr ♠♣♠♥tt♦♥

♦tr ♠♣♠♥tt♦♥ ❱t♦♥

t r♣ sr ♥trs ③③② ♦ ♦♥tr♦r

t r♣ sr ♥tr

r②s ③③② ♦ s②st♠ ♦r ♥r② ♠♥♠♥t

♥r② ♠♥♠♥t sr②

♥r② ♠♥♠♥t sr② s♠♣

r② ♣r♦ss♥

③③② sts s♥ ♠♠rs♣ ♥t♦♥s

r♣③♦ ♠♠rs♣ ♥t♦♥s ♥t♦♥

r♥r ♠♠rs♣ ♥t♦♥s ♥t♦♥

♠rs♣ ♥t♦♥s sts

♠rs♣ ♥t♦♥s ♥tr♦s

③③② rs s♥

③③② rs s♥ ①♠♣

③③② ♦ ♦♥tr♦ sr

♦r♣

①

①

st ♦ s

♥r② ♣rt♠♥t rt rsr

s ♠♥ts

♦♠♣♠♥tr② ♠♥ts

♦♠♣♠♥tr② ♠♥ts

♦♠ t②♣ ③③② ♦s ♣♣t♦♥s

ttrs ♣r♠trs

tr♣t♦r s②st♠ ♣r♠trs

❯ ♣r♠trs s♥ ♥

❯ ♣r♠trs ♦t ♥s

s②st♠ ♣r♠trs

s②st♠ ♦♥tr♦ rqr ♠sr♠♥ts

② s②st♠ ♣r♠trs

s♠t♦♥ ♣r♠trs

❲t rs ♦ t ♥tr t②♣

♥tr♦s ♦ t ③③② s ♦r ∆P

③③② rs

③③② ♦♥tr♦r rs

♦♥rtr ♠t♦♥ ♥ ①♣r♠♥t ♣r♠trs

②♣ ③③② ♦ ♦♥tr♦r ♠t♦♥ ♥ ①♣r♠♥t ♣r♠trs

❱t♦♥ rsts

♦ ♦ts ♦ t ♥ t ♦♠♣tt② t t s♦rs

ttrs ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

❯tr♣t♦r s②st♠ ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

s②st♠ ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

Pr♦ss sr② rsts ③③② s

③③② s s ♥tr ♦♥s

♠t♦♥ ♣r♠trs

①♣r♠♥t stt t♦♥ ♣r♠trs

①♣r♠♥t t♦♥ ♣r♠trs

①

♥tr♦s ♦ t ③③② s ♦r ∆P

Pr♦ss sr② rsts ∆P ♥st s

Pr♦ss sr② rsts ∆SOC ♥st s

①

st ♦ rs

tst

tst ♥ ♦♥strt♦♥

tst ♥ ♦♥strt♦♥ tr ♠♥s

Ps

Ps ♦♥rt♦♥

Ps ♦♥rt♦♥

Ps ♦♥rt♦♥

st♦r②

❱ srs rttr

❱ ♣r rttr

❱ srs♣r rttr

♦♥ ♣♦t ♥♥ ♥r② s♦rs

r♥ ②

r♥ 2 ♦r ♥ s

rq♥② ♣♣r♦s ♦r ♥r② ♠♥♠♥t

r ♣rt♦♥ ♦♥tr♦r ♦r ♥r② ♠♥♠♥t

③③② ♦ ♦♥tr♦rs s ♥ ❱ ♥r② ♠♥♠♥t

③③② ♦ ♦♥tr♦rs s ♥ ❱ ♥r② ♠♥♠♥t

s ♦♥tr♦ ♠t♦♦♦②

ttrs s♠t r♠ ♥ ♦♥strt♦♥

ttrs ♠♣♠♥t ♥

r♦♦s ttrs ♠♦

ttrs ♥ s

ttrs ♥ s

❯ s♠t ♥ tr♦ t ②r ♣♦r r♣rs♥tt♦♥

tr♣t♦rs ♠♣♠♥t ♥

r♥t tr♣t♦r ♠♦s

t♥ ❯ q♥t rt ♠♦

❯ q♥t rt ♣r♠trs ♥tt♦♥ ♦rt

❯ q♥t rt ♣r♠tr ♥tt♦♥ ♠♥ ♣♣t♦♥

❯ q♥t rt ♣r♠tr ♥tt♦♥ ❱t♦♥ rsts

①

❯

❯ q♥t rt ♣r♠tr ♥tt♦♥ ❱t♦♥ rsts

❯tr♣t♦r s②st♠ ♥ ♦♥tr♦ strtr

st s♠t ♥ s②st♠ ♠t♦♠♥ s♣ts

s②st♠ ♠♣♠♥t ♥

♦t♦♦♠♣rss♦r r♦♣

t ③ s♣♣②

st

s②st♠ ♣♦r ♦♥rtr

s②st♠

s②st♠

s②st♠ ③ s♣♣s P

r ♠♦t♦♦♠♣rss♦r r♦♣ P

s②st♠ ♣rt ♦♥tr♦ strtr

② s②st♠ ♠♣♠♥t ♥

s②st♠ ♦♠♦♣♦r s②♥r♦♥♦s ♠♥

② s②st♠ ♥ ♣rt

② s②st♠ tr ♣rt

② s②st♠ ♠♣♠♥t ♥

♦ r ♦② r♠

♥rt r♦s♦♣ ♣rs♥tt♦♥

①♠ ♦♥tr♦ trtr

Prt ♦♥tr♦ trtr

♦rs ♦ ♥rt♥t②

②♣ ③③② ♦ s②st♠s rttr

②♣ ③③② ♦ s②st♠s rttr

♥t♦♥ ③③② ♦ ♠♠rs♣ ♥t♦♥

♥tr t②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥

②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥

♥tr t②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥

♥r t②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥

♥tr t②♣ ③③② ♦ ♣r♠r② ♥ s♦♥r② s

r♣③♦ ♠♠rs♣ ♥t♦♥s ①♠♣

r♥r ♠♠rs♣ ♥t♦♥ ①♠♣

♥ ♥tr t②♣ srts ♥t♦ p ♥tr t②♣ s

♥tr t②♣ srts ♥t♦ ♥tr t②♣ s

♦rt t♦ ♦♠♣t t t ♣♦♥t ♦ t ♥tr♦

♠rs♣ ♥t♦♥s ♦r ♥♣t x1

♠rs♣ ♥t♦♥s ♦r ♥♣t x2

③③r ①♠♣

③③r ①♠♣

①

❯

♥r♥♥♥ r♥ r ♦r ♣r♦t ♥r♥

♥r♥♥♥ r♥ rs ♦r t tt rs

♥r♥ ♥♥

♦rt t♦ ♦♠♣t t rt ♣♦♥t ♦ t t②♣r st

♦t♣t ♣r♦ss♦r ①♠♣

♦t♣t ♣r♦ss♦r

♦♥rtr

♦t♣t ♦t ♦♥tr♦r

♣♦r ♦♥rtr ♦t ♦♥tr♦r

t♣ ♥t♦♥ ♦ t t②♣ ③③② ♠♠rs♣ ♥t♦♥s

t♣ ♥t♦♥ ♦ t t②♣ ③③② ♠♠rs♣ ♥t♦♥s

②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

♥t♦♥ ♠♠rs♣ ♥t♦♥s

②♣ ③③② ♦ ♦♥tr♦ srs ❯ ❯ ♥ ❯

♦♥rtr ①♣r♠♥t st♣

♠t♦♥ rsts

①♣r♠♥t rsts

♦ s ♠♣♠♥t ♥ t ♠♥

ttrs stt♦r ♦♥tr♦ strt②

ttrs t♦♥ ♣♦r ♦rrt♦♥

ttrs ♦ ♥r② ♠♥♠♥t strt②

❯ rr♥ ♣♦r ②♥♠ ♠tt♦♥

❯tr♣t♦r ♦ ♥r② ♠♥♠♥t strt②

❯ stt♦r ②♥♠ rr♥

♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s t♦ r♣rs♥t ∆P

♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s t♦ r♣rs♥t ∆SOC

♥r② ♠♥♠♥t t②♣ ③③② ♦ ♥♦r♠s ♦♥tr♦ sr

s②st♠ ♦ ♥r② ♠♥♠♥t strt②

♦ s ♠♣♠♥t ♥ t ♠♥ t

r ♦♣rt♦♥ strt② r

r ♦♣rt♦♥ strt② ❯ r

s♠t♦♥s rsts ♦r♠s r♥ ②

s♠t♦♥s rsts r♥ ②

tt t♦♥ s♠ t ①♣r♠♥t st♣ rt

①♣r♠♥t rsts tt t♦♥ ♦ trt②

①♣r♠♥t rsts tt t♦♥ ❯ ♦ strt②

①♣r♠♥t rsts tt t♦♥ ♦ strt②

tst r♥ t♦♥ t P

①①

❯

①♣r♠♥t rsts r t♦♥

①♣r♠♥t rsts r t♦♥

①♣r♠♥t rsts r t♦♥

①♣r♠♥t rsts r t♦♥ ❱

♦rt t♦ ♦♠♣t t rt ♣♦♥t ♦ t ♥tr♦

t②♣ ♠♠rs♣ ♥t♦♥s ♥ ts ♥tr♦

③③t♦♥ ♦rt

♥r♥♥♥ ♦rt

♦rt t♦ ♦♠♣t t t ♣♦♥t ♦ t t②♣r st

t ♣♣t♦♥ t♦ ♦♠♣t t ③③② ♦ sr

②♣ ♥ t②♣ ③③② ♠♣s ♥ tr r♥

❱ ③③② ♥r② ♥♠♥t r② P

❱ ③③② ♥r② ♥♠♥t r② P

❱ ③③② ♥r② ♥♠♥t r② P

❱ ③③② ♥r② ♥♠♥t r② P

♥tr♦s ♦ t ♥tr t②♣ ③③② s r♣rs♥t♥ ∆P

♠♠rs♣ ♥t♦♥

①①

♥tr♦t♦♥

♥ ♦ t ts ♦ t ♦st♦♥ ♦ ♦r s♦t② s tt ♣♦♣ tr ♠♦r ♦r♥

♦♥r st♥s r r♦♠ tr ♦r ♣ ♥ ♦♥s♠ ♦♦s r♦♠ r♦♥ t

♦r r♦r t s ♥♦ ♦♥♥ tt t tr♥s♣♦rt ♦ ♣♦♣ ♥ ♦♦s r♣rs♥ts

♠♦r t♥ ♦ t ♥r② ♦♥s♠♣t♦♥ ♥ s ♦♥ ♦ t ♣r♥♣ s♦rs ♦ ♣♦

t♦♥ ♦r r ♦rts ♠st ♦♥ t♦ r t ♦ ♣♥♥ t ♥r②

♦♥s♠♣t♦♥ ♥ t ♥r♦♥♠♥t ♠♣t ♦ tr♥s♣♦rt s②st♠s

♥ ts ♣rs♣t t r♥ r♠② s s♥ ♥ ♦♥strt t tr

♥ ♦♠♣♦♥♥ts t♦♥ t s ♠♦ ♦rt♦r② t♦ t ♥r

r ♦♥t♦♥s t tr ♦♠♣♦♥♥ts ♦ ②r tr ❱s ❱s tt r

t ♥r② ♦♥s♠♣t♦♥ ♥ t ♣♦t♦♥ ♠ss♦♥ ♦ ♦♥♥t♦♥ s ♣r♠ts

t♥ r♥t ♥r② s♦rs s s ttrs s ♥tr♥ ♦♠st♦♥ ♥♥s

tr♣t♦rs ♦r ②s

♣r♦t ♥♦②s ♥ s♦♥ ♣s s ♦♣ ♥ ♦♥t ♦♦♣rt♦♥ t

t ♦rt♦r② ♦ t ❯♥rst② ♦ r♥♦♠té ♥ t♦ ♥str ♣rt♥rs

♥ P ♥r ♥s t ♠s t♦ st② t ♠♣♠♥tt♦♥ ♦♥tr♦

♥ ♥r② ♠♥♠♥t ♦ r♥t ②r s♦rs

s rsr ♦♣ ♦♥ t s♦♥ ♣s ♦ t ♣r♦t t ♣r♥♣

♦t ♦ ts tss s t♦ s♥ t♦ ♠♣♠♥t ♥ t♦ t ♥ ♥r② ♠♥♠♥t

s♣rs♦♥ s②st♠ ♥ t ❱ s tss ♣r♦♣♦ss ♥ ♦r♥ ♥r② ♠♥♠♥t

strt② s ♦♥ ①♣rt ♥♦ ♥ t②♣ ③③② ♦ s♥ ♦ t ③③② ♦

♦♥tr♦r s ♦♥ ② s♥ ♥♦ ♥♥r♥ s t♥q ♦s ①trt♥ ♥♦

r♦♠ sr ①♣rts s♥ sr②s ♦♥srt♦♥ ♦ t②♣ ③③② ♦ s②st♠s

♥s ♠♦♥ t ♥rt♥t② ♥ t ♥srs ♦ t ①♣rts

s tss ♣rs♥ts s♦♥ ♣♣t♦♥ ♦ t②♣ ③③② ♦ t ♦t rt♦♥ ♦

♣♦r ♦♥rtr ♣r♥♣ ♠♦tt♦♥ ♦r ♦♣♥ ts ♣♣t♦♥ s tt

t s sr t♦ ♠♣♠♥t ♥ ♦rt♦r② t rt② ♦ ♦st ♥ t ♣r♠ts t②

t♦♥ ♦ t②♣ ③③② ♦ ♦r ♥ ♠♣♠♥tt♦♥ ♥ t ♠♦ ♦rt♦r②

s s s s ♦♥ ♦ t ♠♥ ♥s ♦ ts tss s t♦ r t t♠ t♦

rst ♣s ♦ t ♣r♦t s ①♣♥ ♥ ♣tr

♥tr♦t♦♥

①♣r♠♥t② t t ♥r② ♠♥♠♥t s②st♠ s s rqr t♦ rs♣t t

t♠ s ♦♥str♥ts ♥ t♦ r t ♦sts ss♦t t♦ tr t ♣rt♥rs ♦ t

♣r♦t t P ♦t♦♥s ♥ ♥tr♠♥

s tss s strtr ♥ ♦r ♣trs ♥ t ♠♥ ♦② ♥ t♦ ♣trs ♥ t

♣♣♥① ♦r♥s s ♦♦s

♣tr ♣rs♥ts t rsr r♦♥ ♥ rt stt ♦ t rt

rst② ts ♣tr ♥tr♦s t ♦♥t①t ♦ t rsr ♥ ♣rs♥ts t

rsr ♣r♦t ♥ t ♥tr♦s t ②r tr s ♥ ♣rs♥ts tr

tr r ♦t t t♥qs ♥ ♠t♦♦♦s s ♥ tr ♥r② ♠♥♠♥t

t t ♠♥t♠ t ①♣♦ss t ♠♦tt♦♥s t♦ ♣rr ③③② ♦ t♦ ♣r♦r♠ t ♥r②

♠♥♠♥t ♥ ❱ tr tt t ♣tr ♣rs♥ts t ♥rt r♦s♦♣

♣rs♥tt♦♥ t♥q s t♦ r♣rs♥t t ♥ t♦ ♥t② ts ♦♥tr♦

strtr ♥② t ♣tr ♥tr♦s t ♠♦tt♦♥s t♦ ♦♥sr s♥ t②♣ ③③②

♦ ♥ ♥♥r♥ ♣♣t♦♥s ♥ ♣rtr② t ♥r② ♠♥♠♥t ♦ t

❱ ♥② t ♣rs♥ts trtr r ♦t ♦r♠r ♣♣t♦♥s s ♦♥ t②♣

③③② ♦ s②st♠s

♣tr s ♦t t♦ st② t ♥r② s♦rs t ♦♥ t ♠♦

♦rt♦r② t♦ t ttrs s②st♠ ♥ ♥ tr♣t♦r s②st♠

♦r ♦ t s♦rs ♥ ♠♦ ♦rt♦r② ts ♣tr sts tr

rtrsts tr ♠♦♥ tr ♥ tr ♦♥tr♦ strtr ♥♦ ♥

♥rst♥♥ ♦ t ♥ts ♥ rs ♦ ♦ t s♦rs s ♥♠♥t t♦

st② tr ♠♣♠♥tt♦♥ ♥ t♦ ♥ tr ♥r② ♠♥♠♥t strts ♦♥

♥ ♣r♠tr ♥tt♦♥ s s t♦ s♠t t ♥ ts ♥r② ♠♥♠♥t

♦♠♣s♦r② st♣ ♦r ♣r♦r♠♥ ♥② ①♣r♠♥t ♠♣♠♥tt♦♥ s s

t♦ ♥t② t ♠sr♠♥ts ♥ st♠t♦♥s ♥ t♦ ♥ ♣rt ♦♥tr♦ strtr

♦ t

s ♣tr s♦ ♣rs♥ts ♥ ♦r♥ ♣r♦r t♦ ♥t② t q♥t tr rt

♦ ♥ tr♣t♦r s ♣♣r♦ s ①♣r♠♥t② ♠♣♠♥t ♥ t

♣tr ♥tr♦s t②♣ ③③② ♦ sts ♥ s②st♠s t s♦ ♣rs♥ts t rst

♣♣t♦♥ ♦ t②♣ ③③② ♦ ♦♥tr♦ ♦♣ ♥ ts rsr t ♦t rt♦♥

♦ ♣♦r ♦♥rtr

tr ♣rs♥t♥ t ♦♥♣t ♦ ♥rt♥t② ♥ t②♣ ③③② ♦ s②st♠s ts ♣tr

♥tr♦s ♥ t t ♥tr t②♣ ③③② ♦ s②st♠s ♦♥sr ♥ ts

rsr ♣tr ①♣♥s ② s♥ ♥♠r ①♠♣s t ss②st♠s ♦ ♥

t ③③② sts rt♦r t ③③r t ♥r♥ ♥♥ ♥ t ♦t♣t ♣r♦ss♦r

t♦♦♦① s ♦♣ t♦ ♠♣♠♥t ♦r t s ♣rs♥t ♥ ♣♣♥①

♥tr♦t♦♥

♦ ♥tr♦ t ♣♣t♦♥s ♦ t②♣ ③③② ♦ ts ♣tr ♣rs♥ts ③③② ♦

s②st♠ s t♦ ♦♥tr♦ t ♦t♣t ♦t ♦ ♦♥rtr ss strtr ♦

③③② ♦ ♦♥tr♦r s ♠♣♠♥t t♦ ♦♠♣r t ♣r♦r♠♥ ♦ t②♣ ♥ t②♣

③③② ♦ s②st♠s t♦♥ ♦ t ♦t ♦♥tr♦r s ♣r♦r♠ ② s♠t♦♥

♥ ② ①♣r♠♥tt♦♥

♣tr s ♦t t♦ t s♥ ♠♣♠♥tt♦♥ ♥ t♦♥ ② s♠t♦♥ ♥

①♣r♠♥tt♦♥ ♦ t ♥r② ♠♥♠♥t s②st♠ ♦♥sr ♥ t ❱

s ♣tr ♣rs♥ts t ♥t♦♥ ♥ t ♦ ♥r② ♥♠♥t trt②

♠♣♠♥t ♥ t s ♦♥srs t ♥ts ♥ rs ♦

t r♥t s♦rs s ①♣♥ ♥ ♣tr s s♦r s ♥♣♥♥t② ♦♥tr♦

t ♦ s ♥ ♦ s ♦r ♦ t s♦rs ♦ ♦r t

s②st♠ s s ♦♥ sr②s t②♣ ♦ s②st♠ ♦ tt t tr ♦

ts ♣tr t s♥ ♦ ts s ♣rs♥t ♥ ♣♣♥①

♣r♦♣♦s s t ② s♠t♦♥s ♥ ② ①♣r♠♥tt♦♥ s♠t♦♥s

r s ♦♥ t ♠♦ ♦ t ♦♣ ♥ ♣tr ①♣r♠♥t② t

s t ♥ t♦ st♣s rst② ② ♦♥♥t♥ r rsst♥ t♦ t s

♦ t s♦♥② ② r♥ t ♥ r♥ ②

♣♣♥① ♣rs♥ts t s♦tr ♦♣ t♦ rt t t②♣ ③③② ♦ ♦♥tr♦

srs

s s♦tr s s t♦ ♠♣ ♦♥ t ♥tr t②♣ ③③② ♦ s②st♠s s ♥

♣trs ♥ s♦tr s ♣rs♥t ② s♥ ♦rts ♥ strtr ♣r♦r♠

♠♥ s ♣♣♥① s♦ ♣r♦♣♦ss t♦♦♦① t♦ ♠♣♠♥t ♥trt②♣ ③③② ♦

s②st♠s ♥ t s ♥ ♥t rr♥ ♦tr t♦♦♦①s ♣rs♥t ♥ trtr

♦r ♦ ♦s ♥♦t rqr t s ♦ t t ③③② ♦ t♦♦♦①

♣♣♥① ♣rs♥ts t s♥ ♦ ③③② ♦ s②st♠ s ♥ ♣tr

t②♣ ③③② ♦ s②st♠ s ♥ ♥r② ♠♥♠♥t s②st♠ s s♥ ②

s♥ ♠♥ ♥♦ ♥ ♥r② ♠♥♠♥t sr② s ♦♥t ♠♦♥ ①♣rts ♥

②r tr s t sr② ♦s ①trt♥ ①♣rts ♥ t ♦r♠ ♦

rs sr② s ♠♥② ♣r♦r♠ ♠♦♥ t ♣rt♣♥ts ♦ t ❱ P♦r

♥ Pr♦♣s♦♥ ♦♥r♥ ♣t♠r ♥ r♥

♥tr♦t♦♥

♣tr

r♦♥ ♥ ♦tt♦♥

s ♣tr ♣rs♥ts t rsr r♦♥ ♥ rt stt ♦ t rt

rsr ♣rs♥t ♥ ts ssrtt♦♥ ♦ss ♦♥ t st② ♦ ♥r② ♠♥♠♥t

♦ ②r tr ❱s ❱ ♥ t②♣ ③③② ♦ tr ♥tr♦♥ t ♦♥t①t

♦ t rsr ts ♣tr ♣rs♥ts ♥ ♦♠♣rs t t♥qs ♥ ♠t♦♦♦s s

♥ ❱ r♣rs♥tt♦♥ ♠♦♥ ♥ ♥r② ♠♥♠♥t s s ♦♥ t♦ ♥t② t

♠♦st ♣t t♥qs t♦ s ♥ ♥①t sts ♦ t rsr ♥② t②♣ ③③②

♦ s ♣rs♥t s ♣t t♥q t♦ ♣r♦r♠ ♥r② ♠♥♠♥t ♥ ❱

s ♣tr s ♦r♥s s ♦♦s t♦♥ ♣rs♥ts t rsr r♦♣ r t

rsr s ♣r♦r♠ s ♣rs♥t ♥ t♦♥ t♦♥ ♥tr♦s

s♦♠ s ♦♥♣ts ♦ ②r tr ❱s ❱ ♥ tr ♥r② s♦rs

trtr r ♦t ❱ ♥r② ♠♥♠♥t t♥qs s ♣rs♥t ♥ t♦♥

t♦♥ ♣rs♥ts t ♥rt r♦s♦♣ ♣rs♥tt♦♥ ♦r♠s♠ s t♦

st② ♠t♣②s s②st♠s s ❱ t♦♥ ♣rs♥ts s♦t ♦♠♣t♥ ♥ ♥tr♦s

t t②♣ ③③② ♦ ♥② t♦♥ ♣rs♥ts t ♦♥s♦♥s ♦ t ♣tr

sr ♦r

s rsr s ♣r♦r♠ ♥ t ②r s②st♠s ♥ s②st♠s P

rsr r♦♣ ②stè♠s ②rs t s②stè♠s P ❨ rsr ♣rt♠♥t ♦

t ♦rt♦r② ♦rt r♥ ♣rt ♦ ts rsr s ♦♥t s ♦♥t

♦♦♣rt♦♥ t t ♥tr ♦r ♦♠♣tt♦♥ ♥t♥ ♦♥t♦rt ❯♥rst②

t str ❯♥t ♥♦♠

rsr s s♣♣♦rt ② t ❯♥rst② ♦ r♥♦♠té ♥r t

♦♥trt t t r♥ r♠② ♥r rt♦♥ tr♥♥ t t s

♣rt② ♥♥ ② t ♦t♦r ♦♦ ♦ ♥♥r♥ ♥s ♥ r♦t♥qs

P ♦ t ❯♥rst② ♦ r♥♦♠té

r♦♥ ♥ ♦tt♦♥

♦rt♦r②

r♥♦♠té tr♦♥q é♥q r♠q t ♣tq ♥s

t ♥♦♦s s ♦♥t rsr ♥t s t t t r♥ ♥tr ♦

♥t sr t ❯♥rst② ♦ r♥♦♠té ❯ t t♦♥ ♦♦

♦ ♥ ♥♥r♥ ♥ r♦t♥♦♦② ♥ t ♦rt♦♥tér

❯♥rst② ♦ ♥♦♦② ❯

s ♦r♥s ♦r♥ t♦ t ♦♦♥ rsr ♣rt♠♥ts t♦♠t

♦♥tr♦ r♦tr♦♥ ②st♠s ♣rt♠♥t ♥r② ♣rt♠♥t ♣♣

♥s ♣rt♠♥t r♦ ♥♦ ♣rt♠♥t ♣ts ♣rt♠♥t ♥ ♠

rq♥② ♣rt♠♥t

❨ rsr ♣rt♠♥t

❨ ♣rt♠♥t ♦ s ♥♦ ♥ ♣♣ rsr ♠♥② r♦♥

t ♦♦♥ ♦r ①s

r♠ ♦s ♥ ♦♠♣① s

❯♥♦♥♥t♦♥ tr♠ ♥ tr ♠♥s

s②st♠s

②r ♥r② s②st♠s ♥ ②r tr s

❨ ♣rt♠♥t s ♦t ♥ t ♥♦rt ♦ t r♥♦♠té r♦♥ ♥ ♠♥②

♦ t rsr ♦♣ ♥ ts ♣rt♠♥t s ♣r♦r♠ ♥ ♦♦♣rt♦♥ t r♦♥

♥str ♣rt♥rs s st♦♠ ♦r P P♦ttr♦ë♥ r♦♣ ♠♦♥ ♦trs

P rsr r♦♣

s♥t ♠ ♦ t P rsr r♦♣ s r♦♥ s②st♠t ♣♣r♦ ♦

♠t♣②ss s②st♠s s s s②st♠s ♦r ②r tr s r♦♣ ♦♦s

♦rr t♦ ♦♣ ♦r♥ ♠♦♥ ♣♣r♦s rt♠ ♥ ss①♣♥s ♥♦st

♥ ♦♥tr♦ s②st♠s ♠ ♦ t rsr ♣rs♥t ♥ ts ssrtt♦♥ s r②

♥t t t ♦ts ♦ t P rsr r♦♣ ♠t♣②ss s②st♠s ♠♦♥

♥ ♦♥tr♦ tr s ♥ ♥r② s♦rs

♦r♠r rt rsr

rsr ♦♣ ♥ ts ♣r♦t s t ♥tr ♦♥t♥t♦♥ ♦ t ♥ ♦ rsr

♥ ♦♣♠♥t rs t ❨ ♣rt♠♥t r♦♠ t st ②rs r♦♠ t st② ♦

s②st♠s ♦♥tr♦ strtr t♦ ♦♣t♠st♦♥ ♦ tr ♠♥s s ♥ tr

s st ♦ ①♠♣r② ♣t♦♥s rt t ts rsr ♥ ♦♣ ♥

r st ♥

tst ②r tr

♥r② ♣rt♠♥t rt rsr

♦♠♥ ♣♣t♦♥ r♥s

❱ s♥ tst ♥ ❬Ps❪ ❬s♣❪ ❬ ❪ ❬❪ ❬♦❪

♥r② ②r ♦♣trs ❬s♥❪ ❬♥❪ ❬♥❪

♠♥♠♥t tr② ♥ ②t② s ❬❲❪ ❬❲❪❬♦❪

♦♥tr♦ ② s ❬♦❪ ❬r❪ ❬r❪

❯r♥ s ❬r♥❪ ❬r♥❪ ❬❪ ❬❪ ❬♦❪

♥r② ttrs ❬r❪

s♦rs ♦r ②rst♦♥ ❬❪

❯tr♣t♦rs ❬♥❪ ❬♦❪ ❬❪

tr♥ ♠♦t♦r ❬r❪ ❬②❪ ❬②❪

♥♦ss ❬r♥❪ ❬r❪ ❬❲st❪ ❬❨♦s❪ ❬❨♦s❪

s②st♠s P ♠♦♥ ♥ ♦♥tr♦ ❬r❪ ❬♠❪ ❬ss❪ ❬❪ ❬♦❪ ❬♥❪

♠♦♥ ♥ ♦♥tr♦ ❬♥❪ ❬②❪ ❬❲♥❪

♥rs ❬❪ ❬❪ ❬r❪ ❬r❪ ❬❪

♥tr ♦r ♦♠♣tt♦♥ ♥t♥

♦♣s ♥♠♥t t♦rt ♥ ♣rt s♦t♦♥s t♦ r ♦r ♣r♦♠s

s♥ rt② ♦ ♦♠♣tt♦♥ ♥t♥ ♣r♠s sr rr ♦t t♥ t

♥tr s ♦♥t ② tr ♠♥ t♠s ♦ rsrrs ♦t ♥♦r♠ts ③③② ♦

♥ ♥t♥t ♠♦ r♦♦ts ♥ rt ♦♠♣t♥ ③③② ♦ r♦♣ s ♥trst

♥ ♥rt♥t② ♠♦s ♥♥ ③③② sts ♥ ♣rtr② ♥ t②♣ ③③② ♦

tst ②r tr

tr ♥ ♦♠♣♦♥♥ts t♦♥ s rsr ♣r♦t s♣

♣♦rt ② t r♥ r♠② ♥r rt♦♥ rt♦♥ é♥ér r♠♠♥t

s ♠♦ ♦rt♦r② s s ♦r rsrs ♥r r ♦♥t♦♥s ♦♥ t♥♦♦ s♦

t♦♥s ♦r ②r tr s s r♥ ♦r t rst t♠

♦♥ s ♣rs♥t ♥ r

r tst

r♦♥ ♥ ♦tt♦♥

s ❱ s♣② s♥ ♦r r♦r t♦♥ ♦ tr ♦♠♣♦♥♥ts

s s tr ♠♥s ♣♦r ♦♥rtrs ♥r② s♦rs ♦r ♥r② ♠♥♠♥t s②s

t♠s ts trt♦♥ ♥ s ♦♠♣♦s ② ♦r ♥♣♥♥t② ♦♥tr♦ tr ♠♥s

r t t♥ s ♠♦t♦rs ♦r r♣rt t r♥ ♥r② t♥ s ♥

rt♦rs ♦ s♥ r♥t ②r ♦♥rt♦♥s ♠♦r ♥ q♣♣

t r♦s ♥r② s♦rs s s ②st♠s ♥tr♥ ♦♠st♦♥ ♥♥s

❯tr♣t♦rs ❯ ttrs ♥♦r ② ②st♠s ❲

Ps ♦ ♣r♦t s ♦t t♦ s♥ ♦♥strt♦♥ ♥ t♦♥

♦ t rs ♥ s ♣s ♦s ♦♥ t ♦♥rt♦♥ s♦♥ ♥

r t st② ♦ ♥r② ♠♥♠♥t ♦ t trt♦♥ ♥ ❬Ps❪ ♥ t ♥r②

s♦rs ❬♦♣❪ ♥ t t♦♥ ♦ t ttrs tr st② ❬ ❪ ♥

tr ♠♥s ❬s♣❪

r tst ♥ ♦♥strt♦♥

r tst ♥ ♦♥strt♦♥ tr ♠♥s

Ps ♦ ♣r♦t ♦ss ♦♥ t ♥trt♦♥ ♦♥tr♦ ♥ ♠♥

♠♥t ♦ r♥t ♥r② s♦rs ♦r tr♥s♣♦rt ♣♣t♦♥s ❯ ttr

s ♥ ❲ Ps ♦ t ♣r♦t s ♠♥ ② t ❯♥rst② ♦

r♥♦♠té ♥ ♦♥ts t t ♣rt♣t♦♥ ♦ t ♦♦♥ ♥str ♣rt♥rs

P♥r ♥r ♥s ♥t r♠♥ ♦r r♥ s♣♣r ♦ ♠tr②

s ♥ r ♦ t ♠♥ ♥trt♦♥ ♥ t ② s②st♠ ♦♣♠♥t ♥

♦♥ ②r♦♥ P♦r ①♥Pr♦♥ r♥ ssr② ♦ r r♦♣ s♣♣r ♦

t

rs ♥ ♣rs♥ts t r♥t ②r ♦♥rt♦♥s t ♦♥ ♣s

♦ ts ssrtt♦♥ ♦ss ♦♥ t st② ♦ t s♦♥ ♦♥rt♦♥ r

♣rs♥ts t♠♥ rs♠s s♦♠ ♦ t rsr ♦♣ ♥ ♠♦

♦rt♦r②

②r tr s

r Ps r Ps ♦♥rt♦♥

r Ps ♦♥rt♦♥ r Ps ♦♥rt♦♥

r st♦r②

②r tr s

❱ ♣♣t♦♥s rqr ♣♦r s♣♣② t t♦♥♦♠② ♥ ♦t♣t ♣♦r st

②♥♠ rs♣♦♥s ♥ ♣♦ss ♥r② r♦r② ♥ st t♦ rr ♦r t s ♥♦t

s② t♦ ♥ ♥ ♥r② s♦r s ts rqr♠♥ts ② ts t rs♦♥

♦st ②r tr ❱s ❱ ♦♠♥ t♦ ♦r ♠♦r ♥r② s♦rs t st ♦♥

tr t♦ ♥t r♦♠ tr r♥t rtrsts ♠♣r♦♥ t♦♥♦♠② rrst②

♥ ②♥♠ rs♣♦♥s ♦r ②rst♦♥ ♠♣♦ss ♥ t♥ ts s s

♥r② ♠♥♠♥t

r♦♥ ♥ ♦tt♦♥

❱ sst♦♥

❱ r ♥r② ss ♦r♥ tr ♣♦rtr♥ rttr ♥ srs ♣r

♥ srs♣r ❬ ♥ r❪

• rs ❱ trt♦♥ ♣♦r s ♦♥rt r♦♠ trt② ♥ ♦ ♥r②

s ♦♥ ♥ tr♠s ♦ tr ♣♦r ♥r② ♥ s s s t s ♥ ♥

❱ tt ♥s ♥ t s ♥♦t ♠♥② ♦♣ t♦ t ♣♦rtr♥ s

♥ ♦♥♥t♦♥ s ♥ ♥st t s s t♦ r ♥ tr ♥rt♦r

s♣♣s ♥r② t♦ t s s srs ❱ ♥ t ♥ ♦ ♣♦r s

♦♥ ♥ s srs rttr s ♣rs♥t ♥ r

• Pr ❱ t tr ♠♥s ♥ t r ♦t ♦♣ t♦ t ♣♦

rtr♥ s♥ ♠♥ tr♥s♠ss♦♥s s ♦♥sq♥ t ♥ ♦ ♣♦r s

♦♥ ♥ tr♠s ♦ ♠♥ ♣♦r s rttr s ♣rs♥t ♥ r

• rs♣r ♦r ♦♠♥ ❱ ts rttr s ♦♠♥t♦♥ t♥

srs ♥ ♣r r t ♦ s tr t♦ r t ♣♦rtr♥ ♦r t♦

s♣♣② ♥r② t♦ t s s rttr s strt ♥ r

r ❱ srs rttr r ❱ ♣r rttr

r ❱ srs♣r rttr

❱ ♥r② s♦rs

②r s ♥ q♣♣ t rt② ♦ ♣♦r ♥ ♥r② s♦rs s s

ttrs ②st♠s ♥tr♥ ♦♠st♦♥ ♥♥s ❯tr♣t♦r

②st♠s ❯ ♦r ② ②st♠s ❲ s s♦rs r♥t rtrsts

♥ ♥t♦♥s ♥ r ss ♦r♥ t♦ t ② t② t t tr ♥r②

❱ ♥r② ♠♥♠♥t

♥r② ♦♥rs♦♥ ♦rs t ♠ ♥r② r♦♠ s

♦r ②r♦♥ ♥ ♦♥rt t ♥t♦ tr ♥r② ② ♣r♦ t ♦

♠♦♥t ♦ ♥r② rqr t♦ ♣r♦♣ t ② r ♥♦t rrs t② ♥

s♣♣② tr ♥r② t t② ♥♥♦t r t

♥r② t♦r ♦rs t tr ♥r② r♦♠ t ♥ ♥ t②

r r ♣r♦ ♥r② t♦ t s②st♠ ♥r② t ♠♥ ♥r② ♣r♦ ② ♥

t♥s t♦ ③r♦ ♦r ♥ ♣♥ tr s t t t ♥r② r♦♠ ♥

①tr♥ tr s♦r ♥ ♣r♦ t ♦ ♠♦♥t ♦ ♥r② rqr ② t

♣tr ♦ ts ssrtt♦♥ s ♦t t♦ t st② ♦ t ♥r② s♦rs s ♥

②rst♦♥ ♦ s♦rs

②rst♦♥ ♦ s♦rs ♦♥ssts ♦ ♦♠♥♥ t♦ ♦r ♠♦r ♥r② s♦rs t♦ ♥t r♦♠

tr r♥t rtrsts rrst② t♦♥♦♠② ②♥♠ ♥sr ♦♥ r♠

❬♦❪ ♥ r ♦♠♣rs t ♥r② s♦rs rr♥ tr s♣ ♥r② t

t② t♦ s♣♣② ♥r② ♦r rt ♦♥ ♣r♦s ♦ t♠ ♥ s♣ ♣♦r t t② t♦

s♣♣② ♠♦♥ts ♦ ♣♦r ♥ s♦rt ♣r♦s ♦ t♠ s rqr ♥ rt♦♥ t ♥

♥rr r♦♠ ts rt tt ♥ ❯ ②r s♦r t ❯ ♦s st ②♥♠s ♥

t ♦s ♥ ①t♥ t♦♥♦♠② ❬P rr r♥ ♦ ①❪

♥ t ♦♥trr② ❯ ♥ ❲ ♣rs♥t s♠r rtrsts ♥ tr ♦ r

♥ts ♥ ♥trt♥ ♦t ♥ t s♠ ❱

r ♦♥ ♣♦t ❬♦❪ ♥♥ ②r tr ♥r② s♦rs

❱ ♥r② ♠♥♠♥t

❯♥ ♦♥♥t♦♥ s r ♦♥② t s♣♣s t ♦ ♠♦♥t ♦ ♥r②

②r s ♠t♣ ♥r② s♦rs t♦ t ♥r② s♣♣② ♥ ♥

♦ ♥r② ♠♥♠♥t ♦♥ssts ♥ ♣r♦♣♦s♥ ♣♦r strt♦♥ t♥ t r♥t

s♦rs t♦ ♠t t ♠♥ st ♠t♥ s♥ rqr♠♥ts s s ♦♠♦rt ♦r ♠♥

♠s♥ ♥r② ♦♥s♠♣t♦♥ ♦r ♣♦t♥t ♠ss♦♥s ♥r② ♥♠♥t s rs s♥

sr r♥t t♥qs ss ♥ t♦ r♦♣s rst r♦♣ tt rqrs ♣r♦s

♥♦ ♦ t r♥ ② ♥ s♦♥ r♦♣ tt ♦♥② s rt♠ ♥♦r♠t♦♥

r♦♥ ♥ ♦tt♦♥

♥ strts

♥ ♠t♦s s ♥t t♥qs ♥t ♦rt♠s ②♥♠ ♣r♦r♠♠♥

sr♠ ♣rt ♦♣t♠st♦♥ t♦ ♠♥♠s t ♥r② ♦♥s♠♣t♦♥ ♦r ♣♦t♥ ♠ss♦♥ ♥

♣rsts r♥ ②s s t♥qs r ♣♣r♦♣rt ♥ t r♥ ② s

rt② s② t♦ ♥♦ ♥ ♥ ♥ rr♦ ♣♣t♦♥s ❬❪ ♦r ♣ tr♥s♣♦rt

♣♣t♦♥s ❬❳❪

♦r♠s r♥ ②s ♠ t♦ r♣rs♥t r r♥ ♦♥t♦♥s ♥ r s t♦ ssss

t ♣r♦r♠♥ ♦r t♦ ♦♠♦♦t s ♠♦♥ ts r♥ ②s t ♦r♠s

r♦♣♥ r♥ ② strt ♥ r s ♣r♦r♠ t♦ ♠sr t

♣♦t♦♥ ♠ss♦♥ ♥ t♦ r♥t 2 s ♣♦t♦♥ ♠ss♦♥s r ♣♥s t

t① ♦r ♦ ♠ss♦♥s r rr t rt♦♥ ♥ t ♣r ♦ ♥ s

r♥ 2 é♦♦♥s♠s s strt ♥ r ♥ t♥qs r

r s t♦ ♠♥♠s ts ♠ss♦♥s ♥ t♥ t♦ ♦t♥ rt♦♥ ♦♥ t ♣r ♦r t

t① ♥ t♦ ttrt ♠♦r ♥ts

r r♥ ②

r r♥ 2 ♦r

♥ s

♠♥ r ♦ ts ♣♣r♦ s tt t ♦♥s♠♣t♦♥ s ♦♣t♠s ♦♥② ♦r

♣rtr ♥ ♣rtr ♦♥t♦♥s ♣r♦② ♥r r♣t ♥ r

s ♥ ② t rt♦♥ r♦♠ t♦ ♠ ts ♠♦r t♥ s ♥

t ♣r♦r♠ ss t♥ ♠ ♠♦♥ ts r♦♣ ②♥♠ ♣r♦r♠♠♥ ♥

rq♥②s ♠♥♠♥t strts r ♥♦ ♣rs♥t

②♥♠ ♣r♦r♠♠♥

②♥♠ Pr♦r♠♠♥ P s t♥q s t♦ ♥ ♦♣t♠ s♦t♦♥s t♦ ♥♦♥♥r

♥ ♦♥str♥ ♣r♦♠s s♥ rrs qt♦♥s s t♥q s ♥ ♣rs♥t

t♦ ♠♥♠s ♥ ♠ss♦♥s ♥ ❱s ❬♥ Pr ❱♥♦❪ ♦♠ rs ♦ ts

t♥q r tt P s t t♦ ♠♣♠♥t ❬Pr❪ ♥ s ♥♦t st ♥ ♦♠♣①

♠♦s ❬♥❪

❱ ♥r② ♠♥♠♥t

rq♥②s ♥r② ♠♥♠♥t strts

♣♦ ❬♣❪ ♣r♦♣♦s t♦ trt t ♣♦r ♣r♦ s♥ ♦rr rq♥② ♥

②ss ♣♦r strt♦♥ s s ♦♥ t rtrsts ♦ t s♦rs ♥ ♦♥

tr♥ rq♥② t ♥r② s♦rs t s♣ ♥r② s♣♣② t ♦ rq♥

r♠♦♥s t ♥r② s♦rs t s♣ ♣♦r s♣♣② t rq♥② r♠♦♥

s

❬❪ ♣rs♥ts rq♥②s strt② ♦r ♥r② ♠♥♠♥t ♥ ♦♦♠♦t

♥♥ ♥ ♥tr♥ ♦♠st♦♥ ♥♥ ② s②st♠ ♥ ttrs ♥tr♥

♦♠st♦♥ ♥♥ ♦rs t ♦♥st♥t ♣♦♥t t ❲ s♣♣s t rq♥② ♥

t ttrs s♣♣② t ♦ rq♥② ♣♦r s♠ ♦r ts rq♥② ♣♣r♦ ♥r②

♠♥♠♥t s s♦♥ ♥ r

r rq♥② ♣♣r♦ ♦r ♥r② ♠♥♠♥t ❬❪

s♠r strt② ♣rs♥t ♥ ❬r❪ ♦♥srs t ♣r♦♣s♦♥ ♣♦r s t t♦♥

♦ ♠♥ ♣♦r ♥ r♣♣ ♣♦r ts ♦ ♦♥ ♦♥② ♦r ♣rtr♠♥ ②s

♠♥ ♣♦r s s♣♣ ② t ♥ t r♣♣ ♣♦r s s♣♣ ② t

♥♥ strts

s♦♥ r♦♣ ♦ ♥r② ♠♥♠♥t strts ♦s ♥♦t rqr ♥♦r♠t♦♥ ♦t

t tr s strts ♦♥② ♦♥sr rt♠ ♥♦r♠t♦♥ s♣ ♦r rt♦♥ ♦

t ♣♦r ♦t rr♥t ♦r stt♦r ♦ t ♥r② s♦rs ♦r ♦s s

t♥qs r ♥r② s ♦♥ rs ♥ ♦♥♥ ♦♣t♠st♦♥

r ♦♥t♦♥s r ② r♥♦♠ ♣♥♥ ♦♥ t tr t②♣ ♦ r♦ t

rr st② s ❬♥ r♣ ♦s ②❪ ♦r t tr ♦♥t♦♥s ♦r♦r

♥ ♠tr② ♣♣t♦♥ t r♥ ② s ♥♦t ♥♦♥ ♣r♦r ♥ ♣♦t♦♥ ♠ss♦♥

rt♦♥ s ♥♦t ♣r♦rt② ♥♥ t♥qs t♦t ♣r♦s ♥♦ ♦ tr r

♦♥t♦♥s ♣♣rs t♦ ♠♦r qt t♦ ♣r♦r♠ ♥r② ♠♥♠♥t ♥ r♦ s

♥ ♣rtr② ♥ ♠tr② ♣♣t♦♥s

r ♦ ts t♥qs s tt t② ♣r♦♣♦s s♦t♦♥ s ♥♦t ♥ssr②

t ♦♣t♠ ♠♦♥ ♦♥♥ t♥qs ♦t ♦r stt♦r rt♦♥ ♥ ③③②

♦ ♥r② ♠♥♠♥t strts r ♥♦ ♣rs♥t

r♦♥ ♥ ♦tt♦♥

♦t rt♦♥

♥r② ♠♥♠♥t strts s ♦♥ ♦t rt♦♥ ♦s ♦♥ t ♠♥♠♥t

♦ tr♥s♥t ♣♦r ♣s ♥ r♥rt r♥ ② rt♥ t ♦t s♥ t

♥r② st♦r ♥ t ♥r② st♦r s♦rs ❯ ❲ ♦r ttrs s t♥q ①

♣♦ts t st ②♥♠ rs♣♦♥ss ♦ t t♦ r♥♦r t rt② s♦ ②♥♠s

♦r t sts ♦♥ ts strts r ♣rs♥t ♥ ❬P②♠❪ ♥ ❬♦❪

Prt ♥r② ♠♥♠♥t

♥r② t♦ ♣r♦♣ t ❱ s ♦♣t♠s t♥ ♣rt r♥ ② s

rqrs ♥♦r♠t♦♥ ♦r ②♣♦tss ♦r♠t♦♥ ♦t t tr ♦r ts ♥♦r♠t♦♥

s ♥r② ♠t ♥ ♦s ♥♦t ♦♥sr r♥t r♥ strts ♦r ♦♥t♦♥s ♥

t♦ ♥♣rt ♠♦t♦♥s r♦♠ t ♦r♥ r♥ ②

rt♠ ♣rt strt② t♦ r ♦♥s♠♣t♦♥ s♥ ♦ ♦♣t♠st♦♥

s ♥ ♣rs♥t ② r♠♥ t ❬r♠❪ s ♣♣r♦ ♦s ♥♦t rqr ♣rt♥

t t♠♣♦r ♦t♦♥ ♦ t r♥ ♦♥t♦♥s ♦♥trr② ♣r♦s s r s t♥

♣rt ♦♥tr♦ s♠

♥ ♦♥ ♣rt strt② ♦r ttr② ❱ s ♥ ♦♣ ♥

t ② ♥ t ❬♥❪ s ♠s t♦ ♠♥♠s t ②r♦♥ ♦♥s♠♣t♦♥

② ♦♥ tt ♥rt ♣rt♦♥s ♠② t♦ r ♦♥s♠♣t♦♥s t♥

♥♦♥♣rt strts

♦ ♣♦st♦♥ s ♥r② ♠♥♠♥t s②st♠s

♥ r♦r ♣♣t♦♥s t ♣♦st♦♥ ♥♦r♠t♦♥ ♥ t r♥ ② ♥ ♣rt②

♣rt s♥ ♦ P♦st♦♥ ②st♠s P ♦r ♥♦r♠t♦♥ tr♥s♠tt ♦r srr♦♥

♥ s ❬❪ ❬♦❪ ♦r ❬♠❪ ♠r t ❬❪ ♣rs♥t

♣rt s ♦♥ ③③② ♦ ♦♥tr♦r ♣rs♥t ♥ r ♦♥tr♦ t

r ♥ sr ♦ t ttr②

r r ♣rt♦♥ ♦♥tr♦r ♦r ♥r② ♠♥♠♥t ❬❪

❱ ♥r② ♠♥♠♥t

t♦st ②♥♠ ♣r♦r♠♠♥

♣rs♥t ♦♥ ❬♦❪ ❬❪ ♥ ❬♦♠❪ ss ♦t r♦rs t♦ ♣rt

t tr ♦♥② ♦♥ s♦rt ♦r③♦♥ ② ♦♥st♥t② ♦♣t♠s t ♦♥s♠♣t♦♥ ♦r

ts s♦rt ♣r♦s ♦ t♠ s t♥q s s ♦♥ t r♦ ♣r♦♣rt② t ♦s ♥♦t

r② ♣♦♥ ♣r♦r ♥♦ ♦ tr r♥ ♦♥t♦♥s t ♦♥② ♣♦♥ t rr♥t s②st♠

♦♣rt♦♥

tt♦r rt♦♥

tt♦r s ♥ ♥t♦r ♦ t ♥r② st♦r ♥ t ♥r② st♦r

s♦rs ♥ts ♥r② t ss ♣t② t♦ r♦r ♥r② ♥

♦ ssts ♦ ♥r② t ♠♦r ♣t② ♦r r♦r② ♠st ♠♥t♥

t♥ ♣rsts r♥ t♦ ♦ ♦♣rt♦♥ ♥r ①tr♠s ♦ r

♥r② ♠♥♠♥t ♦ ❯ttrs ②r s♦r s♥ strt② s

♦♥ ♠♥t♥♥ t stt♦r ♦♥ ♦t t ❯ ♥ t ttrs s ♣rs♥t ♥

❬P❪ ❲♦♥ t ❬❲♦♥❪ st t ♦♣t♠ t♦rq strt♦♥ t♥ ♥ ♥tr♥

♦♠st♦♥ ♥♥ ♥ ♥ tr ♠♦t♦r s♣♣ ② ttrs ♥ ♣r

rttr

♦st ♦ t ♦rs ♥ trtr ♣r♦♣♦s t♦ ♠♥t♥ t ❯ stt♦r t♥

stt ♦r ③③② ♦♥s ❬P❪ ❬rr❪ ❬①❪ ♦r ❬②❪ ♦r s♦♠ t♦rs

♣r♦♣♦s t♦ ♥ ②♥♠ rr♥s ♦r t s ♦♥ t s♣ ♦ t t

♦ s♣s t tr ♥r② st♦r ♥ t ❯ s t♦ ♥♦ t♦ ♣r♠t t

rt♦♥ t s♣s t ❯ ♠st sr ♥♦ t♦ ♥ r♥rt

r♥ ❬❪ ❬❪ ♦r ❬♦❪

rt♦♥ s strt②

èr ❬❪ ♣rs♥ts ♥ ♦r♥ ♣♣r♦ t♦ ♥r② ♠♥♠♥t s♥ t r

t♦♥ ♦ t ♥ ❯ttrs ♠r♦s s s ♦♥ ♦ t rst ♦rs s♦ ♦s

ts ssrtt♦♥ ♦♣s ♥ s ♦♥ t rtrsts ♦ t s♦rs ♥

♥♦t ♦♥ ♥♦r♠s r♥ ♦♥t♦♥s ♥ r ♣rtr ♣♣t♦♥ ❯ s ss ♦

♦sss ♦♥sr♥ ts ♥tr♥ rsst♥ ♥ s ♠♦st ♥t t♥ ttrs strt②

♣r t ❯ t♦ s♣♣② t ♣s ♦ ♣♦r t ♣♦r t♦ rt t

♥ t ♣♦r ♥ r♥rt r♥ ♥ t ttrs s♣♣② t ♠♥ ♥r②

③③② ♦ s strts

③③② ♦ ♦♥tr♦rs r ② s t♦ ♣r♦r♠ ♥r② ♠♥♠♥t ♥ ②r tr

s s ♦♥tr♦rs ♦s ♥♦t rqr ♦♠♣① ♠t♠t ♠♦s s rqr ♥

ss ♦♥tr♦ ♥ t s ♥ ♠♦♥strt tt ts ♥ ♦ ♦♥tr♦rs ♦rs ♥ r♦r

♣♣t♦♥s ③③② ♦ s ♣rs♥t ♥ t ♦♥ t♦♥

r♦♥ ♥ ♦tt♦♥

s ♥r r t ③③② ♦♥tr♦r ♦t♣t s ♣♦r rr♥ ♦r t ♥r② ♦♥

rs♦♥ s♦r s r ♦♥sr s ♦t♣t s t t♦ s♣♣② t ♣♦r t♦

♣r♦♣ t ♠♥t♥♥ t ttr② ♥♦r ❯ stt♦r t♥ ♣r

tr♠♥ ♦♥s ❬ rr ♦ r♥ ① ②❪

♥ ts ssrtt♦♥ t ③③② ♦ ♦♥tr♦rs r ss s ♦♥ tr ♦t♣t

③③② s②st♠ ♦t♣t s♦t ♦t♣t rr♥

♦t♣t ♦ t ③③② ♦ ♦♥tr♦r s t s♦t rr♥ ♣♦r ♦ t

♦t♣t ♥ ❲ ❲ ♦♠♣tt♦♥ ♦ t rr♥ ♦s ♥♦t ♦♥sr t ♣r♦s

♦ t ♦t♣t ♣♦r ♣r♥♣ r s tt t rr♥ ♥ r②

♠ str t♥ t r ♦t♣t ♥ ts ♥ ♦r♥t stt② ♣r♦♠s

① t ❬①❪ ♣rs♥t ③③② ♦ ♦♥tr♦r ♦r ♥r② ♠♥♠♥t ♥

❯ ❱ ②r s♦r r t ♥♣ts r t ❯ ♥ t ♠♥ ♣♦r

t ❬❪ ♥ t ❬❪ ♣rs♥t s♠r ♦♥tr♦r ♦r ttr② ❱

♦r ♥ ❬❪ ♥ st♠t♦♥ ♦ t ttr② s s s tr ♥♣t

♦ t ❬♦❪ ♣rs♥t ♥ ♦r ❯ttr② ②r s♦r s

strt② ss tr♥♣t t♦♦t♣t ③③② ♦ ♦♥tr♦r t♦ ♠♥t♥ t ttr② ♥

tr♣t♦r stt♦r

r♥ t ❬r♥❪ ♣rs♥t ③③② ♦ ♦♥tr♦r ♦r ❯ ②r s♦r ♥

ts strt② t ♦ rr♥ ♣♦r s tr s♥ t tr♥s♦r♠ ♥ ♦♥② t

♦ rq♥② ♣♦r s s s ♥♣t ♥ t ③③② ♦ ♦♥tr♦r r strt

t ③③② ♦♥tr♦rs s ♥ s♦t ♦t♣t rr♥

r ③③② ♦ ♦♥tr♦rs s ♥ ②r tr s ♥r② ♠♥♠♥t

❬①❪ ❬❪ ❬r♥❪ ❬♦❪

❱ ♥r② ♠♥♠♥t

③③② ♦t♣t rt♦♥ ♦♥ t s♦t ♦t♣t rr♥

♦t♣t ♦ t ③③② ♦ ♦♥tr♦r s rt ♥ ♥ t rr♥ ♦ t

♦t♣t ♣♦r ♦t♣t ♥ ❲s ❲s ♥t♦♥ ♦ t s♦t rr♥ ♣♦r

rqrs t♥ ♥trt♥ t ♦t♣t s s ♥ s② ② t♦ ♥ t ♣r♦♠

♦ t s②st♠ s♦ ②♥♠s t ♦s rr♥ t ♦r ♥ ♠♣♦ss t♦

♦♦ ② t r s②st♠ s ♦♥tr♦rs ♦♥sr t ②♥♠ ♦ t s s t

♣r♦s ♦t♣t

rrr t ❬rr❪ st② t ♥r② ♠♥♠♥t ♥ ❯ttr② ❱ t

♣r♦♣♦ss tr♥♣t t♦♦t♣t ③③② ♦ ♦♥tr♦r t rs tt ♥s t

t r ♦♥t♦♥ rt♦♥ ② r♦s

② t ❬②❪ ♣rs♥t ♥ ♥r② ♠♥♠♥t strt② s ♦♥ r♥ ♠♦

r♦♥t♦♥ s♥ ③③② ♦ ♦♥tr♦r ♦r ttr② ❱ t s ♥trst♥ t♦

t tt t strtr ♦ t ♣r♦♣♦s ③③② ♦ ♦♥tr♦r s r② s♠r t♦ t♦s s ♥

♣♦r tr♦♥s r ②♥♠ s r② ♠♣♦rt♥t ss ❬ss ♥ ♠❪ r

strt t ③③② ♦♥tr♦rs ts ♦t♣t s rt♦♥ ♦♥ t s♦t rr♥

r ③③② ♦ ♦♥tr♦rs s ♥ ❱ ♥r② ♠♥♠♥t

❬rr❪ ❬②❪

♦ ♠♣r♦ t ♣r♦r♠♥ ♦ ③③② ♦ ♦♥tr♦rs ③③② ♦ s rq♥t② ♦♠♥

t ♥♦tr t♥q ②rst♦♥ ③③② ♦t ♥ ③③② ♦♣rt

r ♣rs♥t rs♣t② ♥ ❬r♥❪ ♥ ❬❪ t♥q t♦ ♦♣t♠s t ③③②

♦ s②st♠s s♥ ②♥♠ ♣r♦r♠♠♥ s st ♥ ❬①❪

③③② ♦ ♦♥tr♦rs s♥

③③② ♦ ♦♥tr♦rs r ♥r② s♥ tr s♥ ♠♥ ①♣r♥ ♦r t r♦♠

t s②st♠

s ♦ t r♦♠ t s②st♠ ♣r♠ts s♥♥ t ③③② sts ♥ rs s♥ ♦♣

t♠st♦♥ t♥qs s s♠t ♥♥♥ ♦r ♥t ♦rt♠s ❬rt❪ ❬♠❪

❬①❪ ❬♥❪ s ♦♣t♠st♦♥s r ♣r♦r♠ ♦r s♣ r ②s ♥ s♣

s ♦r ♥♦t♥ r♥ts tt t t st ♦ ♣r♠trs s st ♣♣r♦

♣rt ♥ r♥t s ♦r ♥ r r ♦♥t♦♥s t♦♥② rt ♠♦s t♦

r♣rs♥t t ♥ t♦ t t ③③② s②st♠ ♣r♠trs r rqr

r♦♥ ♥ ♦tt♦♥

s ♥ tr♥t t♦ s♥ t ③③② s②st♠s t s ♦ ♠♥ ①♣r♥ ♥ ♦♥

sr r②s ③③② ♦ s②st♠s ♣r♠t t♦ ♦♠♥ t ♥♦ r♦♠ r♥t

①♣rts t♦ s♥ t s ❬♥❪ ❬♥❪ ❬♣❪ ❬r❪ ♦r r♥t ①

♣rts ♥ r♥t t r♥t s ♥ r♥t rs ❬♥❪ ②♣

③③② s②st♠s ♣r♠t t♦ ♦♠♥ t ♥♦ r♦♠ t r♥t ①♣rts ♥♥ t

♥rt♥t② ss♦t t t ♠♥♥ ♦ t ♦rs sr②s t②♣ ③③② ♦

s②st♠ s ♥ ♦♣ t♦ ♣r♦r♠ ♥r② ♠♥♠♥t ♥ ♥ s ♣rs♥t

♥ t ♥ ♣♣♥①

♥rt r♦s♦♣ ♣rs♥tt♦♥ s ♦♥tr♦

st② ♦ t ♦♥tr♦ ♦ ♠t♣②ss ♦♠♣① s②st♠s rqrs ♥♥ ♥ ♣t

t♦♦ ♦♦♥ ❬♦❪ s st r♥t ♣♣r♦s t♦ st② ♥r② ♠♥♠♥t ♥

❱ ♦♥ r♣s ❬P②♥❪ ❱ s♦tr ❬r❪ ♣♦r ♦ r♠s ❬t❪ ♦r

♥rt r♦s♦♣ ♣rs♥tt♦♥ ❬♦s❪ ♠♦♥ ♦trs s ♦♥s♦♥ ♦

ts ♦r ♦♣ t t s t ♠♦st ♣t t♥q t♦ ♥②s

t ♥r② ♠♥♠♥t ♣r♦♠ ♥ ❱

s s②♥tt r♣ t♦♦ ♦r t s②st♠t ♥②ss ♦ ♥trt♦♥s

t♥ t ♠♥ts ss②st♠s ♦ ♠t♣②ss s②st♠ s t♥q s ♦♣

♥ t ♦rt♦r② ♦ tr ♥♥r♥ ♥ P♦r tr♦♥s P ❯♥rst② ♦

r♥ t♦ tt t st② ♦ tr♦♠♥ s②st♠s s tr ♠♥s

♦r ❱ ❬♦s❪ tr r♥t ♦rs rs ♥ ts ♦r♠s♠ s t

s t♦ ♥ ♥ sr ①t♥s♦♥ t♦ ♦tr ♣②s s tr♠ tr♠♦②♥♠s s

♠♦♥strt ♥ t ♦rs r♦♥ ②st♠s

♦r♠s♠ s sr ♥ts r♣rs♥tt♦♥ ♦ ♠t♣②ss s②st♠s

s②st♠t t♦♥ ♦ ♦♥tr♦ strtrs ♥ t ♠♣♠♥tt♦♥ ♥ s② ♣r♦r♠

♥r ♦♠♠♦♥ ♦♠♠r s♦tr ♥r♦♥♠♥ts s s t ♠♥ s

♦♥tr♦ s ♥r② ♦♣ ♥ t ♦♦♥ st♣s s strt ♥ r

r♥st♦♥ ♦ t ♠♦ ♦r♥ t♦ rs

♥②ss ♦ t ♥ ♥rs♦♥s ♦♥tr♦

♠♣t♦♥s ♥ st♠t♦♥s

♦♣♠♥t ♦ ♦♥tr♦ strts

t♣ ♥rt r♦s♦♣ r♣rs♥tt♦♥

♠♦ ♦ t s②st♠ s ♦r♥s ♦r♥ t♦ rs ❬♦s❪

ss ♣t♦r♠s r ♥tr♦♥♥t s♥ ①♥ rs rr♦s ♦♦♥ t

t♦♥rt♦♥ ♣r♥♣ ♥ rs♣t♥ t ♥tr st② ♣r♦t ♦ t♦♥ ♥

♥rt r♦s♦♣ ♣rs♥tt♦♥ s ♦♥tr♦

r s ♦♥tr♦ ♠t♦♦♦② ♣t r♦♠ ❬♥❪

rt♦♥ rs t♥ t♦ ♠♥ts s t♦ t ♥st♥t♥♦s ♣♦r ①♥

s② ss r♥t ♣t♦r♠s t♦ r♣rs♥t

• ♥r② s♦rs tr♠♥ ♠♥ts s♣♣s ♦r r ♥r② s s

ttrs ♦r tr ♦s

• ♥r② ♦♥rs♦♥s ♠♥ts ♦♥rts r♥t ♥tr ♥r② s

tr♦♠♥ ♦♥rs♦♥ ♥ tr ♠♥s ♥ t ♠♥ts ♦♥rts s♠

♥tr ♥r② s tr tr♥s♦r♠rs

• ♥r② ♠t♦rs ♠♥ts st♦r ♥r② s s ♥t♦rs ♦r ♠

♥ sts

• ♥r② strt♦♥s ♦♣♥ ♠♥ts ♦r ♥r② strt♦♥ s s ♦r

♠♥ r♥ts

t♣ ①♠ ♦♥tr♦ strtr

♦♥srs t t♦rt t♦♥s ♥ ♠sr♠♥ts rqr ② t

t♦ ts t♦♥s r ♥♦t ②s t♥② ♦r ♥♥② s ts

st♣ s ♥ssr② t♦ ♥rst♥ ♦ t♦ ♣t t strtr t♦ ♣rt ss

①♣♥s ♥ ♣r♣s ♠♦r rst strtr ♦ t t r♥t ♦♥tr♦

♦ts t♦ ♥t ♥ t ♦s r ♥rt rrss ♦ ♣rt

sss t ♦♥rs♦♥ ♦s r rt② ♥rt ♥ t ♠t♦♥ ♦s r ♥rt

s♥ ♦♥tr♦rs ♥ ♦rr t♦ rs♣t ♣②s st②

t♣ Prt ♦♥tr♦ strtr

P s t ♥ st♣ ♥ t s ♠t♦♦♦② t♦ ♥ t ♦♥tr♦ strtr

♦ ♥ s②st♠ t ♦s t♥② ♥ ♥♥② ♦♥tr♦ s②st♠

r♦♥ ♥ ♦tt♦♥

P ♦ rqr ♠♦t♦♥s ♦ t s♥ s♠♣t♦♥ ②♣♦tss ♦ ♦ r♦♠

t t♦ t P t ♠sr♠♥ts tt r ♣②s② ♦r ♦♥♦♠② ♥s r

s♣♣rss ♦s② t② ♥ s♦♠t♠s s♦ r♣ ② s♦ s♦tr s♥s♦rs

♥ t♦♠t♦♥ ts ♦ s♦ ♦srrs ♦r st♠t♦rs

s ♥ s♦♠ ♦♠♣♠♥tr② ♣t♦r♠s ♥ ♦r♠s♠ r strt ♥

s ♥

s ♠♥ts ♣②s ♠♥ts

♠♥t Pt♦r♠ Pt♦r♠

①♠♣♠♦ ♦♥tr♦

ttrs

♦r ❯tr♣t♦rs

♦s

♣t♥

♠t♦♥ ♥t♥

♥ st

♦♥♦♣②s ♦♥rtr

♦♥rs♦♥ r♥s♦r♠r

♣ rt♦r

t♣②s tr ♠♥

♦♥rs♦♥

t♣ ♦ ♦♥tr♦ strt②

st st♣ s t♦ ♥ t ♦♥tr♦ strt② rr♥ t ♦ ♦♥tr♦ ♦ts ♥

t ♣rt ♦♥tr♦ strtr

♦ts ♦ t ♥r② ♠♥♠♥t ♥ r ♣rs♥t ♥ ♣tr s

♥r② ♠♥♠♥t ♦ ts ❱ s ♦♥ ♦ t ♣r♥♣ ♦ts ♦ ts P ssrtt♦♥

ts st♣ s ② sss ♦♥ ♣tr

t ♦rs

♦r ts ♦t ♥ ♦♥ ♦♥ t ♦♦♥ ssrtt♦♥s rs ♦♥ P ♦r

♦ Pr ♥ ♦s②r♦ P ♣rs♥ts t ♥♠♥ts

qt♦♥ rqr ♦r s♣rs♥ P st♥ts ♥ r♥

♥rt r♦s♦♣ ♣rs♥tt♦♥ s ♦♥tr♦

♦♠♣♠♥tr② ♠♥ts ♦♣♥ ♥ st♦rs

♠♥t Pt♦r♠ Pt♦r♠

①♠♣♠♦ ♦♥tr♦

♦♥♦♣②s s

♦♣♥ r♦①

t♣②s r ♦♠♣rss♦r

♦♣♥ st

t♦

st♦r

♦ ❬♦s❪ t P ♦ r ❲ ♦♠♠ P ♦♣s s

♦♥tr♦ strtrs ♦r r♥t ❱s ❬♦♠❪ t P ♦ s r♥♦

♦t t♦ s②st♠s ❬r❪ t P ♦ r ♦♦♥

P st② t ♦ ♥r② s♦rs ❬♦❪ t P ♦ s ♥ P

♦t ♦ ♣♦rtr♥s ♦ ❱ ❬♥❪ ♥ t P ♦ s

èr P ♦t t♦ t st② ♦ s③♥ ♥ ♥r② ♠♥♠♥t ♦ t s♦rs ♥

❱ ❬❪

❲ ts rsr s ♦♥t ♠♦r P st♥ts t r ♦r♥

r♦♥ r ❯♥rst② ♦ ♥ ❬❪ ♦r st

t♦♥r② ②r s♦rs ♣♦t♦♦t s②st♠s r ♥♠é

r♦♦♣tr ♦r ②r ♦♣tr ♦♥tr♦ ♥ ♥r② ♠♥♠♥t ❬♥❪ r ②

♦r ♦♥rt♦♥ ♦ t♠♣rtr ♥ tr♥ ♠♦t♦r ❬②❪

♥ r rt st♦♠ r♥s♣♦rt ♦r ♥r② ♠♥♠♥t ♥ ②r

♦♦♠♦ts ❬r❪

r♦♥ ♥ ♦tt♦♥

♦♠♣♠♥tr② ♠♥ts ♠sr♠♥t st♠t♦rs ♥ ♦♥tr♦

♠♥t Pt♦r♠ ①♠♣

sr♠♥t ♥s♦rs

st♠t♦r ♦♠♣rss♦r rt♦r♣②

♦r ♠♦ t♦rq s s♣

♦♥tr♦

♥r②

♥♠♥t

trt②

♦t ♦♠♣t♥ ♥ t②♣ ③③② ♦

♦t ♦♠♣t♥ t♥qs st② r♦r ♣r♦♠s t t♦ ♠♦ ♥ s♦

t♦♥s ♥♥♦t ♣rs② rt s s ♥r② ♠♥♠♥t ♥ ②r tr

s ♦t ♦ ts r♥ ♦ ♦♠♣tr s♥ s t♦ ♥ ♠♦st①t s♦t♦♥s

t♦ ♦♠♣① ♣r♦♠s s ♦♥sq♥ s♦t ♦♠♣t♥ s rtrs ♦r ts ♠♣rs♦♥

♥ ♥rt♥t②

tr ♣r♥♣ r♥s ♦ s♦t ♦♠♣t♥ r ③③② ♦ ❬❩❪ ♣r♦s

t rs♦♥♥ ❬Pr❪ ♥ ♥r♦♦♠♣t♥ ♥r ♥t♦rs ❬②❪ tr ①♠♣s

r t t♦r② ❬❨♦♥❪ rts ♥ ♦s t♦r② ❬Pt❪ ♥ ②s♥ ♥t♦rs

❬❪ ♦ ts t♥qs r ② s ♥♦t ♦♥② ♥ ♥♥r♥ t s♦ ♥ ♦tr

s♣♥s s s ♠♥ ❬❨r❪ ♦r ♥ ♥ ♠♥ts ❬♦♥❪

③③② ♦

♥ t st ②rs ③③② ♦ ♥s ♣r♦ts s ♦♠ r② ♣♦♣r ♦r

♦r ③③② ♦ s ♥♦t s ♥ ♦♥♣t ❩ ♥ tr ♥♥r ♥tr♦

t t♦rt ♦♥♣ts ♦ ③③② ♦ ♠♦st t② ②rs ♦ ♥ ❬❩❪ s

t♥q ♦s ♥♦t rqr ♦♠♣① ♠t♠t ♠♦s s s ♥ ss ♦♥tr♦ ♥

t s ♥ ② ♠♦♥strt tt t ♦rs ♥ ♥str ♣♣t♦♥s s♥ ♥

♠♠ ♣rs♥ts ③③② ♦♥tr♦r ♦r st♠ ♥♥ ❬♠❪

♣r♦s ①♣r♥ ♦r♥ t ③③②♦ ♥ ♦♠♥s s s ③③② ♦♥

tr♦ ♦ tr ♦♥rtrs ♥ ♠♥s ❬ss❪ ♥r② ♠♥♠♥t ❬Ps❪ ❬❪

❬①❪ ♦r ♥♦ss ❬ss❪ ♣rs♥ts ♥ tt ③③② ♦ s r② ♣♦r t♦♦

♥ tr ♥♥r♥ ♣♣t♦♥s ♥tr ♦♥t♥t♦♥ ♦ t ♦rs ♦♣ t

❨ ♣rt♠♥t ♦ ts ts rsr t♦ ♦♥sr t st② ♦ t②♣

P ♣r♦r♠ t t♦♥ P♦②t♥ ♥sttt ♦ ♦♦s P ② r ss ♥♦ t

♦♥t ♦♦♣rt♦♥ t t P

♣tr ♦♥s♦♥

③③② ♦ s②st♠s ♣♣rs t♦ ♠♦r ♣r♦r♠♥ t♥ ss ③③② ♦ s t

s♦♥ ♥ ♥①t sst♦♥

②♣ ③③② ♦

♦♥♣t ♦ ②♣ ③③② ♦ ts s s♦ ♥tr♦ ② ♦t ❩ ♥

❬❩❪ rtss t rst t②♣ ♦ s②st♠ s ♦♣ ♥ ♣rs♥t ♦♥②

②rs tr ② r♥ ♥ ♥ ❬r♥❪ s ♥ ♥s t②♣ s ♥

①♣♥ ♥ rr ③③② ♦ ♥s t♦ ttr ♥ t ♥rt♥t② ❬♥❪

str♥t ♦ t②♣ ③③② ♦ s tt t ts s ♦♥ ♠♦r st♣ t♦r t ♦ ♦

♦♠♣t♥ t ❲♦rs ♦r t s ♦ ♦♠♣trs t♦ r♣rs♥t ♠♥ ♣r♣t♦♥ ❬♦♥❪

②♣ ③③② ♦ s rt② ♥ ♦ rsr ♥ tr r ss

t♦rs ♦r♥ ♦♥ t tt ♦♥ ②♣ ③③② ♦ ♥②② ♥ st ②rs

s ♥ t♦ ♥trst rsrrs r♦♥ t ♦r t ♥♠r ♦ ♣t♦♥s ♥rss t

rt ♦st ♦ t t♦rs ♦r♥ ♥ s ♦♥sr tt ♥ ♦t♣r♦r♠

tr ♦♥tr♣rt s t② ♥ ♠♦ ♦♠♣① ♣r♦sss ♥ ♦♥tr♦rs r

s② ♠♦r r♦st ♥ ttr t♦ ♠♥t ♦st♦♥s t♥ tr ♦♥tr♣rt

♣rs♥ts s♦rt st ♦ r♥t ♣s ♣♣t♦♥s s ♦♥

s ssrtt♦♥ ♣rs♥ts t rst ♦rs ♦t ♣r♦r♠ t

rst ♥tr ♦t s t♦ ♥rst♥ t♦ r♥ ♦ t♦ s ♥ ♠♣♠♥t ts t♥q

ts s ♣rs♥t ♦♥ ♣tr ♥ ♦♥ t ♣♣♥① ♦ r♥t ♣♣t♦♥s s ♦♥

♣rs♥t ♥ ts ssrtt♦♥ t ♦♥tr♦ ♦ ♦♥rtr ♦♥ ♣tr

♥ t ♥r② ♠♥♠♥t ♦ ②r tr ♦♥ ♣tr

♣tr ♦♥s♦♥

♥r② ♠♥♠♥t st② ♦ ②r tr s r ♦♥sr t s

②t② ♠♦ ♦rt♦r② s♥ t♦ t ♥r r ♦♥t♦♥s r♥t tr

♦♠♣♦♥♥ts s ♦♠♣① ♣♣t♦♥ rqrs t ♥t♦♥ ♦ ♣♣r♦♣rt t♦♦s

• ♥rt r♦s♦♣ ♣rs♥tt♦♥ s ♥t s t ♠♦st ♣♣r♦♣rt ♦r♠s♠

t♦ r♣rs♥t ♥ ♠♦♥ t ♥ ts ♥r② s♦rs s s ♥tr ♦

t♥ ♥ ♦♥t t ♥♦♦ ♦ t ♦rt♦r②

• ♦♥sr♥ t rtrsts ♦ t t t♦ ♠♦ ♥ t♦t ♣r♦s

♥♦ ♦ t r♥ ②s ♦♥♥ t♥qs r rt♥ t♦ ♣r♦r♠ t ♥r②

♠♥♠♥t

• ②♣ ③③② ♦ s ♥ st s t♥q t♦ ♣r♦r♠ t ♥r② ♠♥

♠♥t s s ♥ rt♦♥ ♥ rsr ♣r♦r♠ t

♥ st tt♣s♣s ♠♥ ♣rs♥ts ♦♠♣t st ♦ rr♥s ♦t

r♦♥ ♥ ♦tt♦♥

♦♠ t②♣ ③③② ♦s ♣♣t♦♥s

♦♠♥ ♣♣t♦♥ r♥s

t♦♠♦ ♦♥tr♦r ♦r t ss♣♥s♦♥s ❬♦❪

tr♥s♣♦rt ♦♥s♠♣t♦♥ ♣rt♦♥ ❬❩♦❪

t♠ s♣ ♦♥tr♦ ♦ s ♥♥s ❬②♥❪ ❬②♥❪

r ♠♥♠♥t ♦rst♥ ❬❪ ❬♠❪ ❬❪

❱ sst♦♥ ❬❲❪

♦t ♦ ❬❪

tr tr ♠♥s ♦♥tr♦ ❬r❪ ❬r❪ ❬②❪

♥♥r♥ t rr♥t ♥②ss ❬♦♠❪

P♦r tr♦♥s ❬♥❪ ❬r❪

P♦r s②st♠ stsr ❬♦❪

r♥s♦r♠r ♥♦sts ❬♦r❪

P♦t♦♦t rr② ♠♦♥ ❬❪ ❬❪

♥str rr ♠♣♠♥tt♦♥ ❬❪ ❬♦♣❪

♦♥tr♦ q ♦♥tr♦ ❬❲❪

P♥t ♠♦♥t♦r♥ ♥ ♥♦sts ❬st❪ ❬♥❪

t② ♦♥tr♦ ❬❪

♦♦ts ❬♦♣❪ ❬r❪ ❬❪ ❬r❪ ❬rt❪

t s♣rst♦♥ ❬❪

♠♣rtr st♠t♦♥ ❬♣t❪ ❬♥❪

❱rt♦♥ ♥ ♣rssr st♠t♦♥ ❬♦♠❪ ❬Pr❪

rt♥ ♠♥ rs♦r st♦♥ ❬♦t❪

s♦♥ ♥♠♥t sts ❬♣❪

s♣♣♦rt s st♠t♦♥ ❬r❪ ❬❪ ❬Prs❪

t♦ rt ♥②ss ❬r❪ ❬❪ ❬③❪

♣♣② ♥ ♠♦♥ ❬❪

❯r♥ tr ♠♥♠♥t ❬r❪

♥♦ss ❬♥♥♦❪ ❬♥♥♦❪ ❬ ❪ ❬rt❪ ❬③❪

♦♦② ❬♦♥❪ ❬③♥❪

rt♠♥t ❬♦♥❪ ❬❪

♦tr ♦♥♥t♦♥ ♠ss♦♥ ❬♥❪

♦ ♣♦st♦♥ s②st♠s ❬s❪

♠ ♣r♦ss♥ ❬st❪ ❬♥❪ ❬ ❪ ❬♦♥❪ ❬♥❪

♥ ♣r♦ss♥ ❬r♥❪ ❬st❪

♣ r♦♥t♦♥ ❬❩♥❪

❲tr ♦rst♥ ❬❪ ❬❪

♣tr

♥r② s♦rs ♠♦♥ ♥

♦♥tr♦

s ♣tr s ♦t t♦ st② t ♥r② s♦rs ♦♥

♥♦ ♥ ♥rst♥♥ ♦ t ♥ts ♥ rs ♦ t r♥t

♥r② s♦rs s ♥♠♥t t♦ st② tr ♠♣♠♥tt♦♥ ♥ ②r tr ❱s

❱ ❱ ♣r♠ts t r♦r t♦♥ ♦ t ♦♦♥ ♥r② s♦rs t

trs s②st♠s tr♣t♦r s②st♠s ♥tr♥ ♦♠st♦♥ ♥♥s ♥ ②

s②st♠s s ♣tr ♣rs♥ts t rtrsts ♠♦♥ r♣rs♥tt♦♥ ♥ ♦♥tr♦

strtr ♦ ts ♥r② s♦rs

♠t♦♥ s ♥ssr② st♣ ♦r ♣r♦r♠♥ ♥② ①♣r♠♥t ♠♣♠♥tt♦♥ ♦

♥r② s♦rs t ♠s t♦ ♥ tr ♦♥tr♦ strtr ♦r tr ♥r② ♠♥♠♥t t

rqrs t♦ ♦♣ t♦rt ♠♦s ♥ t♦ ①♣r♠♥t② ♥t② tr ♣r♠trs

♥r② s♦rs ♠♦s r s ♦♥ t♦s ♥ ♥ trtr r ♦♥tr♦ str

trs r ♦♣ s♥ ♥rt r♦s♦♣ ♣rs♥tt♦♥ t♥q ♦st

♦ ts ♣rt ♦ t rsr s s ♦♥ ♣r♦s rsr ♦r ♦♣ ♥

♦rt♦r②

• ttrs ♠♦ ♥ ♣r♠tr ♥tt♦♥ ♦♥ ② r ❬ ❪

• ❯tr♣t♦r ①♣r♠♥t st♣ ♦♣ ② ♥♠é ♥ r ❬♥❪

• r ♦♠♣rss♦r ♠♦ ♥ ♣r♠tr ♥tt♦♥ ♣t r♦♠ t ♦rs ♦ ♥

❬❪ ♥ ♥rr♥♣rr ❬♥r❪ rs♣t②

• ♣r♠trs ♥tt♦♥ r♦♠ t ♦r ♣rs♥t ② ss t ❬ss❪

• s②st♠ ♠♦ ♥ ♦♥tr♦ strtr ♦♣ ② ♦♦♥ ❬♦❪

s t ♥ s♥ ♥ t♦♥ ♠♦tt♦♥ ♦r s♥ t ♣♣r♦ s ts t②

t♦ s rt② ♣r♦s rsr ♦rs ♥ t♦ ♥ t ♣tst♦♥ ♦ t rsr

♦♣♠♥ts ♣r♠♥r② ♦t♥ ♥ t ♦rt♦r②

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

s ♣tr s ♦r♥s s ♦♦s t♦♥ s ♦t t♦ t ttrs ❯tr

♣t♦rs ♥ s②st♠s r st ♥ t♦♥s ♥ rs♣t② ②

s②st♠s r ♥tr♦ ♥ t♦♥ t♦♥ ♣rs♥ts t trt♦♥ ♥ ♥ ♥

rs ♠♦♥ ♥trt♦♥ ♦ t r♥t ♥r② s♦rs ♥ s ♣rs♥t ♥

t♦♥ ♥② t♦♥ ♣rs♥ts t ♦♥s♦♥s ♥ ♦t♦♦s

ttrs ♥ s

ttrs r tr♦♠ ♠t♦rs tt st♦r ♠ ♥r② ♥

♦♥rt ♥t♦ tr ♥r② ♥ s t s rt♦♥ s♦r tr ♥r② ♥

♦♥rt ♥t♦ ♠ ♥r② s ♦ tr s♣ ♥r② ♥ ♣♦r rrst② ♥

rt② ♦ ♦st rr♥ ♦tr t♥♦♦s ttrs r ♦♥ ♦ t ♠♦st ttrt

s♦rs t♦ s ♥ tr ♥ ②r tr s ♦r t② st rqr

♣ rsr ♦♥ sss s rt♦♥ srt② ♦r r②♥ ttrs t♥♦♦s r

♦♠♠♦♥② s ♦♥ ♠ts s ♥ ♠♦r r♥t② t♠ ♦r ♥ ♦r t t

t♠ ❱ s s♥ ♥ ♦♥strt s t ♠♦st ♦♠♠♦♥ t♥♦♦②

♥ t ♠♦st ♥trst♥ rr♥ t ♣r ♥ ttrs ♥ t♥ rt♥ s♦ s

❬♦♠ r♠ ❪

ttrs r ♦♠♣♦s ♦ t♦ tr♦s ♥ ♥ tr♦②t Pb ♣t

♥ ♦① PbO2 ♣t ss♣♥ ♥ s♣r (H2SO4) s strt ♥

r ❲♥ ♥ tr ♦ s ♦♥♥t tr♦ tr tr♠♥s sr t

tr♦s rts t t s♣r ts rt♦♥ rss tr♦♥s tr rr♥t

♥ ♣r♦s s♣t ♥ t tr♦s (PbSO4) ♥ tr H2O ♥ t tr♦②t

rrs rt♦♥ rqrs s♣♣② ♦ tr ♥r② rr s ♦♣rt♦♥

♣r♥♣ s s♠r t t rt♦♥s r ♦♦s② ♥♦t t s♠ ♥ ♦tr ♥ ♦ ttrs

r ttrs s♠t r♠ t ♥ ♦♥strt♦♥ ❬❪ rt

ttrs ♠♥② rs ♥ s♠ qt r r♦♠ t stt♦rt

tr ♥② s♣ ♥r② ♥ ♣♦r r ♠ ♦r t♥ t♠s ♦r ♥

s ttrs rtss ttrs ♥ ♥r r st ♥ ♥tr♠t t♥♦♦②

rr♥ ts s♣s ♣♦r ♥ ♥r② t ♥ ♦sr r♦♠ ♦♥ ♣♦t ♥ r

ttrs ♥ s

tt ttrs ♣rs♥t ss s♣ ♣♦r t♥ tr♣t♦rs ♦r ②s ♥ ss

s♣ ♥r② t♥ s ♦r ts rs♦♥ ttr② ♥r② ♠♥♠♥t s♦t♦♥s ♦

♥♦t r② ♠ t tr r♥t t♥♦♦s

tst ♥ s q♣♣ t ♥ ♦ rt ttrs ♥

srs ♦♥♥t♦♥ s t ❱ ttrs r rt② ♦♥♥t t♦ t s t ♥♦♠♥

♦t ♦ t s s ❱ rs♠s t ♣r♠trs ♦ t ttrs

♥ r strts t ttrs ♠♣♠♥t ♥

ttrs ♣r♠trs

sr♣t♦♥ ❱

r♥t r

♥♦♦②

♠♥ts ♥ srs ❬❱❪

♦♠♥ ♦t ❬❱❪

♣t② ❬❪

r ttrs ♠♣♠♥t ♥

♦♥ ♥ ♣r♠tr ♥tt♦♥

rt♥ ttrs ♠♦ s t ♦♥ ♣rs♥t ② r♦♦ ❬r❪ ttrs

r r♣rs♥t ② ♥ q♥t tr rt ♦♠♣♦s ② tr ♠♥ts tt ♥♦t

♦♥② ♣♥s ♦♥ t ♥st♥t♥♦s s t s♦ ♦♥ ts rsr st♦r② s

♥♦t ②s s s t s ♥ ①♣r♠♥t ♣r♠tr ♥tt♦♥ s

♣rs♥t ♥ ❬ ❪ ♦r♠r P rsr ♦t r♦♦ ♠♦ s strt

♥ r

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

r r♦♦s ttrs ♠♦ ❬r❪

tt♦r

stt♦r s ♠♥s♦♥ss q♥tt② ♥ s t rt♦ t♥ t

rs ♣t② Qresidual ♥ rt ♣t② Qnominal ♦ t ♥r② st♦r s♦r s

♥ ♥ qt♦♥ s ♥ ♥t♦r ♦ ♦ ♠♥② ♥r② s t♦

s♣♣② ♦r ♥ r♦r ♥ ts st♠t♦♥ s ♥♠♥t ♦r ♥r② ♠♥♠♥t ♥

ttrs t ♣♥s ♦♥ ♠t♣ t♦rs s rr♥t sr st♦r② s

sr ♦r ♠♥t t♠♣rtr ♦r ts rs♦♥ st♠t♦♥ ♥ ttrs s r②

t ts

SOC =Qresidual

Qnominal

❲♥ t♦rt ♠♦s r s t♦ st♠t t t rsts r s ♦♥ st♠t

♣r♠trs ♥♦r s♠♣t♦♥ ②♣♦tss r♦♦ ♠♦ str♦♥② ♣♥s ♦♥

t ttrs st♦r② r♥t ♣♣r♦s t♦ st♠t ♥ ♣rs♥t

❬P ❯r ❨♥❪

♥ t ♦♦♠ ♦♥t♥ ♠t♦ s♦ ♥♦♥ s rr♥t ♥trt♦♥ ♠t♦

s rt♥ t♦ st♠t t t ttrs ♦♣♥ rt ♦t ❱ s ♠sr t

t strt♣ ♦ t t♦ st♠t t ♥t Q0 s♥ ♥♦r♠t♦♥ r♦♠ t

♠♥trr ❬❪ ♥ t ttr② rr♥t s ♥trt t♦ st♠t t ♠♦♥t ♦

r s♣♣ ♦r r♦r ♦♥sr♥ ♥ ♥② η ② t ttrs s ♠t♦ s

♦r♠② ♣rs♥t ♥ qt♦♥

SOCbatteries ≈Q0(OCV ) + η

∫

ibatt dt

Qrated

♣r♥♣ rs ♦ ts s♠♣ ♣♣r♦ r ♠♣rs ♠sr♠♥ts

♦ t rr♥t ♥ ♠t♥ rr♦rs t ♦sss r♥ r♥ ♥ sr♥

r t t♦ st♠t ♥ t ♦s ♥♦t ts ♥t♦ ♦♥t t t ♦ ♥ ♥ t

rs ♦♥ t rs ♣t② rtss t ♥trst ♦ ts ♠t♦ s ♥ tr

s♠♣t② ♥ ①t② t ♦ s② ♥♥ ② ♦♥sr♥ t ♦sss ♦r t ♥

ts ❬❪ ❬P❪

ttrs ♥ s

♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

♥ t ttrs r rt② ♦♥♥t t♦ t s ♥ rt ♦♥tr♦ ♦

ts s♦r s ♥♦t ♣♦ss ♥ t s ♦t s ♠♣♦s ② t ttrs s

♦♥sq♥ ♥② s♦r ♦r ♦ ♦♥♥t t♦ t s ② s②st♠ ♥♦r

tr♣t♦r s②st♠s trt♦♥ ♥ ♥ ♥rs ts s rr♥t s♦r isx

r strts t q♥t rt ♦ ts ♦♥rt♦♥ r t ttrs

♠♣♦s t ♦t t♦ t s♦rs ♥ t s♦rs ♠♣♦s t rr♥t t♦ t ttrs

rs♣t♥ ♣②s st② ♥ r♦s s qt♦♥s

r ttrs ♥ s

ibatt = iS1 + iS2 + iS3

Vbus = Vbatt

♥ ♥rt r♦s♦♣ ♣rs♥tt♦♥ ♦r♠s♠ ttrs r r♣rs♥t

s♥ s♦r ♠♥t ♥ t s s r♣rs♥t s♥ ♠♦♥♦♣②s ♦♣♥

♠♥t r♥t rr♥t s♦rs ♦♣ t♦ t s r r♣rs♥t ② s♦r

♠♥ts s s②♥♦♣t ♥ s ♥ r ♣rs♥ts t ♦

t ttrs t s ♥ tr ♥r rr♥t s♦rs ♥ t♦♥ ts ♥r

s♦rs r r♣ ② tr rs♣t

r ttrs ♥ s

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

❯tr♣t♦r s②st♠

❯tr♣t♦rs s♦ ♥♦♥ s tr ♦②r ♣t♦rs ♦r s♣r♣t♦rs r

tr♦♠ s♦rs tt st♦r tr ♥r② tt ♥ rt② s t♦t ♦♥

rs♦♥ ♥ s♦ t ♥② s s♦r s r② s♣ ♣♦r t

♦ s♣ ♥r② ❯tr♣t♦rs ❯ r ② ♦♥sr ♥ tr♥s♣♦rt ♣♣t♦♥s

s ♦ ts s♣ ♣♦r ♥ s♦ s ♦ ts ♥②

s ttrs tr♣t♦rs r ♦♠♣♦s ♦ t♦ tr♦s ♠♠rs ♥ ♥ tr♦②t

tr♦s r ♠ ♦ tt r♦♥ ♥ r♦r ② tr t tr♦②t

♦ q♦s s s (H2SO4) ♦r s (KOH) ♦r ♥♦♥q♦s s s ♣r♦♣②♥

r♦♥t ♦r t♦♥tr ❬P♥❪ ❯ ♣r♦ts r♦♠ t ♦②r ♣t♥ ♣r♥

♣ ts ♥s t♦ ② ♥rs t ♣t♥ ② r♥ t st♥ t♥ t

tr♦s d ♥ ♥rs♥ t t tr♦s sr S s qt♦♥ r

♣rs♥ts t ❯ s♠ts s s t r♣rs♥tt♦♥ ♦ ♣♦r ♥ r♦♥ tr♦

t ②r

C = ǫS

d

r ❯ s♠t t ♥ tr♦ t ②r ♣♦r r♣rs♥tt♦♥ rt ❬♥❪

♣t♥ ♦ ❯ s sr ♦rrs r t♥ ♥ ♦♥♥t♦♥ tr

♣t♦rs t tr♣t♦rs s ♥ ♣rs♥ts ♣t♥ ♦ ♦r

t s ♦ ♥ tr♦②t t♦ ♥rs t ♣t♥ s s♦ ts ♦♥sq♥ t ♠①♠

♦t ♥ ❯ s ② r ♠t t♦ ♦t ❱ ♦ ♥rs t tr♠♥ ♦t

❯ r ♦♥♥t ♥ srs ts ♦r♥ts ♦t ♠♥ t♦ t ♠s♠t ♥ t

rtrsts ♦ t r♥t ❯ ♥ ts ♥ rt s t♦ s♥ t♦ ♦ ts

♦♥♥t♦♥

s q♣♣ t tr♣t♦r ♥s ♥ s ♦♠♣♦s ♦ ♠♦s ♦

❯ t ❯ r ♦♥♥t ♥ srs ❯ s ♦♣ ② ♦r①

r♥ ♥ ts ♦t ♥♥ s②st♠ s ♦♣ ② ♥ ♦♦♣rt♦♥ t t

rsr ♦rt♦r② ♥② r♥ ❬s♣❪ ❯ s ♦♠♣♦s ② t t♦

❯ ♥s ♥ t ♣♦r tr♦♥ t♦ ♦♦st t ♦t ♥ t♦ ♣r♠t t ♦♥♥t♦♥

❯tr♣t♦r s②st♠

t♦ t s ♦♥rtr s ♥ s♣② ♦♣ ♦r ②

t s♦t② ♦♦s r♥

♥ t ♦♦♥ ❯ s s t♦ rr t tr♣t♦rs ①s② ❯tr♣t♦r

s②st♠ ❯ rrs t♦ t ❯ ♥ t ♣♦r ♦♥rtr r s♦s t ❯

♠♣♠♥t ♥ tst ♥ ♥ rs♠s t ❯ rtrsts

r tr♣t♦rs ♠♣♠♥t ♥

tr♣t♦r s②st♠ ♣r♠trs

sr♣t♦♥ ❱

❯ r♥t

♦♥rtr s♣♣r

❯ ♥ srs ❬❱❪ ❬❪

❯ t rr♥t ❬❪

♦♥rtr rt rr♥t ❬❪

❯ t ♦t ♣t♥ ❬❱❪ ❬❪

♦♥

❩t t ❬❩❪ ♦sr tt tr♦♠ tr♣t♦rs qt s♠r

t♦ tr ♣t♦rs t t② s♦ ♦sr ♥ ♣♥♦♠♥♦♥ ♥ ♥tr♥ r

rstrt♦♥ ② ♣r♦♣♦s t♦ ♠♦ t ❯ t ♥ q♥t tr rt ♦♠♣♦s

② ♣ss ♦♠♣♦♥♥ts s ♠♦ ♣rs♥ts ♣r♥♣ r♥ r♣rs♥t♥ t ♥r②

♠t♦♥ ♥ ♠t♣ s♦♥r② r♥s t♦ r♣rs♥t t r rstrt♦♥ ♥

t ssr s ❯ q♥t rt s r♣rs♥t ♥ r

t ❬❪ ♣r♦♣♦s t♦ ♠♣r♦ ❩t ♠♦ ② ♦♥sr♥ t rq♥②

♥ t♠♣rtr t ♥ t ❯ q♥t rt s strt ♥ r P

r♠tr ♥tt♦♥ ♥ ts ♣♣r♦ s rt② ♦♠♣t s st ② ♥♠é ♥

s str ♥tr♥s♣ t ❬♥❪

♥ ❱ ♣♣t♦♥s t ❯ ♦♣rts t rt② ♦ tr rq♥s ♠♦r♦r

♥ ♦♦♥ s②st♠ rts t t♠♣rtr ♥ t ❯ ♦r ts rs♦♥s r

q♥② ♥ t♠♣rtr rt♦♥s r ♥♦t ♦♥sr ♥ t ♠♦ ♦ ❩t s rt♥

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

r r♥t tr♣t♦r ♠♦s ❩t ❬❩❪ t ❬❪ rt

♦r ts ♠♦ ss ♠t♣ s♦♥r② r♥s ♥ r♣rs♥t ② ♦♥②

♦♥ é♥♥q♥t r♥ ♦ rq♥s ②♣♦tss

♣r♥♣ r♥ r♣rs♥ts t ♥tr♥ rsst♥ Ri ♥ t ♥r② ♠t♦♥

② ♦♥sr♥ ♦♥st♥t ♣t♦r Ci0 ♥ ♥♦♥♥r ♣t♦r Ci1 Vceq ♣s ♥♦t

tt Ci1 s ♣rs♥t ♥ ❬❱❪ s♦♥r② r♥ r♣rs♥ts t r rstrt♦♥

② ♦♥sr♥ ♦♥st♥t ♣t♦r C2 ♥ t ssr ② ♦♥sr♥ rsst♥

R2 rt♥ q♥t rt s strt ♥ r

r t♥ ❯ q♥t rt ♠♦

Pr♠tr ♥tt♦♥

❩t ❬❩❪ ♣r♦♣♦s ♣r♦r t♦ ♥ t ♣r♠trs ♦ t ❯ q♥t

rt ♣rtr♠♥ rr♥t st♣ ♦ rr♥t s ♣rs♥t ♦♥ r s ♠♣♦s

t♦ t ❯ t♥ t ♦t♣t ♦t s ♥②s t♦ ♥ t ♣r♠trs ♦r t rr♥t

s ♥ ts ♣♣r♦ ♦s ♥♦t r♣rs♥t r ♦♣rt♦♥ ♦♥t♦♥s

♥ ts ♦r ♥♦ ♣♣r♦ t♦ t♦♠t② ♥ t ♣r♠trs ♦ t ❯s q

♥t rt s ♣r♦♣♦s ♣r♦r s rs♠ ♥ t♦ st♣s t♦ ♠♣♦s ♥♦♥

♣rtr♠♥ rr♥t t♦ t ❯ ❱s ❯ rr♥t ♥ ♥♦r♠ ♦♣rt♦♥ s strt

♥ r ♥ t♦ ♥②s t ♦t♣t ♦t

①♣r♠♥t ♠sr♠♥ts

①♣r♠♥t② r rr♥t s ♠♣♦s t♦ t ❯ ♦t s t♦ ♠sr

t ♦t rt♦♥ rr♥ t rt♦♥ ♦ t rr♥t ①♣r♠♥t t t♠

rr♥t iexp ♥ ♦t Vexp s s t♦ ♥ t ♣r♠trs s♥ ♥ trt ♣r♦r

❯tr♣t♦r s②st♠

♥♠st♦♥ ♥t♦♥ ♦♥str♥ts ♥ ♥tst♦♥ ♣r♠trs

tr ♥t♦♥ ♠♥♠st♦♥ s s t♦ ♥ st ♦ ♣r♠trs Ri Ci0 Ci1 C2

♥ R2 r♣rs♥t t ♦r ♦ t ❯ st ♦ s s t♦ rs♣t ♣②s

♦♥t♦♥s ♠t♠t ♦♥str♥ts ♦ t rs s t ♣r♠trs ♠st

♣♦st t ♣t♥s ♥♥♦t rtr t♥ t ♥♦♠♥ ♣t♥ s♣♣r t

st s s ♣②s ♦♥t♦♥s r ♣rs♥t s ♠t♠t ♦♥str♥ts

Ri, Ci0, Ci1, C2, R2 > 0

Ci0, Ci1, C2 < Cnominal

trt ♣r♦r rqrs t ♥t♦♥ ♦ st ♦ ♣r♠trs ♥ ❵r

s♦♥② r♣rs♥t t ♣②s s s st ♦ ♥tst♦♥ s s s ♥ t rst

trt♦♥ ♥ ♥ t ② t ♦rt♠ ♦♥r ♦r ♥♦t ♦ ♦ ts

s s t♥ ♥♠♥t ♦r t ♦♥r♥ ♦ t s♦t♦♥ ♦♦♥ ss♠♣t♦♥s

♥ ♥tst♦♥ s r rt♥

♦ t ♣t♥ ♥ t ♠♥ r♥ s ♥r r♦♠ t ♦ t ♥♦♠♥

♣t♥ t ♥ ss♠ r♦♠ t②♣ s ♥ trtr s s ❬❩❪ ❬❪

❬❪ ♦r ❬♥❪ tt t t♦t ♣t♥ s q② strt t♥ t t♦

♣t♥s ♦ t r♥

Ci0(0) =Crated

2

Ci1(0) =Crated

2 Vrated

♦ t ♣t♥ ♦ t s♦♥r② r♥ s ①♣t t♦ ♠ ♦r

t♥ t ♣t♥ ♦ t rst r♥ s♦♥r② r♥ ♣t♥ s ♥ s

rt♦♥ ♦ t rst r♥ ♣t♥ s ♦♥ t②♣ rsts ♥ trtr C2 s ♥♦t

r r♦♠ % ♦ Ci0

C2(0) =Ci0

10

♦ t ♠♥ r♥ rsst♥ s ①♣t t♦ t ♥♦♠♥ ♦ t

♥tr♥ rsst♥ t s♦♥r② r♥ rsst♥ s ①♣t t♦ ♠ r t♥ t

♣r♠r② ♥ t②♣② tr rt♦ s ♥♦t r r♦♠

Ri(0) = Rrated

R2(0) = 20 Rrated

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

♥♠st♦♥ ♥t♦♥ trt ♣r♦r

st st♣ ♦ ♣r♠tr ♥tt♦♥ ♦♥ssts ♥t♦ ♥ trt ♣r♦r s ♦♥

t s♠t♦♥ ♦ t ❯ rs♣♦♥s t♦ iexp t rr♥t ①♣r♠♥t② ♠♣♦s t♦ t r

❯ s♠t Vsim ♥ ①♣r♠♥t Vexp r♥ s ♦♠♣r ♠♥ sqr

♣r♠trs Ri Ci0 Ci1 C2 ♥ R2 ♠♥♠ss ts r♥ r rt♥

♥ ♣♣t♦♥ s ♥ ♦♣ ♥ t ♥ t ♠♥ t♦ t♦♠t②

♥ t ♣r♠trs ♣♣t♦♥ s s ♦♥ t ♠♥♦♥ ♥t♦♥ trt

♣r♦r s strt ♥ r ♣♣t♦♥ ♦♣ ♥ t ♠♥ s

strt ♥ r

r ❯ q♥t rt ♣r♠trs ♥tt♦♥ ♦rt

r ❯ q♥t rt ♣r♠tr ♥tt♦♥ ♠♥ ♣♣t♦♥

s ♥t♦♥ ♥ ♠♥♠♠ ♦ ♦♥str♥ ♥♦♥♥r ♠tr ♥t♦♥ ♥ s ①♣♥ ♥ t

t tt♣♠t♦rs♦♠♣t♦♦♦①♦♣t♠♠♥♦♥t♠ t♦rs st

❯tr♣t♦r s②st♠

①♣r♠♥t t♦♥

♦ t t ♣r♦♣♦s ♣r♦r ①♣r♠♥t t♦♥s r ♣r♦r♠

rst t♦♥ s rs ♥ t ♦rt♦r② ♥r ♦♥tr♦ ♦♥t♦♥s s ♣r♦♣♦s ②

❩t s♦♥ t♦♥ s ♣r♦r♠ t t ❯ ♠♣♠♥t ♥ t

♠♦ ♦rt♦r② s t ❯ r s t♦ r t ts s ♥ t♦♥ ♥r

rtst♦♥

r ♣rs♥ts t ♦t♥ rsts ♦r t ♣rtr♠♥ rr♥t ♦♥② ♦♥ ❯

♥ r ♣rs♥ts t ♦t♥ rsts ♦r t r rr♥t ♣r♦ ♦t ❯

♥s s rsts r ♦♥sr stst♦r② ♦r s♠t♦♥ ♣♣t♦♥s s

♥ ♣rs♥t t s ♦r t ♣r♠trs ♦ t q♥t ❯ rt ♠♦ ♥

s

r ❯ q♥t rt ♣r♠tr ♥tt♦♥ ❱t♦♥ rsts

❯ ♣r♠trs s♥ ♥

Pr♠tr ❱

Crated ❬❪

Ci0 ❬❪

Ci1 ❬♠❱❪

C2 ❬❪

Ri ❬♠Ω❪

R2 ❬Ω❪

❯ ♣r♠trs ♦t ♥s

Pr♠tr ❱

Crated ❬❪

Ci0 ❬❪

Ci1 ❬♠❱❪

C2 ❬❪

Ri ❬♠Ω❪

R2 ❬Ω❪

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

r ❯ q♥t rt ♣r♠tr ♥tt♦♥ ❱t♦♥ rsts

tt♦r

r ♥ ♥ tr♣t♦r s rt② rt t♦ ts tr♠♥ ♦t s ♦♥s

q♥ ❯ st♠t♦♥ s ♠ sr ts t♥ ♥ ttrs qt♦♥ ♣rs♥ts

♦♥ ♠t♦ t♦ st♠t t s♥ t s ♦ t ❯ ♦t ❬❪ ♦r ts

♣♣r♦ s t♦ s♥♥t ♣r♦♠s t ♦s ♥♦t ♦♥sr t ♦t r♦♣ ♥ t

♥tr♥ ❯ rsst♥ ♥ ts st♠t♦♥ s r♣rs♥t ② s♦♥t♥♦s ♥t♦♥

t ♦t ♥ ❯ s s♦♥t♥♦s s ♦ ts ♥tr♥ rsst♥ t s

② ♥t♦♥ ♦♥t♥♦s ♦ ♦♥srt♦♥ ♦ ♥r②

UCSOC ≈Vuc

Vrated

♥ ts ssrtt♦♥ ♥ ♠♣r♦ ♠t♦ t♦ st♠t t ❯ s ♣r♦♣♦s t s

s ♦♥ t♦ ②♣♦tss

t r ♥ t ❯ s st♦r ♥ t ♣r♥♣ r♥ ♦ t rt s

♠ r ♣t♥ t♥ t s♦♥r②

t rr♥t ♥ t ❯ ♦s tr♦ t ♣r♥♣ r♥ ♣rs♥ts ♠

♦r ♠♣♥ t♥ t s♦♥r②

st♠t♦♥ ♦ t ♦♥srs t ♦♠ r♦♣ ♦t ♥ t ♥tr♥ rsst♥ ♦ t

❯ t ♦t ♥ t ♣t♦r s ② ♥t♦♥ ♦♥t♥♦s ❯ s st♠t

s♥ t q♥t rt ♣r♠trs t rr♥t ♥ ♦t s s ♣r♦♣♦s ♥

qt♦♥ r t ♥♠rt♦r r♣rs♥ts t st♦r r ♥ t rst r♥ s

r t ♥♦♠♥t♦r r♣rs♥ts t ❯ r t rt ♦t

UCSOC ≈Vceq

2 (Ci0 + Ci1 Vceq)

Vrated2 (Ci0 + Ci1 Vrated)

s②st♠

r

Vceq = Vuc − iuc Ri

♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

♥ t ❯ ts s rr♥t s♦r s♣♣②♥ ♦r r♥ rr♥t t♦ r♦♠

t s ts ♦t s ♠♣♦s ② t ttrs ❯ r r♣rs♥t s♥

s♦r ♠♥t t ♣♦r ♦♥rtr s r♣rs♥t s ♥ ♦♥rs♦♥ ♠♥t ♥ ♥

♠t♦♥ ♠♥t s s t♦ r♣rs♥t t ♦♥rtr q♥t ♠♣♥

❯ ♣rs♥ts ♦♥② ♦♥ ♦♥tr♦ ♥♣t t ♣♦r ♦♥rtr t②②

♦♥tr♦ ♦t s ♥t s t ♣♦r r ② ts s♦r s t ♦t s

♠♣♦s t♥ rr♥t ♦♥tr♦r s ♠♣♠♥t

①♠ ♦♥tr♦ trtr ♦ t ❯ s ♦t♥ r♦♠ rt ♥rs♦♥

♦ t s t ♦♥sr ♦♥② rqrs ♦t ♥ rr♥t ♠sr♠♥ts

t Prt ♦♥tr♦ trtr P ♥ ts s r♠♥s t t♦t ♥② ♥

r ♣rs♥ts t ♥ ♦♥tr♦ strtr ♥ P ♦ t ❯ ts

r s♦ strts ♦ t ♦s ♦♦ ♥s t st② ♦ t ♦♥tr♦rs s ♥♦t

♦♥sr ♥ ts tss

r ❯ ♥ ♦♥tr♦ strtr ♥ P t t rt

s②st♠

s②st♠ s ♠t♣②s s♦r tt ♦♥rts ②r♦♥ ♥ ♦①②

♥ ♥t♦ tr ♥r② ♥ t ♥ tr ts rrs ♣r♦ss s t tr♦②ss ♦

tr t ♦♠s ♠♦r ♥ ♠♦r ♥trst♥ ♥ ♣r♦♠s♥ ♥r② s♦r t♦ t ♥st

♦ ♣♥♥ ♥ t♦♠♦t ♥str② ♥ stt♦♥r② ♣♦r ♣♥ts ❬Pr❪ ♦r s

t s ♥♦t ss② rrs s♦r t ♥♥♦t ♦♥sr ♦♥ ♦r tr

s ❱ ♥ss tr ♥r② ♥♥♦t r♦r r♥ r♥ ❯ ♦r ttrs

t♥ t♦ ss♦t

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

s ♥ tr♦♠ s♦r ♦♠♣♦s ② t♦ tr♦s s♣rt ② ♥

tr♦②t s ttrs ♥ tr♣t♦rs tr♦s r r♦r t t②st

♥s t ♠ rt♦♥s t②♣ ♦ tr♦②t ♥s t ♦♣rt♦♥ ♥

t♠♣rtr ♦ t♠♣rtr s s t Pr♦t♦♥ ①♥ ♠r♥

P ♦r t ♦t t♠♣rtr s s t ♦ ①

♦♣rt t t♠♣rtrs ♦t

♦♣rt♦♥ ♦ ♦ t♠♣rtr rqrs sr ♥rs ♦♠♣rss♦r

♠r ♣♦r ♦♥rtr ♦r ts rs♦♥ t ♥② ♦ t s ② r

rr♥ t st ts ♦r♦r t ②♥♠ rs♣♦♥s ♦ t s ②

♠t ② t s s♣♣② ♥ t♥ t s②st♠ s r② ♦♥str♥ t♦ s♣♣②

rq♥② ♣♦r t♠ ♦♥st♥ts ♥ s ♦ r ♠ r t♥ ♥ tr r

♣rs♥ts t st s ♦r♥ ♣r♥♣ ♥ t s♠t

r st s♠t t ♠t♦♠♥ s♣ts rt ❬r❪

tst ♥ s q♣♣ t ♥ ❬❲❪ P st s ♦♣

② ①♥Pr♦♥ r♥ ♦r t P ♣r♦t ♠ t♦

♦♣ st ♦r ♣♦r tr♥s♣♦rt ♣♣t♦♥s t ② ②r ♦♦♠♦t

❬❪ ♥ t ②r t s t ♠♦st ♣♦r ♦♣ ♥ r♥

♦r tr♥s♣♦rtt♦♥ ♣♣t♦♥s ♥ s strt ♥ r tr rtrsts r

rs♠ ♥

r♦r♦s st② ♦ t s②st♠ ♠♦♥ ♥ r♣rs♥tt♦♥ t ♦♥tr♦ ♣r

♣♦ss s ♥ ♦♣ ♥ t P ssrtt♦♥ rs ② r ♦ï ♦♦♥ ♥ t

♦rt♦r② ❬♦❪ ♦ tt t st② ♦ t s②st♠ t r

t♥ ♠♦ s ♥ ♦r ♣rts t ♠♦t♦r♦♠♣rss♦r r♦♣ t♦ ♦♠♣rss t

r t ②r♦♥ ♥ ♦①②♥ s♣♣② ♥♥s t st ts ♥ t

♣♦r ♦♥rtr

s②st♠

r s②st♠ ♠♣♠♥t ♥

s②st♠ ♣r♠trs

sr♣t♦♥ ❱

♣♣r r

♠♥ts ♥ srs

①♠ r♦ss ♣♦r ❬❲❪

①♠ ♦t ❬❱❪

P♦r rt ♥ ❬s❪

♦t♦r♦♠♣rss♦r r♦♣

r s♣♣ t♦ t st s ♦♠♣rss s♥ ♠♦t♦r♦♠♣rss♦r r♦♣ r♦tr②

sr ♦♠♣rss♦r ♦♣ t♦ Pr♠♥♥t ♥t ②♥r♦♥♦s ♥ P

♦♠♣rss♦r ♠♦ s ♦♣ ♥ t P ssrtt♦♥ rs ② ♥ ❬❪

rt♥ P ♠♦ s tt ♣rs♥t ② ♦② ❬❪ r ♦♠♣rss♦r ♥

P ♣r♠tr ♥tt♦♥ s ♣rs♥t ♥ ❬♥r❪

♦ t P s ♥ ♣rs♥t ② ♦s②r♦ t ❬♦s❪ tr

♠♥ s r♣rs♥t ② t♦ ♠t♦♥ ♠♥ts r♣rs♥t♥ t ♥t♥ ♦ t

tr s ♥ t st ♥ t ♠♥ s tr♦♠♥ ♦♥rs♦♥ s

r♣rs♥t ② ♠t♣②ss ♦♥rs♦♥ ♠♥t

♥ ♦r♠s♠ t ♦♠♣rss♦♥ s r♣rs♥t ② ♠t ♣②ss ♦♠♥

♦♣♥ ♦r ♦t ss t r ♥♣t ♣rssr Pin ♥ t st

♣rssr PO2 r ♠♣♦s t♦ t ♦♠♣rss♦r ♥ t ♦♠ ♦s qV in ♥ qV out r

♦♥sr s ♦t♣ts ♥ t ♠♥ s t ♥♣t s t r♦tt♦♥ s♣ ♦ t

♠♦t♦r ♥ t ♦t♣t s t ♠♥ t♦rq Tcomp ♣♣ t♦ t st ❬♦❪

r ♣rs♥ts t ♦ t ♠♦t♦r♦♠♣rss♦r r♦♣ ♥♥ t ♣♦r ♦♥

rtr r♣rs♥t ② ♠♦♥♦♣②s ♦♥rs♦♥ ♠♥t s r♣rs♥tt♦♥ ts

t t tt ♥ t tst ♥ t ♥r② rqr ② t ♠♦t♦r♦♠♣rss♦r r♦♣

s rt② s♣♣ r♦♠ t s

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

r ♦t♦♦♠♣rss♦r r♦♣

s s♣♣②

♥ t ♦♥sr ♠♦ ♦ t t ②r♦♥ s t♦ t st ②

t♥ s s♣♣♦s t♦ ♣rt② ♦♥tr♦ t ♦①②♥ s ② t r ♦♠♣rss♦r

♣rs♥t ♥ ♣r♦s sst♦♥ r ♣rs♥ts t ♦ t s s♣♣② ts s

s ♦r ♦t t O2 ♥ tH2 s s♣♣② ♠♦♥♦♣②s ♦♥rs♦♥ ♦s r♣rs♥ts

t ♥♣t ♥ ♦t♣t ♣rssr r♦♣s ♥ t rt s t♥ t t♥ ♦r ♦♠♣rss♦r ♥

t tr♦s ♦ t st ♠t♦♥ ♦ r♣rs♥ts t ②r ♣t♥

♦ t rt

r♥ t ♦r♥ ❬♦❪ t♦ ♥♦r♠st♦♥ ♦s r ♥ t♦ ♥♦r

♠s t s ♦ t♦t ♦ ♥♣t ♦ t st qstack s ♥ t ♥♠r ♦

s ♦ t st Ncell ♥ ♥ t sr ♦ t S s s q♥t t♦ s♣♣② s♥

t sr ♦ 1cm2 ♦r♠st♦♥ ♦s ♥ r ♥ ② qt♦♥s

♥ rs♣t② s s♣♣② s r♣rs♥t ♥ r r t ♥① x

r♣rs♥t t s ts s ♥ t ♥♦ ♥ ♥ t t♦

qxcell =qxstackNcell S

qxoutstack = qxoutcell Ncell S

st

♠♦ ♣rs♥t ♥ ❬♦❪ s rt♥ ♥ ts tss st ♥ s s♣♣②

♦ t st s s ♦♥ tt ♣rs♥t ♥ ❬♦❪ ♦r t♦ s♠♣② t

st② t s ♥ st② ♠♦ ② s♥ ♥♦r♠st♦♥ ♦s t♦ ♣r♦r♠ ♥♦r♠s

s♠t♦♥s

s②st♠

r t ③ s♣♣② O2 and H2

r ♣rs♥ts t ♦ t st tr♠♦②♥♠s ♣♦t♥t

♦ ♥s t rrs ♣♦t♥t ♣s t ♦t r♦♣ t t ♦♥sr ♣rssr

♥ t♠♣rtr ♠t♣②s ♦♣♥ ♦ ♥② ♥♦r♠st♦♥ ♦ s s t♦

♦r t ♥♦r♠s rr♥t ♥sts A/cm2 rr♥t s ♥♦r♠s ② t sr

♦ t qt♦♥ ♥ t ♦t♣t ♦t s ♥♦r♠s s♥ t ♥♠r ♦

s qt♦♥

r st

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

jcell =jstackNcell S

Vstack = Vcell Ncell

P♦r tr♦♥s

♦♦st ♦♥rtr s s t♦ ♦♣ t t♦ t s ♣♦r

♦♥rtr s ♠♦ s ♥ ♦♥rtr r♣rs♥t ② ♦♥rs♦♥ ♦ ♥

ts tr ♠♣♥ r♣rs♥t ② ♥ ♠t♦♥ ♦ ♦ t ♣♦r

♦♥rtr ♣rs♥t ♥ r

r s②st♠ ♣♦r ♦♥rtr

s②st♠

r ♣rs♥ts t ♣r♦♣♦s t♦ r♣rs♥t t ♦ s②st♠

①♠ ♦♥tr♦ strtr

♦ ♦♥tr♦ ♦ts r ♥t ♥ t t r ♣♦r ♥ t st ♦t

s ttrs ♠♣♦s t ♦t t ♣♦r ♦ t s ♠♥ ② ♦♥tr♦♥

ts rr♥t t t② ② ♦ t ♦♥rtr mFCS ♥ r st

♦t s ♦♥tr♦ ② ♦♥tr♦♥ t r ♥ ②r♦♥ s♣♣② mGMC ♥ qH2 stack ref

♥ r ♦ t s ♦♥ ② rt ♥rs♦♥ ♦ t ♦s s

s♦♥ ♥ r s r s♦ ts t ♦♥sr ♦♥tr♦ ♥s

Prt ♦♥tr♦ strtr

♦♥tr♦ ♦ t ♣♦r ♦t♣t s ♥♦ ♦♥str♥ts ♦♥② rqrs rr♥t ♥

♦t ♠sr♠♥ts ts ♦♥tr♦ strtr ♦ rt② ♠♣♠♥t t♦t ♠♦

t♦♥s ♦r t strtr t♦ ♦♥tr♦ t st ♦t s ② ♦♥str♥

♥ s t♦ s♠♣

s②st♠

r s②st♠

r s②st♠

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

s ♦♥ t ♣♣r♦ t ♦♥tr♦ rqrs t s①t♥ ♠sr♠♥ts st

♥ ♠♦♥ t♠ tr r ♥♦♥ ♣②s ♠sr♠♥ts s s t tr♦♠♦t

♦r t ②r♦♥ ♥ ♦①②♥ t②t ♣rt ♣rssrs ♥ t ♦r

♣♦t♥ts r r s♦ rt② ①♣♥s ♠sr♠♥ts r ♥ ②r♦♥ ♦t♣t

♦s ♥ P t♦rq r♦r t ♦ ♥trst♥ t♦ ♦♥sr ♦♥② t ♦tr

♣②s q♥tts t♦ sts Prt ♦♥tr♦ trtr ♦ t ②r tr

♠♣t♦♥s

s♠♣t♦♥ ♦ t s ♠ ♦♥ t ss tt t t♠ ② ♦ t s ♥ t

s♣♣② ♥♥s ♥ ♥t s ②♣♦tss s st s t t♠ ♦♥st♥ts ♦

t s ♦ ♥ ♥t rr♥ t rt② s♦ ♥rt ♠♥ ♦♥ t

s ♥ s♦ ♥ t♦ t t tt t ❯ r♥ts t s ♣♦r stst ②♥♠s

s ♦♥sq♥ ♦ ts s♠♣t♦♥ t rr♥s ♦ t s ♦s r ♥ t♦t

♦♥sr♥ t s ② ♥ t s♣♣② ♥♥s s s r♣rs♥t ♥ r

r r♦♠ ♦♠♣t t♦ s P s②st♠ s s♣♣s

st♠t ❱rs

♦r t ♥♦♥ ♠sr ♣②s q♥tts t s ♠♣♦rt♥t t♦ st♠t t♦s tt ♣r♠t

♥rt♥ t ♦♥tr♦ ♥ st♠t♦rs ♥ t ♦♣♥ ♦♦♣ ♦♥tr♦ r

♦♠♣rss♦r t♦rq ♦♠♣rss♦r t♦rq s st♠t r♦♠ t r♦t♦r s♣

s♥ ♠♣♣♥s ❬♥r❪

P s tr♦♠♦t ♦r s st♠t s♥ t ♠sr P r

r♥t ♥ s♣

r ♦♠♣rss♦r ♥♣t r ♣rssr ♥♣t ♣rssr s ♦♥sr s t st♥r

t♠♦s♣r ♣rssr s ♥♦ st♠t♦r s ♦♥sr t ts

② s②st♠

♦t♦r♦♠♣rss♦r r♦♣

P ♦ t ♠♦t♦r ♦♠♣rss♦r r♦♣ ♥ ♦♣ r♦♠ ts ♦♥sr♥

t s♠♣t♦♥s ♥ st♠t♦♥s t t♦rq s st♠t s♥ rt♦r♣② s♣

t♦rq s st♠t s♥ t P qt♦♥s ♣rs♥t ② ♦② ❬❪

♠♦t♦r♦♠♣rss♦r r♦♣ P s ♣rs♥t ♥ r

r r♦♠ ♥ ①♣♥s t♦ ♥ ♦r P r ♠♦t♦♦♠♣rss♦r r♦♣

♦♠♣t P

♦ s♠♠rs t tr♥s♦r♠t♦♥ r♦♠ t t♦ t P t rst st♣ s t♦ ♥t②

t ♦♥str♥ts tr tt s♠♣t♦♥s r ♣♣ ♥ t ♥♦♥s ♠sr♠♥ts

r st♠t s ♦♥ t t ♦♥tr♦ ♦ t rqrs ♠sr♠♥ts

s ♦♥ t P t rqrs ♦♥② ♠sr♠♥ts ♥ ♠sr♠♥ts r ♦ s♥

s♠♣t♦♥ ②♣♦tss ♥ t♦ ♠sr♠♥ts r ♥♦ st♠t s♠♠rss

t rqst ♠sr♠♥ts ♦r ♦♥tr♦ strtr ♥ r ♣rs♥ts t

♦♠♣t P

② s②st♠

♥t ♥r② Ek st♦r ♥ ♠ss r♦tt♥ t ♥r s♣ ♦ ω t ♠♦♠♥t

♦ ♥rt J s ♥ ② qt♦♥

Ek =1

2J ω2

② s②st♠s ❲ r tr♦♠♥ s tt st♦r ♥t ♥r② s♥

② ♦♣ t♦ s♣ tr ♠♥ ❬r♣♠❪ s ♦ ts

①t♥ t♠ ♥ rt② ② s②st♠ ♣♣r t♦ ♥ ttrt s♦r t♦

s ♥ ❱ ♥ ♠♥② ♥ ♣♦r♥r② ♣♣t♦♥s s rr♦ tr trt♦♥

❬♥♦ ♦♠ ♦❪

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

s②st♠ ♦♥tr♦ rqr ♠sr♠♥ts

♠♥t P②s q♥tt② ♠♣ st♠t P

♦t♦♦♠♣rss♦r ♣ ① ①

♦t♦♦♠♣rss♦r ♦rq ① ①

♦t♦♦♠♣rss♦r r ♥♣t ♣rssr ① ①

P ① ①

st ♦t♣t ♦ ① ①

st ♦t♣t ♦ ① ①

st t②t Prssr ① ①

st t②t Prssr ① ①

st ♠♣rtr ① ①

st r♣♦t♥ts ① ①

s ❱♦t ① ①

st t♣t ❱♦t ① ①

st t♣t rr♥t ① ①

♦t♦♦♠♣rss♦r r♦♣ rr♥t ① ①

②st♠ t♣t rr♥t ① ①

P rr♥t ① ①

r s②st♠ ♣rt ♦♥tr♦ strtr

② s②st♠

② s②st♠ ♣r♠trs

sr♣t♦♥ ❱

❲ ♥♦♠♥ ♣♦r ❬❲❪

② ♠①♠ s♣ ❬r♣♠❪

P♦r t♦♥♦♠② ❬❲❪ ❬s❪

♣ rr rt♦

tst ♥ q♣♣ ♥ t st st ♦ t ♣r♦t t ②

s②st♠ s ❲ rs ♦♥t♥♦s ♣♦r ♦ ❬❲❪ ❬r♣♠❪ ♥ ♥ ♦r

r ♦ ❬❲❪ ♦r ❬s❪ ❲ ♥trts ♥ ♥tr♥ ♦♠st♦♥ ♥♥

♠♥ tr♥s♠ss♦♥ ♥ t♦ ②s ♦♣ tr ♠♥s ♦ ♠t t ②r♦

s♦♣ t t ②s r ♦♥trr♦tt♥ ♠♣♠♥t ♥ r♦tt t t s♠ s♣

② s②st♠ s strt ♥ r ♥ t rtrsts r rs♠ ♥

r s♦s t tr ♠♥ ♦♣ ② ♦♠♣♥②

t♦ r♥ ❬rt❪

r ② s②st♠ ♠♣♠♥t ♥

r s②st♠ ♦♠♦♣♦r s②♥r♦♥♦s ♠♥ ❬rt❪

s♥♥ ♥ ♦♥strt♥ r② s♣ s②st♠ s ♥ ♥ r♦s s♣ts

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

② ♦♠♣♦♥♥ts t♦ ② ♦♣t♠s t♦ s♣♣♦rt ♠♥ s♣s ♥

tr st♥ rq♥s ② s②st♠ ♦♥t♥♠♥t ♠st r♥t t

srt② ♦ t ♥ ts ♣ss♥rs ♦sss s s rt♦♥ s t♦ ♠♥♠s

t♦ ♦ ssr

♥ ❲ t r♦tt♦♥ s♣ s s t♦ st♠t t qt♦♥ ❯s② ♥

❲ t ♠♥♠ ♦♣rt♦♥ s♣ s ♦ t rt s♣ ♥ t♥ ♦♥② ♦ t

rt ♥r② s s ♥ ❯ s st♦♥

FWSSOC ≈ωfw

2

ωfwmax2

♣rs♥tt♦♥

tr t ♠♦♥ ♥♦r t ♦♥tr♦ ♦ ts s♦r s ♦♥sr ♥ ts tss ♦r

♥ ♥rt ♠r♦s♦♣ r♣rs♥tt♦♥ s ♣r♦♣♦s ♦ tt t st② t

❲ s ♥ ♥ tr ♥ ♠♥ ♣rt

♥ ♣rt

♠♥ ♣rt ♥s t t tr♥s♠ss♦♥ ♥ t ②s s

♠♦ t rt♦r♣② t♦rq s♣ ♦♥s♠♣t♦♥ ❬ ❪ ♥ r♣rs♥t

② s♦r ♠♥t ❬♦❪ t s r♣rs♥t t t t♦stts ♦ ♥

s♣♣♥ ♣rs♥t ② ♦♠♠ t ❬♦♠❪

②s ♥ t st ♦ t s ♠♦t♦r r r♣rs♥t s♥ ♥r② ♠

t♦♥ ♠♥ts ♥ t t s ♦ t ② s②st♠ s♣ s rt② ♣♥♥t

t♦ t s ♠♦t♦r s♣ ♥ ♦♥② ♦♥ ♠t♦♥ ♠♥t s ♦♥sr ♥ t t

s s♣♣♥ t s♣ ♦ t ② s ♥♣♥♥t r♦♠ t ♠♦t♦r s♣ ♥ t♥ t♦

♠t♦♥ ♠♥ts r ♦♥sr s s ♣rs♥t ♥ r

r ② s②st♠ ♥ ♣rt

rt♦♥ ♥ ♥ ♥rs

tr ♣rt

tr ♣rt ♥s t s②♥r♦♥♦s ♠♥ t ♥♣♥♥t ①tt♦♥ ♥

t ♣♦r ♦♥rtr s s ♣rs♥t ♥ r

r ② s②st♠ tr ♣rt

② s②st♠

② s②st♠ s ♣rs♥t ♥ r

r ② s②st♠ ♠♣♠♥t ♥

rt♦♥ ♥ ♥ ♥rs

trt♦♥ ♥ s r② t t♦ ♠♦ r♥t ♠♦t♦rs ♦♥rtrs ♥

♠♥ tr♥s♠ss♦♥s t♥♦♦s r ♠♣♠♥t ♥ s♠♣ ♠♦

r♣rs♥tt♦♥ s t♥ ♦♥sr trt♦♥ ♥ s r♣rs♥t ② rr♥t s♦r

r♣rs♥ts t q♥t ♣♦r ♦♥s♠♣t♦♥ s♣♣ ② t s

♥rs ♦♥s♠♣t♦♥ ♣♠♣s ts ♣♦r str♥ s s♦ t t♦ st♠t

♥ ♦r t② ♥ ts ♦r t s ♦♥sr s ♦♥st♥t rr♥t s♦r iaux

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

♦♥ ♦ t trt♦♥ ♥

trt♦♥ ♥ ♣♦r ♦♥s♠♣t♦♥ s st♠t s♥ ss ②♥♠ qt♦♥s

s ♣rs♥t ② r♠♥ ❬r♠❪ ♦ st♠t t ♦r t♦ r t ♦♦♥

♦rs r ♦♥sr

• ♦r t♦ rt t s ♣r♦♣♦rt♦♥ t♦ ts ♠ss m ♥ t ♠♥t

♦ t rt♦♥ ♥ s t t♠ rt ♦ t ♦t② v s ♦r

♠ ♥t ♥ r♥ s ♥ ② qt♦♥

Fa = m a = mdv

dt

• ♠♥ ♦r ♥ t♦ r t ♥ r♦ t s♦♣ ♥ ♦ Θ

s ♥ ② qt♦♥ r g r♣rs♥ts t rt♦♥ t♦ rt②

Fhc = m g sinΘ

• r♦♥ rsst♥ ♦r t♦ t rt♦♥ t♥ t t②r ♥ t r♦ s ♥r②

♥♣♥♥t ♦ t ♦t② ♥ ♦♥sr s ♦♥st♥t rt♦♥ ♦♥t µrr

♣♥s ♦♥ t r♦ ♥ t②r ♣r♠trs ♣r♠ts t♦ st♠t ts ♦r

s ②s ♦♣♣♦s t♦ t ♠♦t♦♥ ♥ s ♥ ♥ qt♦♥

Frr = µrr m g

• r♦②♥♠ r ♦r s t rt♦♥ t♦ t r rsst♥ ♦♣♣♦ss t♦

t ♠♦♠♥t ♦ t ♥ s ♥ ② qt♦♥ r S r♣rs♥ts t

r♦♥t sr ♥ Cd s♣ ♦♥st♥t ♦ t ♥ ρ t r ♥st②

Fad =1

2ρ S Cd v2

♥② t trt♦♥ ♦r t♦ r Ftr ♦♥ s♦♣ r♦ s t s♥

t♦♥s s♦♥ ♦ ♠♦t♦♥ s ♥ ♥ qt♦♥ r ♦② r♠ r♣rs♥t♥

t r♥t ♦rs t♥ ♥ t ②♥♠s s ♣rs♥t ♥ r

Ftr = Fa + Frr + Fhc + Fad

r ♦ r ♦② r♠ ♣t r♦♠ ❬r♠❪

r♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

♠♥ ♣♦r t♦ r t ♥♦ ♥ ♦♠♣t s t trt♦♥ ♦r

♥ t ♦t② r ♥♦♥ s q♥tt② s ♦♠♣t s♥ qt♦♥

Pmec = Ftr v

tr ♣♦r t♦ r t s♣♣ ② t s Pel sup s st♠t ♥

♦♥sr♥ ♦ ♥② η 0 < η < 1 s ♥② r♣rs♥ts t ♦sss ♥ t

♠♥ tr♥s♠ss♦♥ ♣♦r tr♦♥s ♥ tr ♠♥s tr ♣♦r

t♦ r t s t♥ r t♥ t ♠♥ ♥ s ♣rs♥t ♥ qt♦♥

Pel sup = Pmec/η

♦s② ts rt♦♥ ♥s ♥ r♥rt r♥ ♥ t r♦r tr

♣♦r s ♦st t♥ t ♠♥ t s ♣rs♥t ♥ qt♦♥

Pel rec = Pmec η

♥② t rr♥t ♦ t rr♥t s♦r s t r♦♠ t ♦t ♥ t s

qt♦♥

itrac =Pel

Vbus

♣rs♥ts t s s ♦r ♠♦♥ ♥ s♠t♦♥ t tst ♥

♦ ♦ t ♣r♠trs t♦ ♠♦ t rt♦♥ ♦♥t ♥ t s♣ t♦r s s

♦♥ t②♣ s ♣rs♥t ♥ ❬r♠❪

s♠t♦♥ ♣r♠trs

sr♣t♦♥ ❱

ss ❬❪

rt♦♥ ♦♥t

r♦♥t sr ❬m2❪

♣ ♦♥st♥t

r♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

♦ t ttrs ♥ s ♣rs♥t ♥ r s ♠♦ t♦ ♥ t

r♥t s♦rs ♥ ❯ ♥ ♦s r ♦♠♣rss♦r ♥rs ♥ trt♦♥

♥ ♦ ♦♠♣t t ♦ t t ♣t♦r♠s r♣rs♥t♥ ts s♦rs

r r♣ ② tr ♦♣ s s s s♦♥ ♥ r s r s♦

ts t ♦♥tr♦ ♥ ♦r tr ♦♥tr♦ ♦ts ①♣♥ ♥ ♣r♦s sst♦♥s

♥② t ♠①♠ ♥ ♣rt ♦♥tr♦ strtrs ♦ t r s♦♥ ♥ rs

♥

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

r ♥rt r♦s♦♣ ♣rs♥tt♦♥

r♣rs♥tt♦♥ ♥ ♦♥tr♦ strtr

r ①♠ ♦♥tr♦ trtr

r Prt ♦♥tr♦ trtr

♥r② s♦rs ♠♦♥ ♥ ♦♥tr♦

♣tr ♦♥s♦♥

♥r② s♦rs ♦ ♠t♣②s ♠ts♦r r st rr♥ tr

♥ts ♥ rs s s s t♦ ♥ ♦ s♦r ♥ s ♥ t

♥r② strt♦♥ ♦ t

♥ tr♣t♦r rt ♠♦ s♠♣t♦♥ ♦ ❩t ♠♦ ❬❩❪ ♦r ②r

tr s♠t♦♥ ♥ t ♣r♦r t♦ ♥t② ts ♣r♠trs s ♣r♦♣♦s s

s t rst ♦♥trt♦♥ ♣rs♥t ♥ ts tss rt ♠♦ ♥ ♣r♠tr ♥t

t♦♥ s ①♣r♠♥t② t ♥ ♦rt♦r② ♥ ♥ r ②r tr t

tst ❯ ♠♦ s ♣t t♦ s ♥ ❱ s♠t♦♥

s st s t♦♦ t♦ r♣rs♥t t ♥ ts s♦rs t ♣r♠ts t ♥t

t♦♥ ♦ t ♦♥tr♦ strtr ♥ ♥s s♥ rt② ♣r♦s rsr ♣r♦r♠ ♥

♦rt♦r② ♦♥tr♦ strtr ♦ ♦♥rt♦♥ ♦ ♥♥ t

trs tr♣t♦r s②st♠ ♥ s②st♠ s ♦♣ ♥ ♣rs♥t t ②

s②st♠ st tr ♥ ♣r♦t

♦♥sr♥ t ♥r② ♠♥♠♥t ♥ t ♥ ♦♥ tt

• ttrs s ♥ r ♥♦t qt t♦ s s ♣r♥♣ ♥r②

s♦r ♥②♠♦r s s t♦ t ts tt ts s♦r ♣rs♥ts t ♦st

♥② ♥ ②t② ♦ t s♦rs ♥ t♥② t ♦t rt♦♥

♦ t s s r② rstr♥ ♦t rt♦♥s ♦t ♦ ♣rsts

♠ts s ♠♥t♦♥♥ ♥ t ♦r ❯ ♣♦r ♦♥rtrs ♦♥s

r ♥r② ♠♥♠♥t strt② ♠st ♠ t♦ ♠♥♠s t s ♦ t ttrs

• s②st♠ ♣rs♥ts t st s♣ ♥r② ♦ t ♦♥sr s♦rs ♦r

t ②♥♠ ♦ ts s♦r ♥ t♦ t ♥rs ②♥♠ s ♠t ♥ t♥ t

s t t♦ s t t♦ s♣♣② ②♥♠ ♣♦r ♥ t ♥r②

♠♥♠♥t strt② s♦ ♠ t♦ s ts s♦r ♥ ♦ rq♥s t♦ ①t♥ ts

t♠ s ts s t ♦♥② ♥r② ♦♥rs♦♥ s♦r ts s♦r ♠st rt t

stt♦r ♦ t r♠♥♥ ♥r② s♦rs

• r♥ ts ②t② ♥② ♥ ②♥♠ rs♣♦♥s t tr♣t♦r s②s

t♠ s r② t ♠♦st ♥trst♥ ♣♦r s♦r t♦ s ♥ ♥r②

♠♥♠♥t ♥ ♠st ♣r t s ♦ ts s♦r ♦r s ts s♣

♥r② s ♥♦t ♥♦ t♥ ♦tr s♦rs ♣rtr② t t♦ rt

ts stt♦r

♣tr

②♣ ③③② ♦ ♦♥tr♦ ♦

♦♥rtr

s ♣tr ♠s t♦ ♥tr♦ t②♣ ③③② ♦ s ♣♦r t♦♦ ♥ tr ♥♥r♥

♥ t s♦♥ ♣rt ♦ ts tss t♦ ♣♣t♦♥s ♦ t②♣ ③③② ♦ ♦♥tr♦ r

♣rs♥t rst ♣♣t♦♥ s t ♦t♣t ♦t rt♦♥ ♦ ♣♦r

♦♥rtr ♣rs♥t ♥ ts ♣tr s♦♥ ♣♣t♦♥ s t ♥r② ♠♥♠♥t ♦

t ♠♦ ♦rt♦r② ♣rs♥t ♥ ♣tr

s ♣tr ♥tr♦s t t②♣ ③③② s②st♠s ♥ tr r♥t ss②st♠s t

t ♠♥t♠ ♥♠r ①♠♣s r ♣rs♥t t♦ tt tr ♥rst♥♥ ♥

③③② ♦ ♦♥tr♦r s ♦♣ t♦ ♣r♦r♠ t ♦t♣t ♦t rt♦♥ ♦

♣♦r ♦♥rtr s ②♣ ③③② ♦ ♦♥tr♦rs r ♥♦♥ ♥ ts

♣♣t♦♥ t ♦t s t♦ ♦♥sr t②♣ ③③② ♦ ♦♥tr♦rs ♦t

♦♥tr♦r s ♠♣♠♥t t ♥ ♦♠♣r s♥ ♦♥ ♥ s②st♠s

② s♠t♦♥ ♥ ② ①♣r♠♥tt♦♥

♣r♥♣ ♠♦tt♦♥s ♦r ♦♣♥ ts ♣♣t♦♥ s tt t s s② t♦ ♠♣♠♥t

♥ ♦rt♦r② t rt② ♦ ♦st t ♣r♠ts t② t♦♥ ♦ t②♣ ③③② ♦

♥ t ♣♣t♦♥s ♦r ♥ ♠♣♠♥tt♦♥ ♥ t ♠♦ ♦rt♦r②

s ♣tr s ♦r♥s s ♦♦s t♦♥ ♦ ts ♣tr ♥tr♦s s♦♠ ♠♦t

t♦♥s ♦r s♥ ♥st ♦ ♦♥tr♦ s②st♠s t♦♥s t♦ r ♦t t♦

♣rs♥t t t②♣ ③③② s②st♠s rttrs s s tr r♥s ♥ s♠rts

t t②♣ ③③② ♦ s②st♠s t♦♥ s ♦t t♦ t s♥ ♦ t ♦t ♦♥

tr♦r t♦♥ ♣rs♥ts t s♥ ♦ t r♥t ③③② s②st♠s s ♥ t ♦t

♦♥tr♦r t♦♥ ♣rs♥ts ♥ sss t t♦♥ rsts ♥② t♦♥

♣rs♥ts t ♦♥s♦♥s ♦ t ♣tr

♦♠♣♠♥tr② t♦ ts ♣tr t s♦tr ♠♣♠♥tt♦♥ ♦ s②st♠s s ♣r

s♥t ♥ ♣♣♥①

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

③③② ♦ ♦♥tr♦ ♥ ♥rt♥t②

r♦♠ ♥ tr ♥♥r♥ ♣♦♥t ♦ ③③② ♦ ♦s s♥ ♥st s ♥

♠♥ ♥♦ t♦ r♣rs♥t ♦r ♠♦ ♣②s ♣r♦ss ♥ t♦ s♥ tr ♦♥tr♦

s②st♠s ③③② ♦♥tr♦ s ♥ s ♥ r♥t ♣♣t♦♥s s s ♦t ♦♥tr♦ ♥

♣♦r ♦♥rtrs ♦r s♣ ♦♥tr♦ ♥ tr ♠♥s

r♥ ② strts t ♦♥♣t ♦ ③③② ♦♥tr♦ ♣♦♣ ♦s ♥♦t ♥ t♦

♠sr t s♣ ♦r t rt♦♥ t♦ t♦ ♦♥tr♦ t s♣ r♥ ♥ s

♦♥t♦♥s ♠♥ r♥ ♣r♦ss ♥st s s s♦ st ♥r ♦r r ♥ ♣r♦r♠s

♦♥tr♦ t♦♥s s rt ♦r r

❯♥rt♥t②

❯♥rt♥t② s ♥♦ t ♥② stt♦♥ t s♦♠ ♦ ♥♦r♠t♦♥ t ♠②

♥♦♠♣t ♠♣rs r♠♥tr② ♥♦t ② r ♦♥trt♦r② ♦r ♥t ♥

s♦♠ ♦tr ② ❬r❪ r♥t t♦rs ♥ ♥ ss② r♥t t②♣s ♦ ♥r

t♥t② sst♦♥ ♣r♦♣♦s ② Pr ♦♦s ts t♦ sr ♥rt♥t② ♥ tr

♥♥r♥ ❬♦♦s❪ s sst♦♥ s strt ♥ r

r ♦rs ♦ ♥rt♥t② ♣t r♦♠ ❬♦♦s❪

❯♥rt♥t② s s♦ ♣rs♥t ♥ ③③② ♦ s②st♠s s ①♣♥ ② Pr ♥ ❬♥❪

• ❯♥rt♥t② ♦t t ♠♥♥ ♦ t ♦rs tt r s ♥ t rs

• ❯♥rt♥t② ♦t t ♦♥sq♥ tt s s ♥ r

• ❯♥rt♥t② ♦t t ♠sr♠♥ts tt tt t ③③② ♦ s②st♠s

• ❯♥rt♥t② ♦t t t s t♦ t♥ t ③③② ♦ s②st♠ ♣r♠trs

②♣ ③③② sts s s ♥ ♦s ♥♦t r♣rs♥t t ♥rt♥t② s s t rs♦♥

② ❩ ♣r♦♣♦s t♦ r♣rs♥t ts ♥rt♥t② ② s♥ t②♣ ③③② sts ❬❩❪

②♣ ③③② sts ♥ s②st♠s r st② r♥t r♦♠ t♦s s ♥ ss ③③② ♦

s ♣rs♥t ♥ r ①t st♦♥s ♣rs♥ts ts r♥s ② ♥tr♦♥ t

ss②st♠s ♦ s②st♠ s ♣rs♥t ♦♥ r s rr♥ ♣rs♥ts ♥ ♣tr r② ♥trst♥ sss♦♥ ♦t ♥rt♥t②

s

r ②♣ ③③② ♦ s②st♠s rttr ♣t r♦♠ ❬♥❪

r ②♣ ③③② ♦ s②st♠s rttr ♣t r♦♠ ❬♥❪

s

r s ♦s r♣rs♥tt♦♥ ♦ ♠♥ ♥♦ ② s♥ ♥st s

ss ③③② r ♣rs♥ts t s♠ strtr s ♦

s♦♠ ♦♥t♦♥s r r ♦ s♦♠t♥ ♦ s♦♠t♥ r♥t

♥r② t ③③② rs r ♦r♥s s♥ ts ♦t s t♦ r♣rs♥t

t r♥t ♦♠♥t♦♥s ♠♦♥ t ♥♣ts ♦ t s②st♠ strtr ♦ t rs

♦s ♥♦t r② t♥ t②♣ ♥ t②♣ ③③② ♦

♠rs♣ ♥t♦♥s

♠rs♣ ♥t♦♥s s ♥ sts♥ rt♦♥s♣ t♥ ♥♠r s

♥ ♥st s ②♣ ③③② s r t♦ ♠♥s♦♥ ♥ r♣rs♥t t

♠♠rs♣ r µ ♦r r x ②♣ ③③② s r tr ♠♥s♦♥

t② ♦♥sr ♥ ♥rt♥t② U ♦ t ♠♠rs♣ r s r ♣rtr s

♦ s r t ♥rt♥t② s ♠rs♣ ♥t♦♥s r ss s

• ♥t♦♥ s µ s t ♥ s♥ ♣♦♥t ♦ t ♦♠♥ µ s

• ♥tr t②♣ s µ s ①♣t ♥ t ♥tr ♥ ② ts t ♥ rt

♦♥s ❬lb rb❪ r µ lb < x < lb

• ②♣ s µ s rs♣ r② t♥ 0 ♥ 1

• ②♣ s µ s r♣rs♥t ② s♦♥r② r µA

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

②♣ s r ss ♥

♥tr t②♣ s µA(µ, x) s ♥ ♥tr t②♣

♥r t②♣ s µA(µ, x) s t②♣

rs ♥ rs♣t② strts s♥t♦♥ ♥tr t②♣ ♥

tr t②♣ ♥ ♥r t②♣ ♠♠rs♣ ♥t♦♥s

♥tr t②♣ ♠♠rs♣ ♥t♦♥s

♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s r s② t♦ ♠♣♠♥t ♥ t♥ ♥

s ♥ ♠♦st t ♦rs ♦t t②♣ ③③② ♦ ♦r s♠♣t② rs♦♥s

♥tr t②♣ ♠♠rs♣ ♥t♦♥ s ♥ s♦ st ♦r ts rsr

r ♥t♦♥ r ♥tr t②♣ r ②♣

r ♥tr t②♣ r ♥r t②♣

♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s ♥ rt r♦♠ t♦ t②♣ s ♥

❯♣♣r ♠rs♣ ♥t♦♥ ❯ r♣rs♥ts t ♠①♠♠ ♥ ♦r

♠rs♣ ♥t♦♥ r♣rs♥ts t ♠♥♠♠ ♦ µ ♦r x

♥rt♥t② U s r♣rs♥t ② t r t♥ t ❯ ♥ t s r♦♥ s

♦♦t♣r♥t ♦ ❯♥rt♥t② ❯ ♥ s strt ♥ r

②♣ s r ♣rtr s ♦ s ♦s ♥♦t ♦♥sr t ♥rt♥t②

t s♠ r♣rs♥ts ♦t t ❯ ♥ t ♥ t r ♦ t ❯ s ③r♦

♠rs♣ ♥t♦♥s

r ♥tr t②♣ ③③② ♦ ♣r♠r② ♥ s♦♥r② s

♠rs♣ ♥t♦♥s rt♦♥

r♥r ♥ tr♣③♦ ♠♠rs♣ ♥t♦♥s rt♥ ♥ ts ♦r r ♥ s♥

♥r ♥t♦♥s ♦♠♣t② sr ② ♣♦♥ts ♥ s ♥ ♥ qt♦♥s

♥ ♥ strt ♥ r r♥r s r ♣rtr s ♦

tr♣③♦ s r s strt ♥ r

Trapezoid(x, a, b, c, d, e) = max (0, min (y1, y2, e) )

y1(x, a, b, c) = ex− a

b− a

y2(x, c, d, e) = ed− x

d− c

r r♣③♦ ①♠♣

a = −0.8, b = −0.4, c = 0.2, d = 0.6, e = 0.8

r r♥r ①♠♣

a = −0.5, b = c = 0, d = 0.5, e = 1

♥tr♦ ♦ ♥ ♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥

♥ ♥tr t②♣ ♠♠rs♣ ♥t♦♥ ♥ ♣♣r♦①♠t② r♣rs♥t

♦r st ♦ p ♥tr t②♣ ♠♠rs♣ ♥t♦♥s s ♦t t t ♣♦♥ts xi ♥

t ♣♣r ♥ ♦r ♦♥s µUMF (i) ♥ µLMF (i) s strt ♦♥ r

♥tr♦ ♦ t s t♥ ♦♠♣t s t ♥tr♦ ♦ t p s ♦s②

t ①tt ♦ t ♦♠♣tt♦♥ ♣♥s ♦♥ t ♦ p ①t ♥tr♦ s ♦♥

♥ p → ∞

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

r ♥ ♥tr t②♣ srts ♥t♦ p ♥tr t②♣ s

♥tr♦ ♦ t②♣ srts ♥ p ♣♦♥ts s ♦t t x = c s ♣♦♥t s

♥ ② qt♦♥

c =

∑pi=1 µ(xi) · xi∑p

i=1 µ(xi)

♠r② t ♥tr♦ ♦ ♥ ♥tr t②♣ srts ♥ p ♥trs s ♦t t

t ♥tr ❬cl cr❪ ♥ ② qt♦♥

[cl, cr] =

[∑pi=1 µ

∗(xi) · xi∑p

i=1 µ∗(xi)

,

∑pi=1 µ

∗∗(xi) · xi∑p

i=1 µ∗∗(xi)

]

❲r µ∗(xi) ♥ µ∗∗(xi)r tr µUMF (xi) ♦r µLMF (xi) t s ♠♥♠s

♠①♠s t t r ♥ qt♦♥ ❬♥❪ ♦ ①♠♣② ts t ♥tr♦

♦ t ♥ r srts ♥ s s ♣rs♥t

r ♥tr t②♣ srts ♥t♦ ♥tr t②♣

❯r♣③♦① r♣③♦①

s srts ♥t♦ t ♦♦♥ s

Θ1 ❬ ❪ t x1

Θ2 ❬ ❪ t x2

Θ3 ❬ ❪ t x3

Θ4 ❬ ❪ t x4

♠rs♣ ♥t♦♥s

s♠♠rss t ♣♦ss t rs ♥ ♥ qt♦♥ s

tr r p s ♥ t♦ ♦♥s ♦r tr r 2p t rs

❲t rs ♦ t ♥tr t②♣

x1 x2 x3 x4 µ(x1) µ(x2) µ(x3) µ(x4)∑4

i=1 µ(xi)·xi∑4i=1 µ(xi)

t ♥ ♥♦t tt t s ♠♥♠s ♥ ♠①♠s t t rs

r rs♣t② ❬cl cr❪ ❬ ❪ s s ♥ ♣♣r♦①♠t♦♥ ♦r t ♥tr♦ ♦

t

r♥♥ ♦rt♠

❲♥ t ♦ p s ♥r♠♥t t♦ ♥ ttr ♣♣r♦①♠t♦♥s ♦ t ♥tr♦ t

♥♠r ♦ t rs ♥rs ①♣♦♥♥t② ♥ t ♦♠♣t♥ t♠ s t♥ ♣r♦

t r♥ ♥ ♥ ♣r♦♣♦s ♥ trt ♦rt♠ t♦ ♥ t ♦♥s cl ♥

cr rs t ♥♠r ♦ trt♦♥s t♦ ♥ t s♦t♦♥s ♦♥ t r ♦r

trt♦♥ r♥♥ ♦rt♠ s ①♣♥ ♥ t ♥ ❬r♥❪

♥tr♦ ♦ t s♦♥ ♥ r s ♦♠♣t s♥ t

♣rs♥ts t rsts ♦ t ♥tr♦ ♥ r♥t s ♦ srtst♦♥ p r ♦♥sr

t ♣rs♥ts t ♥♠r ♦ trt♦♥s t♦ ♥ t ♦ t ♥tr♦ s t ♥

♥♦t t ♣r♠ts ♥♥ t ♥tr♦ s♥ r srtst♦♥ ♥

♦♥sr② r♥ t ♦♠♣tt♦♥ t♠

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

♥tr♦s ♦ t ③③② s ♦r ∆P

srtst♦♥ p ♥tr♦ trt♦♥s 2p trt♦♥s

❬ ❪

❬ ❪

❬ ❪

❬ ❪ ·1019

❬ ❪ ·1077

❬ ❪ 2p ·10308

r s♦s t ♦rt srs t r♥♥ ♦rt♠ ♥ t

s s t♦ ♦♠♣t t rt ♣♦♥t ♦ t ♥tr♦ ♦ t②♣ ③③② ♦rt♠

s t♦ ♦♠♣t t t ♣♦♥t s r② s♠r ♥ s ♣rs♥t ♦♥ ♣♣♥①

r ♦rt t♦ ♦♠♣t t t ♣♦♥t ♦ t ♥tr♦

③③r

③③r ♠♣s rs♣ ♥♣t x1 x2 xn ♥t♦ t ♥tr t②♣ ♠♠rs♣

♥t♦♥s t♦ ♣r♦ st ♦ ♥tr t②♣ ③③② sts ♥♠r ♦ sts ♣♥s ♦♥

t ♥♠r ♦ ♥♣ts ♥ t ♥♠r ♦ ♠♠rs♣ ♥t♦♥s

③③r

③③r ①♠♣

♥ ♦rr t♦ strt t ♠t♦♦♦② t♦ ♠♣♠♥t t ③③r ♥ t ss②st♠s

♦ ♥ ♥tr t②♣ ③③② s②st♠ ♥♠r ①♠♣ s ♣rs♥t t ♦ ♣r♦ss

t♦ ♦♠♣t rs♣ ♦t♣t r♦♠ rs♣ ♥♣t s ♦♥sr st♣ ② st♣ ③③t♦♥

♥r♥ t②♣rt♦♥ ♥ ③③t♦♥

①♠♣ ♦♥ssts ♥t♦ ♥♥ t ♦t♣t ♦ t ♥tr t②♣ ③③② ♦ s②st♠

♦s s r ♣rs♥t ♥ rs ♥ ♥ r s s ♣rs♥t ♥

rs♣ ♥♣t ♦ x1 x2 s ♦♥sr

r ♠rs♣ ♥t♦♥s ♦r ♥♣t x1

r ♠rs♣ ♥t♦♥s ♦r ♥♣t x2

rst st♣ s t♦ ③③② t ♥♣t ♥t♦ t s t ♥ ♥ rs

♥ tt t rst ♥♣t s ③③ ♥ t♦ s ♥ ♥ t s♦♥ ♥♣t s

③③ ♥t♦ tr s ♥ ❩ s s strt ♥ r ♥ s♠♠rs

♥ r

r ♦♥♥ ③③ sts ♦r x1 ♥ ♥ x2 ♥

s ③③② s②st♠ s ①♣♥ ♥ t ♦♥ ♣tr r t ♥trst s ♦♥ t ♥♠r s ♦

tr s ♥ rs

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

r ③③r ♠♣s rs♣s ♥♣ts ♥t♦ t②♣ ③③② sts ♦t♣ts

③③② rs

x1 s ♥ x2 s ♥ Out s

❬ ❪

❬ ❪

❩ ❬ ❪

❬ ❪

❬ ❪

❩ ❬ ❪

♥r♥ ♥♥

♥r♥ ♥♥ ♠♣s t st ♦ ♥tr t②♣ ③③② s ♥t♦ t s s t♦

r♣rs♥t t rs ♦t♣t s st ♦ t②♣ ③③② s ♥♠r ♦ s s q

t♦ t ♥♠r ♦ t ♦r r rs

♥r♥ ♥♥ ①♠♣

♦♥t♥♥ t t ①♠♣ tr r tt rs ♥ tt s ♦r

♥♣t ♥ rs♣t② s♠♠rss t tt rs ♥ ts ①♠♣

t rs r r♣rs♥t ② ♥tr t②♣ s ♦♠♣t st ♦ rs ♦♥ s

♥ r strts t ♥r♥ ♥♥ ♦r r ❩ r♣rs♥ts t

r ♥ ❲ ts r♥ s① t②♣ ③③② sts ♦♥ ♦r tt r r

s♦♥ ♥ r r s♠♠rss t rsts ♦ t ♥r♥ ♥♥

r ♥r♥♥♥ r♥ r ♦r ♣r♦t ♥r♥

t♣t Pr♦ss♦r

r ♥r♥♥♥ r♥ rs ♦r t tt rs

r ♥r♥ ♥♥ ♠♣s t②♣ ③③② sts ♥♣ts ♥t♦ t②♣ ③③② sts ♦t♣ts

t♣t Pr♦ss♦r

♦t♣t ♣r♦ss♦r ♦♠♥s t t②♣ ③③② sts ♦♥ ♦r tt r t♦

♦t♥ t rs♣ ♦t♣t ♦ t ③③② ♦ s②st♠ ♦t♣t ♣r♦ss♦r s t ♣r♥♣

r♥ t♥ ♥ s②st♠s ♦r t ♦t♣t ♣r♦ss♦r ♦

s②st♠ ♥ s ♥ s②st♠s ♥♦t rs t②♣ ♦t♣t ♣r♦ss♦r s

♥t♦ t t②♣rr ♥ t ③③t♦r

②♣rr

t②♣rr ♦♠♥s t②♣ ③③② sts ♥t♦ ♥ ♥tr t②♣ ③③② t

t②♣r st ♥♠r ♦ ♥♣t ③③② sts ♦rrs♣♦♥s t♦ t ♥♠r ♦ tt

rs r s ♦♥② ♦♥ ♦t♣t t t②♣r ③③② s s ♦♠♣t ② s♥

t r♥♥ ♦rt♠ ♥♣t t♦ t ♦rt♠ r t sts Wi ♥ Zi

r t ♦t♣t ♦ t ♥r♥ ♥♥ r s♦s t ♦rt srs t

r♥♥ ♦rt♠ ♥ t s s t♦ ♦♠♣t t rt ♣♦♥t ♦ t t②♣r

st ♦rt♠ s t♦ ♦♠♣t t t ♣♦♥t s ♣rs♥t ♦♥ ♣♣♥①

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

r ♦rt t♦ ♦♠♣t t rt ♣♦♥t ♦ t t②♣r st

③③t♦r

③③t♦r tr♥s♦r♠s t t②♣r ③③② st ♥t♦ rs♣ ♦t♣t t s t

s♠♣st ss②st♠ t rs♣ ♦t♣t s ♦♠♣t s t r ♦ t ♦♥s ♦

t t②♣r st

t♣t Pr♦ss♦r ①♠♣

r♥♥ ♦rt♠ s ♣♣ t♦ ♦♠♥ t ③③② sts ♥ r

♦t♣t ♣r♦ss♦r rsts r s♦♥ ♥ r ♥ s♠♠rs ♥ r

r ♦t♣t ♣r♦ss♦r ①♠♣ t

r ♦t♣t ♣r♦ss♦r ♦♠♥s t②♣ ③③② sts ♥t♦ rs♣ ♦t♣t

♦♥rtr ♦t ♦♥tr♦r

♦♥rtr ♦t ♦♥tr♦r

♦♥rtr s ♥ tr s t♦ ♦♣ ♦t s♦r t♦

♦ ♦♥tr♦♥ t q♥tt② ♦ ♥r② s♣♣ ② t ♦r♠r ② r♥ t

♦t ♦♥rtr strtr s ♣rs♥t ♦♥ r ♦s tr♥st ♦ ♥r②

r♦♠ t s♦r t♦ t ♦ t ♥♦t rs

r ♦♥rtr

♦t♣t ♦t ♦ t ♦♥rtr ♣♥s ♦♥ r♥t ♣r♠trs ♥ ♦♣rt♦♥

♦♥t♦♥s s t ♥♣t ♦t t t② ② t st♥ rq♥② ♥ t ♥

t♥ ♣t♥ ♥ ♦ s ♥r② t st♥ rq♥② t ♥t♥ ♥

t ♣t♥ s r ♦♥st♥t ♥♣t ♦t ♥ s♦ ♦♥sr s ♦♥st♥t

♦r ♥♦♥ ♦♥tr♦ s t ♦ s ♠♣♦s t ♦t♣t ♦t s ♦♥tr♦ ② ♦♥tr♦♥

t t② ②

r

♦t ♦♥tr♦r rqrs ♦♥ s♥ ♥♣t s t rr♦r s♥ t♥ t

rr♥ ♥ t ♠sr ♦t Vref ♥ V0 ♦t♣t ♦ t ♦♥tr♦r s t t②

② ♦ t ♦♥rtr δc ♦♥tr♦r ♦♠♣ts ♥ ♦t♣t ♦r s♠♣ t♠ ♥♦t

k s♠♣♥ ♣r♦ Tech s ♦♥st♥t P❲ s ♣r♦r♠ t ♦♥st♥t st♥

rq♥② fsw

♦t s t♦ t r♥t ③③② ♦ s②st♠s ♦♥ ♥ t♦

s②st♠s s♥ t s♠ ♦♥tr♦r strtr s s♦♥ ♥ r

r ♦t♣t ♦t ♦♥tr♦r

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

♥♣t

rr♦r t♥ t rr♥ ♥ ♠sr ♦t s ♥ ♥ qt♦♥

e(k) = Vref (k)− V0(k)

rr♦r rt♦♥ s s♦ ♦♥sr ♥ s ♥ ♥ qt♦♥

de(k) = e(k) − e(k − 1)

♥♣t ♥♦r♠st♦♥

③③② ♦ ♦♥tr♦r ♥s ♥♦r♠s ♥♣ts ♦♠♥ ❬ ❪ s ♥ ♥ q

t♦♥s ♥ ♥r② t ♦ en s ① ♥ den s s s ♥ ♦♣t♠st♦♥

♣r♠tr

e∗(k) = max

(

−1, min

(

e(k)

en, 1

))

de∗(k) = max

(

−1, min

(

de(k)

den, 1

))

③③② ♦ ♦♥tr♦r

♦♥tr♦r ♥s t rt ♥ ♥ t t② ② s ♥ ♥ qt♦♥

s♥ ♦ t ③③② ♦ s②st♠s s ♣rs♥t ♥ ♥①t st♦♥

∆δc(k)∗ = f (e∗(k), de∗(k))

③③② ♦ ♦♥tr♦r ♦t♣t ♥♦r♠st♦♥

♦t♣t ♦ t ③③② ♦♥tr♦r s ♥♦r♠s s♥ ♥♦r♠st♦♥ t♦r gm t♦

♦t♥ t rt ♥ ♥ t t② ② s ♥ ② qt♦♥ ♥♦r♠

st♦♥ t♦r gm s ♥r② s s ♥ ♦♣t♠st♦♥ r

∆δ(k) = ∆δ(k)∗ gm

♦♥tr♦r t♣t t② ②

♥② t rt ♥ s ♥trt t♦ ♥ t t② ② ♦ t ♦♥rtr ② s♥

♥ ♥trt♦r s ♥ ② qt♦♥

δ(k) = max (0, min (1, δ(k − 1) + ∆δ(k) Tech))

③③② ♦ ♦♥tr♦r

r ♣rs♥ts t ♦t ♦♥rtr ①♣♥ ♥ ts st♦♥

③③② ♦ s②st♠ s♥

r ♣♦r ♦♥rtr ♦t ♦♥tr♦r

③③② ♦ s②st♠ s♥

r r♥t s②st♠s ♥ ♦♣ t♦ ♣r♦r♠ t ♦t rt♦♥ ♦ t

♦♥rtr r♥ t♥ t s②st♠s s tr ♥rt♥t② U rst

s ♥ ♥rt♥t② ♦ t s♦♥ ♥ t tr ♦♥sr ♥ ♥rt♥t② ♦

♥ rs♣t② s♥ ♦ t t②♣ ③③② ♠♠rs♣ ♥t♦♥s

s s ♦♥ t ♣♣r♦ ♣rs♥t ♥ ❬ss❪ ❲ ♣r♦♣♦s ♥ ♣♣r♦ t♦ ♦♥sr t

♥rt♥t② ② s♥ ♥tr t②♣ ♠♠rs♣ ♥t♦♥s

♦t ♦ ts ♦r s t♦ st② t t② ♦ t s ♦ t②♣ ③③② ♦ ♥

r ♣♣t♦♥s ♥ ts t ♦♣t♠st♦♥ ♦ t ③③② ♦ s②st♠ s ♥♦t ♦♥sr

rtss r♥t s ♦ ♥rt♥t② ♥ t ♠♠rs♣ ♥t♦♥s r ♦♥sr

s ♦ ♣r♠ts t♦ t ♥ ♦♠♣r t②♣ ♥ t②♣ ③③② ♦♥tr♦rs ♥r

r② s♠r ♦♥t♦♥s

♥♣t ♥ ♦t♣t ♠♠rs♣ ♥t♦♥s r ♥ s ss② ♦♥ ♥ ts

rt♠ ♣♣t♦♥ tr♥r ♠♠rs♣ ♥t♦♥s ♦r t t♦ ♥♣t ③③② sts ♥

s♥t♦♥ ♠♠rs♣ ♥t♦♥s ♦r t ♦t♣t ③③② st

s s♥

♣rs♥ts t ♦♥sr ss ♥t♦♥ r s s♥ ♥st

s r t t ♦ t ❱r② ♦ ❱ ❩r♦ ❩

P♦st ❱r② ♦ ❱ P♦st ♦ P ♥ P♦st P

♥♣t ♠♠rs♣ ♥t♦♥s s♥

t♦ ♥♣t ③③② sts ♦r e ♥ de r ♦♠♣♦s ♦ s♥ ♠♠rs♣ ♥t♦♥s

s r s②♠♠tr r♦♥ t ③r♦ ①s ♥ r ♥ ♥ t♦ st♣s ② s♥ ♦♥②

tr ♣r♠trs

♥ t②♣ ♠♠rs♣ ♥t♦♥s ❯♥rt♥t② r ♥ ② t♦ ♣r♠trs

s strt ♥ r

• ❩ s ts ♣ t x = 0 ♥ ts rt s t x = pvlx

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

③③② ♦♥tr♦r rs

∆δ

e ↓ de → ❱ ❩ P❱ P P

❱ ❩

❱ ❩ P❱

❱ ❱ ❩ P❱ P

❩ ❱ ❩ P❱ P P

P❱ ❱ ❩ P❱ P P P

P ❱ ❩ P❱ P P P P

P ❩ P❱ P P P P P

• P❱ s ts t s t x = 0 ts ♣ t x = pvlx ♥ ts rt s t

x = plx

• P s ts t s t x = pvlx ts ♣ t x = plx ♥ ts rt s t

x = 1

• P s ts t s t x = plx ts ♣ t x = 1

r t♣ ♥t♦♥ ♦ t t②♣ ③③② ♠♠rs♣ ♥t♦♥s

s ♥st s ♥ ♣♣rs ♥ ts ♣r♠trs ♥ ♦rs

♥rt♥t② U ♥ t ♠♠rs♣ ♥t♦♥s s t tr ♦♥sr ♣r♠tr

t②♣ ♠♠rs♣ ♥t♦♥ s ♠♦ s strt ♥ r r

tr r♥t ♥rt♥ts r ♦s♥ ♥

Pr♠trs

♦ ♦ t ♣r♠trs plx ♥ pvlx ♥♥ t ③③② sts s s ♦♥ ♣r♦s

♦rs ♦t ③③② ♦♥tr♦ ♦ ♣♦r ♦♥rtrs ❬ss❪

• ♦ r♥t st ♦♥r♥ ♦ t ♦♥tr♦r t ♣r♠trs ple ♥ pvle

♥ t rr♦r e ♠♠rs♣ ♥t♦♥s r rt② ♦s t♦ ③r♦ ❱s ♦

ple = 0.15 ♥ pvle = 0.3 r rt♥

• ♦ r t ♥♦s ♠♣t♦♥ ♦ t ♦♥tr♦r t ♣r♠trs plde ♥ pvlde

♥ t rr♦r r♥t de ♠♠rs♣ ♥t♦♥s r rt② ♦s t♦

♦♥ ❱s ♦ ple = 0.4 ♥ pvle = 0.7 r rt♥

③③② ♦ s②st♠ s♥

r t♣ ♥t♦♥ ♦ t t②♣ ③③② ♠♠rs♣ ♥t♦♥s

st♦♥ ♦ t s s ♦♦s② st t t st t ♣r♠ts t♦ st ♦

♣r♠trs t♦ t ♥ ♦♠♣r t ♦♥sr t②♣ ③③② ♦ ♦♥tr♦rs rs

♥ strt t ③③② sts ♦r ♥rt♥t② s ♦ ♥

rs♣t②

r ②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

r ②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

r ②♣ ③③② ♠♠rs♣ ♥t♦♥s U t♦ r♣rs♥t e ♥ de

t♣t ♠♠rs♣ ♥t♦♥s s♥

♦r s♠♣t② rs♦♥s t ♦t♣t ③③② st s ♦♠♣♦s ② s♥t♦♥ ♠♠rs♣ ♥

t♦♥s ♥♦t ♥tr t②♣ s ♥ t ①♠♣ ♣rs♥t ♥ ♣r♥t st♦♥s s♥t♦♥s

r ♥♦r♠② strt r♦♥ t ♦♠♥ ♦ t ③③② sts s strt ♥ r

r ♥t♦♥ ♠♠rs♣ ♥t♦♥s

③③② ♦ ♦♥tr♦ srs

③③② ♦ s②st♠ s ♦♠♣t② ♥ ② ts ♠♠rs♣ ♥t♦♥s ♥ ③③②

rs tr ♥♦r♠s ♦♥tr♦ srs ♥ ② qt♦♥ r ♠♣♣ ♦♥

♥ ♣rs♥t ♦♥ r

r ②♣ ③③② ♦ ♦♥tr♦ srs ❯ ❯ ❯

③③② ♦♥tr♦r t♦♥ ♥ t♦♥

③③② ♦♥tr♦r t♦♥ ♥ t♦♥

♣r♦♣♦s ♦t ♦♥tr♦r s t ② t♦ ♠t♦s ② ♦♠♣tr s♠t♦♥s

♥ ①♣r♠♥t②

♠t♦♥ st♣ ③③② ♦♥tr♦r ♥ t ♦♥rtr r ♠♣♠♥t ♥

t ♠♥ s♥ t P♦r ②st♠s t♦♦♦①

①♣r♠♥t st♣ ③③② ♦♥tr♦r s ♠♣♠♥t ♥ t ♠♥ ♥

♣♦ t♦ P ♣r♦r♠♠ ♦♥tr♦r ♥rts t s♥ t♦ r

t tr♥sst♦rs ①♣r♠♥t st♣ s strt ♥ r

r ①♣r♠♥t st♣

s ♥ rs♠ t ♣r♠trs s ♥ t t♦♥ ♦ t ♦t ♦♥tr♦r

♦♥rtr ♠t♦♥ ♥ ①♣r♠♥t ♣r♠trs

sr♣t♦♥ Pr♠tr ❱

rs ♥t♥ L ❬♠❪

Pr ♣t♥ C ❬♠❪

① ♦ rsst♥ R0 ❬Ω❪

t ♦ rsst♥ Rch ❬Ω❪

P❲ t♥ rq♥② fsw ❬③❪

♥♣t ♦t Vi ❬❱❪

r♥ ♦t♣t ♦t Vref ❬❱❪

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

②♣ ③③② ♦ ♦♥tr♦r ♠t♦♥ ♥ ①♣r♠♥t ♣r♠trs

sr♣t♦♥ Pr♠tr ❱

Pr♦ss♦r s♠♣♥ t♠ Tech ❬µs❪

rr♦r ♥♦r♠st♦♥ en ❬❱❪

rr♦r r♥t ♥♦r♠st♦♥ den 5 ❬❱❪

♥♦r♠st♦♥ t♦r gm

t♦♥ ♦ t ♦♥tr♦r

t♦♥ ♦ t ♦♥tr♦r rs♣♦♥s s ♣r♦r♠ ② ♠♣♦s♥ ♥ ♥t ♦♥t♦♥

♥ tr r♥t ♦♣rt♦♥ ♦♥t♦♥s

♥tst♦♥ ♦t♣t ♦t rr♥ s ♥t② ① t ❬❱❪

trt ♣ t t = 0 ❬s❪ t ♦t rr♥ ♥s t♦ ❬❱❪ ♦ s ♦♥st♥t

r♥ ts ♣r♦ Ω

♦ rt♦♥ t t = 1 ❬s❪ st ♦ rsst♥ s st ♦

♦ rsst♥ r♦♠ Ω t♦ Ω

♦ rt♦♥ t t = 1.5 ❬s❪ st ♦ rsst♥ s st ♦♥

♥ ♦ rsst♥ r♦♠ Ω t♦ Ω

♦ ♦♠♣r t tr ③③② ♦♥tr♦rs t ♥tr s♦t rr♦r rtr♦♥ s

rt♥ s ♥ ♥ qt♦♥

IAE∆V =

∫ t

0|Vref (t) − V0(t)| dt.

❱t♦♥ rsts

♠t♦♥ ♥ ①♣r♠♥t rsts r rs♠ ♥ ♥ strt ♥ rs

♥ ♦t rt♦♥ s ♣r♦r♠ s ①♣t t t rsts r ♥♦t ♥

r♠♥t t s♠t♦♥ ♥ s♠t♦♥ t st rsts r ♦♥ t ♥ ♥rt♥t② ♦

♥ ①♣r♠♥t t st rsts r ♦♥ t ♥ ♥rt♥t② ♦ r♥

t♥ s♠t♦♥ ♥ ①♣r♠♥tt♦♥ rsts ♦ ①♣♥ ② t t tt ♥

s♠t♦♥ ♦ ♥♦t ♠♦ t ♥♦s s ②s ♣rs♥t ♥ ①♣r♠♥tt♦♥

t s ♥rtss ♠♦♥strt tt t②♣ ③③② ♦ ♦♥tr♦rs ♥ s t♦ ♦♥tr♦

t ♦t ♦ ♦♥rtrs ♦r t s ♥♦t ♣♦ss ②t t♦ r♠ tt t②♣ ③③②

♦ ♦♥tr♦rs r ttr ♣r♦r♠♥ t♥ t②♣ ③③② ♦ ♦♥tr♦rs s s ♥♦t

♥①♣t s ♦ ♥♦t ♦♥sr ♦♣t♠st♦♥ ♦ t ③③② ♦♥tr♦rs

♣tr ♦♥s♦♥

❱t♦♥ rsts st rst t r♦♥ ♦rst rst r r♦♥

♠t♦♥ ①♣r♠♥t

②♣ ③③② ♦ ❯

②♣ ③③② ♦ ❯

②♣ ③③② ♦ ❯

♣tr ♦♥s♦♥

♥ ts ♣tr ♥tr♦ t②♣ ③③② ♦ ♥ ①♣♥ ♦ tr ss②st♠ ②

s♥ ♥♠r ①♠♣s ♦t ♦♥tr♦ ♦ ♦♥rtr ♦♥ ♦ t

ss ♣♣t♦♥s ♦ ③③② ♦♥tr♦ ♥ tr ♥♥r♥ s ♣rs♥t ♦♣

♥ t s♥ t②♣ ③③② ♦ ♥ ♦r♥ ♠t♦ t♦ ♥rt t ③③② sts

s ♣r♦♣♦s

♠t♦♥ ♥ ①♣r♠♥t rsts sst tt ♥ s ♥ ts ♣rtr

♣♣t♦♥ ♦r t s t♦♦ r② t♦ r♠ tt ♦♥tr♦rs r ttr t♥

♦♥tr♦rs tr rsr t ♦s ♦♥ t st② ♦ t t♥♥ ♥

♦♣t♠st♦♥ ♦ t ♣r♠trs ♦ t②♣ ③③② ♦ s②st♠s rsts ♦t♥ r

♥ t♦♥ ♠♦tt♦♥ t♦ s t②♣ ③③② ♦♥tr♦ ♥ ♦tr ♣♣t♦♥s s s ♥r②

♠♥♠♥t ♥ ②r tr s

s♦tr ♦♥sr t♦ ♠♣♠♥t s②st♠s s ♥ ♥ ♣♣♥① t s

s ♦♥ ♦rts ♥ strtr ♣r♦r♠♠♥ ♥ ♦s ♥♦t rqr t s ♦ t

t ③③② ♦ ♦♦♦①

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

r ♠t♦♥ rsts t♣t ♦t t② ②

♦t♣t ♦t ts ♥ t

♣tr ♦♥s♦♥

r ①♣r♠♥t rsts t♣t ♦t t② ②

♦t♣t ♦t ts ♥ t

②♣ ③③② ♦ ♦♥tr♦ ♦ ♦♥rtr

♣tr

♥r② ♠♥♠♥t strt②

s ♦♥ t②♣ ③③② ♦

s ♣tr ♣rs♥ts t ♥r② ♠♥♠♥t strt② ♠♣♠♥t ♥ t tst ♥

s♦♥ ♣♣t♦♥ ♦ t②♣ ③③② ♦ ♣rs♥t ♥ ts rsr s t ♥r②

♥♠♥t trt② ♦ ②r tr ❱ ❱ r s ♣♣t♦♥

s ♣rs♥t r t ❱ t ts ♣rtr♠♥ rttr ♦♥str♥ts ♥

s♣t♦♥s s ♣rs♥t ♥ t♦♥ ②r s♦r ♠♣♠♥t ♥ t

s ♦♠♣♦s ② ttr② ♥ ♥ ❯tr♣t♦r ②st♠ ❯ ♥ ②st♠

s s ♣r♦r♠ t t♦ ♦♥tr♦ s rst ♦♥tr♦ ♥♠② t ♦

s rs ♥ r t♠ ♦r s♦r s♦♥ ♦♥tr♦ tt s t ♦

s ♥sr t t s②st♠ t♦ ♦♦r♥t t ♣♦r ♦ ♦ ss②st♠

♦ s ♥ t♦ ♦♥tr♦ t s♦rs t ♦ s ♥ t♦ s♣rs

t ♦ s②st♠

t②♣ ③③② ♦ ♦♥tr♦r s s t♦ ♣r♦r♠ t ♦ ♠♥♠♥t ♦ t

s♥ ♦ t ③③② ♦ ♦♥tr♦r s ♦♥ ② s♥ ♥♦ ♥♥r♥ t♥q s

t♥q ♦s ①trt♥ ♥♦ r♦♠ ①♣rts s♥ sr②s ♦♥srt♦♥ ♦

t②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥s ♥s ♠♦♥ t ♥rt♥t② ♥ t ♥srs

♦ t ①♣rts

♥t♦♥ ♥ ♦ s♦t♦♥ ♦ t ♥r② ♠♥♠♥t ♣r♦♠ r ♣rs♥t ♥

t♦♥ ♦ ♠♥♠♥t strts ♦r ttrs ❯ ♥ r ♥tr♦ ♥

t♦♥s ♥ rs♣t② ♥r② ♠♥♠♥t ♥ r ♦♥rt♦♥s ♦

s ♥②s ♥ t♦♥ ♥r② ♠♥♠♥t strt② t♦♥ ② s♠t♦♥

♥ ①♣r♠♥tt♦♥ r rs♣t② ♣rs♥t ♥ t♦♥s ♥ ♥② t♦♥

♣rs♥ts t ♦♥s♦♥s ♥ ♦t♦♦s ♦ ts ♣tr s♥ ♦ t t②♣ ③③②

♦ s②st♠ ♠♠rs♣ ♥t♦♥s ♥ ③③② rs s ♣rs♥t ♥ t ♥ ♣♣♥①

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦ ♥r② ♠♥♠♥t strt②

♥ ❱ ♥♥ t ❯ ♥ ttrs ♣♦r rr♥s t♦ s♣♣② t

♣♦r ♦♥s♠♣t♦♥ ♠♦t♦r rs ♥ ♥rs s♠s t♦ t ♥tr ♦t

♦ t ♥r② ♠♥♠♥t strt② s ♥ ② qt♦♥ ♦r s t

ttrs r rt② ♦♥♥t t♦ t s s r t ♣♦r ♦ ♦ ts

s♦r ♥♥♦t rt② ♦♥tr♦ s ts ♥ ts s ♠t t♦ ♥♥ t

❯ ♥ ♣♦r rr♥s

Pmotor drives + Pancillary = Preference = PFCS + Pbatt + PUCS

❲ ♦♦s t♦ ♦♣ ♥ ♥r② ♠♥♠♥t strt② s ♦♥ t ♣♦r ♣♦r

strt♦♥ ♥ ♥ rt② tr♥s♦r♠ ♥t♦ rr♥t strt♦♥ s

t s♦rs r ♦♥♥t t♦ t s♠ s s s s ♥ ①♣r♠♥t t♦♥

r t rr♥s t♦ t r ♦♥tr♦ s②st♠s r ♥ tr♠s ♦ rr♥t ♥ ♥♦t ♥ ♣♦r

♦ ♥r② ♠♥♠♥t strt② ♦ts

rst st♣ t♦ s♥ t s t♦ ♥ ♦ rr♥ t rtrsts

♥ ♦♥str♥ts ♦ ♦t t ♥ t ②r s♦r s♦♥ ♦♥tr♦ ♦ t

s ♥ t♦t ♦♥sr♥ t ♥r② s♦rs s♣rt② ♦ ♦ts

♦ t r st ② ♣r♦rt② ♦rr

• ♦ ♠①♠s t rt② ♦ t ♣♦r s♦rs

• ♦ r♥t t ♥r ♣♦r ♥ ♥ t♦ r♦r t ♠①♠ ♠♦♥t ♦ r

♥ ♥r② qt♦♥ ♥s ♠♥ r♥ s ♣♣

• rr♥ts stts♦r ♣♦rs ♥♦r ♦ts ♥ ♥ rts ♠st r♠♥

t♥ ♣rtr♠♥ ♥ ♦♥str♥t ♠ts

• ♦ ♠♥♠s t ttr② s ♦t rt♦♥ ♥ t♦ ♠♥♠s t s ♦ ts

s♦r s t s ss ♥t ♥ ♣rs♥ts ♦r rt② t♥ t ❯

• ♥ st② stt t ♣♦r s t♦t② ♣r♦ ② t s②st♠ st ♥ s②

t♦ rr ts s♦ t ♦♥② r ♥r② s♦r ♦♥ t

• ❯ ♥srs t ②♥♠ ♥sr ♥ r♥t ♥♦ ♥r② t♦ rt t

♥ ♥♦ ♣t② t♦ r♦r ♥r②

• ♥s r ♦♣rt♦♥ r ♦ ♥② ♦ t ♣♦r s♦rs

♦ ♥r② ♠♥♠♥t strt② ♥♣ts

s rs t♦t ♥♦ ♦ tr r♥ ♦♥t♦♥s t ♦♥② ss r

t♠ ♥♦r♠t♦♥ t♦ ♦♠♣t t ♦t♣t ♣♦r rr♥s

♦ ♥r② ♠♥♠♥t strt②

• r♥ ♣♦r ♣♦r t♦ r t ♠♦t♦rs ♣♥s ♦♥ t s♣ ♦ t

♥ ♦♥ t rt♦r ♥ r ♣s ♣♦st♦♥s ①r② ♣♦r ♣♥s

♦♥ t ♥r② ♠♣♠♥t ♦♥♦r ♦r ①♠♣ ♦♠♣rss♦rs ♦r ♣♠♣s

• ♣♦r t ♦ t ♦t♣t ♣♦r ♦ t ♠sr tr ♣♦r

tr♦♥s s ts s t ♥t ♦♥trt♦♥ ♦ t t♦ t ♣♦r sr♥

• ttrs st♠t ttrs stt♦r st♦♥

• ❯ st♠t tr♣t♦r stt♦r st♦♥

• ❯ ♦t ♠sr ♦t t t tr♣t♦r ♥ ♦r ♣♦r tr♦♥s

• s ♦t ♠sr ♦t ♦ ttrs

• ❱ s♣ ♠sr s♣

♦ ♥r② ♠♥♠♥t strt② ♦t♣ts

s t ♦♦♥ t♦ ♦t♣ts

• ❯ ♦t♣t rr♥ ♣♦r t ♣♦r ♦r t rr♥t s♣♣ ② t ❯

• ♦t♣t rr♥ ♣♦r t ♣♦r ♦r t rr♥t s♣♣ ② t

ttr② ♣♦r rr♥ ♦ s♦ ♥♠rt s ♥ ♥tr♠t ♦t♣t ♦r

t ♣♦r ♦ ts s♦r s r ♥♦t rt② ♦♥tr♦ r strts t s

♠♣♠♥t ♥ t ♠♥

r ♦ s ♠♣♠♥t ♥ t ♠♥

♦ ♥r② ♠♥♠♥t strts ♦r

s t ♦♥tr♦ ♦ t s♦rs s ♥♣♥♥t② rs t ♥①t st♣ s t♦ ♥t②

♦ ♦ts ♦r s♦r rst ♦♥tr♦ s s ♦♥ ② ♦♠♣r♥ t

rtrsts ♦ t s♦rs t t ♦ ♦ts s ♣rs♥t ♥

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦ ♦ts ♦ t ♥ t ♦♠♣tt② t t s♦rs

t ❯ ttrs

♦ s♣♣② ♥r② t♦ t r

♦ ♠①♠s t ♥r② r♦r ♥ r♥

♦ ♠♥♠s t s ♦t rt♦♥

♦ rt t ❯ ♥ ttrs

♦ s♣♣② ②♥♠ ♣♦r

② s♥ t t ♥ ♥ tt t ❯ s♣♣s t ②♥♠ ♣♦r rqr

② t ♦ ♥ s ♦♥sr t♦ r♦r② r♥ ♥srs t t♦♥♦♠② ♦ t

♥ rt t stt ♦ r ♦ t st♦r s♦rs ttr② ♣♦r ♦s

r ♠♥♠s t♦ r t ♦t rt♦♥s ♦♥ t s ♥ s♦ t♦ ♥rs t

rt② ♦ t ttr②

ttrs ♥r② ♠♥♠♥t strt②

♥ ♥ s tt ttrs r rt② ♦♥♥t t♦ t s ♥

♥♥♦t rt② ♦♥tr♦ ♣♦r ♦♥rtr ♦ ♦♥sr s ♠♦r ①♣♥s

s♦t♦♥ ♣r♦♣♦s s♦t♦♥ t♦ ♥ ts ♣r♦♠ s t♦ ♥rt② ♠♥ t ttr②

s♥ t r♠♥♥ s♦rs ♥ ❯ stt♦r ♦♥tr♦ s ♠♣♠♥t ts

♦♥tr♦ s s ♦♥ tt ♣rs♥t ② ♥ss♦ t ❬♥❪

ttrs ♦ ♣r♠trs

♦ r♦♣s ♦ ♣r♠trs r ♥t ♦r t ttrs ♠♣♦s ♣r♠trs tt

♣♥s ♦♥ t s♣t♦♥s ♦ t ♥♦r t ttrs ♥ strt② ♣r♠trs

tt ♥ s ♦r ♦♣t♠st♦♥

• s ♠♣♦s ♣r♠trs t ♦♥srs t s ♥♦♠♥ ♦t t ♠①♠

♥ t ♠♥♠ ♦t s ♥♦t ♦♥② ♦r t ttrs t s♦ ♦r t s

♦♥♥t t♦ t s s s t ❯ ♦r ♣♦r ♦♥rtrs ♦r t ♥r②

• s♦♥ r♦♣ ♦ ♣r♠trs ♦♥srs ♠tt♦♥s ♥ t stt♦r ♥ ♥

t ♣♦r s♣♣ ② t ttr② ♠tt♦♥ ♥ ♣♦r s ♦♥ t♦ ♥rt② ♠t

t rs r♦♣ ♦ t s ♦t ♥ r sr ♦ t ttr② ts ♣♦r

♥ st♠t s♥ t ♦ t ♥tr♥ rsst♥ ♦ t ttr②

ttr② ♣rs♥t ♦♥ ts st♦♥ rqrs t ♥t♦♥ ♦ t ♣r♠trs

♥♠rt ♥

ttrs ♥r② ♠♥♠♥t strt②

ttrs ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

Pr♠tr sr♣t♦♥ ②♣

Vbusref s ♦t rr♥ ♣t♦♥s ♣r♠tr

Vbattmin ttrs ♠①♠ ♦t ♣t♦♥s ♣r♠tr

Vbattmax ttrs ♠♥♠ ♦t ♣t♦♥s ♣r♠tr

SOCbatthigh ttrs ♠①♠ stt♦r trt② ♣r♠tr

SOCbattlow ttrs ♠♥♠ stt♦r trt② ♣r♠tr

dPbattmax ttrs ♠①♠ rsr ♣♦r trt② ♣r♠tr

ttrs t♦♥ ♣♦r stt♦r ♦♥tr♦

s t ♦♥② s t t ♥ t ❯ qt♦♥ ♦ r♥

t♦ ♠ ♣♣r t ttr② ♣♦r ♥ t ♦ s ♦♠♥ ❯ s♦r

♣♦r rr♥ PUCS&FCS∗ s t s t t♦♥ ♦ t rr♥ ♣♦r ♥ ♥

t♦♥ ♣♦r t♦ ♦♥tr♦ t ttrs dPbatteries s s ♥ ♥ qt♦♥

PUCS&FCS∗ = Preference + dPbatteries

t ttr② stt♦r s rtr t♥ tr rr♥ dPbatteries ♦♠s

♥t t ❯ ♦♠♥ s♦r s♣♣s ss ♥r② ♥ t♥ t ttr②

s♣♣s tt r♥ ttrs sr ♥t ♠t♥ t rr♥

t♦♥ ♣♦r dPbatteries s ♦♠♣t s♥ qt♦♥s ♥ s s strt ♥

r ♠①♠ ♦ dPbattmax s st t♦ ♦ ♦r ♦r ♥r ♦ts

t♦ t ♥r② ♠♥♠♥t

dPbatteries∗ = dPbattmax

αSOCbatt

r

αSOCbatt= min

1, max

−1,

SOCbatthigh+SOCbattlow

2 −SOCbatt

SOCbatthigh−SOCbattlow

2

ttrs t♦♥ ♣♦r ♦rrt♦♥ ♦t ♠tt♦♥s

ttrs ♦♥tr♦ s sr ♥ qt♦♥ ♦ r♥ t ♦t ♦t

♦ t ♦♥sr ♠ts ttr② rr s♠t♥♦s② t r♣rt r♥

♦ s ♥ ♦r♦t ♦ ♦ ts stt♦♥ ♦rrt♦♥ ♦ t t♦♥ ♣♦r

s ♣♣ ttrs ♦t ♣♣r♦s t ♠①♠ ♠♥♠ ♠ts t♥ r

sr ♠tt♦♥ s ♣♣ s ♠tt♦♥s r sr ② qt♦♥s ♥

♥ r strt ♥ r

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

dP batteries = (dP batteries∗) αVbatt

r

αVbatt=

min(

1, max(

0,(

Vbusref−Vbatt

Vbusref−Vbattmax

)) )

if dPbatteries∗>0

min(

1, max(

0,(

Vbatt−Vbattmin

Vbusref−Vbattmin

)) )

if dPbatteries∗<0

r ttrs stt♦r ♦♥tr♦ strt②

r ttrs t♦♥ ♣♦r ♦rrt♦♥ αV batt

s t ttrs r rt② ♦♥♥t t♦ t s t ♥② ♥ ♥ t s ♣♦r

t ttr② t rst s♦r t♦ t s s t rs♦♥ ② t r ♦♥trt♦♥

♦ ts s♦r ♥ r♥t r♦♠ t rr♥ ♠♥② ♥ tr♥s♥t s ♦♥stt ♥

s♠t♦♥ ♥ ①♣r♠♥t t♦♥ ttrs s strt ♥ r

❯ ♥r② ♠♥♠♥t strt②

❯ s t ♠♦st ♥t s♦r ♥ t ♦s s♦ t r♦r② r♥ ♥

②♥♠ r♣♦♥s t t s ♦ s♣ ♥r② s t s ♠t t♦ ♥

st ♣♦r ②♥♠s ♥ t ttrs ♣♦r s ♠ t♦ ♠♥♠s t ❯ ssrs

t ②♥♠ ♥ t ♦ ♣♦r s♣♣② s②st♠ ♦ ♦♥srs ♦♥tr♦ ♦ t

❯ ♦r ts s ♥rt② ♦♥ ② t s st♦♥

❯ ♠♥♠♥t strt② ♣r♠trs

♦ ♦ t ❯ s ♥ ② s♥ s♣t♦♥ ♥ strt② ♣r♠trs

❯ ♥r② ♠♥♠♥t strt②

r ttrs ♦ ♥r② ♠♥♠♥t strt② ♦ t

• s ♠♣♦s ♣r♠trs t ♦♥srs ♠tt♦♥s ♥ rr♥t ♥ t ❯ s s

♥ t ❯ ♦t ss ♦ t ♣♦r ♦♥rtr ♠tt♦♥ ♥ ❯ ♦t ♥rt②

♦♥ ② ♠t♥ t ❯ ♠①♠♠

• s strt② ♣r♠trs t ♦♥srs ♥ ♦ s r ♦♥

sr t♦ trr r ♥ sr ♠tt♦♥s rs♣t② ♠tt♦♥ ♦♥ t

sr ♠♥♠♠ t♦ ♦ ♦♣rt♦♥ ♥ ♦ ♥② r♦♥s ❬❪

❯ rqrs t ♥t♦♥ ♦ t ♣r♠trs ♥

❯tr♣t♦r s②st♠ ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

Pr♠tr sr♣t♦♥ ②♣

iUCSmax ❯ ♠①♠ rr♥t sr ♣t♦♥s ♣r♠tr

iUCSmin ❯ ♠♥♠ rr♥t r ♣t♦♥s ♣r♠tr

iUCmax ❯ ♠①♠ rr♥t sr ♣t♦♥s ♣r♠tr

iUCmin ❯ ♠♥♠ rr♥t r ♣t♦♥s ♣r♠tr

SOCucmax ❯ ♠①♠ stt♦r ♣t♦♥s ♣r♠tr

SOCucmin ❯ ♠♥♠ stt♦r trt② ♣r♠tr

SOCuchigh ❯ r ♠tt♦♥ trs♦ trt② ♣r♠tr

SOCuclow ❯ sr ♠tt♦♥ trs♦ trt② ♣r♠tr

❯ rr♥ ♣♦r

rr♥ ♣♦r ♦ ts s♦r PUCS∗∗ s ♦♠♣t s t r♥ t♥ t

❯ ♦♠♥ s♦r ♣♦r rr♥ qt♦♥ ♥ t ♠sr ♣♦r

s s ♥ ♥ qt♦♥

PUCS∗∗∗ = PUCS&FCS

∗ − PFCS

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

❯ ♣♦r rr♥ ②♥♠ ♠tt♦♥

♠tt♦♥ t♦r s ♦♥sr t♦ ♠t t r ♦r sr ♥ ts s♦r qt♦♥s

♥ ♥ t ♠tt♦♥ t♦r strt ♥ r

PUCS∗∗ = PUCS

∗∗∗αSOCUC

r

αSOCUC=

min

(

1, max

(

0,

(

SOCUCmax−SOCUC

SOCUCmax−SOCUChigh

)) )

if PUCS∗∗∗> 0

min(

1, max(

0,(

SOCUC −SOCUCmin

SOCUClow−SOCUCmin

)) )

if PUCS∗∗∗< 0

r ❯ rr♥ ♣♦r ②♥♠ ♠tt♦♥

❯ rr♥ ♣♦r stt ♠tt♦♥

①♠ s ♥ rr♥t ♥ t ❯ ♥ ♥ t ❯ r ♦♥sr rr♥t ♥ t

❯ ♥ ♥ t ❯ r ♦♠♣t s♥ t ♦ t ♣♦r PUCS∗∗ ♥ qt♦♥s

❯ ♥ qt♦♥ ❯ ttr s t ♦♥rtr ♦sss ♥ rt♦r♣②

s ♦sss s ♦♣t ♣♦r Plosses(PUCS∗∗

iUCS∗∗ =

PUCS∗∗

Vbatt

iUC∗∗ =

PUCS∗∗ + Plosses(PUCS

∗∗)

VUC

♠tt♦♥ ♥ t ♠♥t ♦ t rr♥t s ♣♣ s ♥ ♥ qt♦♥s

❯ ♥ ❯

iUCS∗ = min (iUCSmax , max (iUCS

∗∗, iUCSmin) )

iUC∗ = min (iUCmax , max (iUC

∗∗, iUCmin) )

s rr♥ ♥ rr♥t ♥ rt② s s ♥ ①♣r♠♥t t♦♥ ♦♥

t♦♥ ❯ ♣♦r rr♥s s ♥ ♥ qt♦♥ rr♥ ♥ t

♣♦r ♠st rs♣t t t♦ ♠tt♦♥s ♥ rr♥t

♥r② ♠♥♠♥t strt②

PUCS∗ = min (iUCS

∗ Vbatt, iUC∗ VUC)

♦ ❯ ♥r② ♠♥♠♥t s②st♠ s s♦♥ ♥ r

r ❯tr♣t♦r ♦ ♥r② ♠♥♠♥t strt② ♦ t

♥r② ♠♥♠♥t strt②

s♣♣s t ♦ ♠♦♥t ♦ ♥r② ♥ s ♦♥sq♥ t

♠st ♦♥tr♦ t ttrs ♥ ❯ stts♦r ♠st ♦♥sr t t tt

s ♠tt♦♥s t♦ ♥ ②♥♠s ③③② ♦ s st t♦ ♠♥ t

s♥ ♦ t ③③② ♦ ♦♥tr♦r s ♦♥ ② s♥ ♥♦ ♥♥r♥ t♥q

tt ♦s ①trt♥ ♥♦r♠t♦♥ r♦♠ ①♣rts s♥ sr②s ❬♥❪

s②st♠ ♥r② ♠♥♠♥t ♣r♠trs

s♣t♦♥ ♣r♠trs r t ♠①♠♠ ♥ ♠♥♠♠ ♦t♣t ♣♦r

♠♥♠♠ ♣♦r t♦ ♦ ♦rs ♥ ♦ ♥② r♦♥s ②♥♠ ♦ t

s②st♠ s ♦♥sr ② ♠t♥ t rt ♦ ♣♦r rt♦♥ ♠①♠♠ s♣ ♦ t

s ♦♥sr t♦ ♦♥tr♦ t ❯

strt② ♣r♠trs r rt t t ❯ ♦♥tr♦ t ❯

rr♥ t ♠①♠♠ s♣ ♥ t ♥t ♥r② ♠t ♥ t s

♠①♠ ♥ t ❯ rr♥ t s♣ ③r♦ ♥ t ♥t ♥r② ♠t ♥

t s ③r♦ s②st♠ ♣rs♥t ♦♥ ts st♦♥ rqrs t ♥t♦♥

♦ ♣r♠trs ♥

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

s②st♠ ♦ ♥r② ♠♥♠♥t strt② ♣r♠trs

Pr♠tr sr♣t♦♥ ②♣

Pfcsmax ♠①♠ ♣♦r ♣t♦♥s ♣r♠tr

Pfcsmin ♠♥♠ ♣♦r ♣t♦♥s ♣r♠tr

dPfcsmax ♠①♠ ♣♦r rt ♥ ♣t♦♥s ♣r♠tr

speedmax ❱ ♠①♠ s♣ ♣t♦♥s ♣r♠tr

SOCUCrefmax❯ rr♥ t ♠①♠ s♣ trt② ♣r♠tr

SOCUCrefmin❯ rr♥ t s♣ ③r♦ trt② ♣r♠tr

③③② ♦ ♦♥tr♦r ♥♣ts

s♣♣s t ♣r♦♣s♦♥ ♣♦r ♥ st② stt ts s t rs♦♥ ② t rst

♥♣t ♦ t ③③② ♦ ♦♥tr♦r s t r♥ t♥ t ❯ ♦♠♥

s♦r rr♥ ♣♦r qt♦♥ ♥ t ♠sr ♣♦r qt♦♥

s♦ ♦♥tr♦s t ❯ ♦r ts rs♦♥ t s♦♥ ♥♣t ♦ t ③③② ♦♥tr♦r s

t r♥ t♥ t ❯ stt♦r ♥ ts ②♥♠ rr♥ ♣rs♥t ♥

♥①t st♦♥ qt♦♥

∆P ∗ = PUCS&FCS∗ − PFCS

∆SOC∗ = UCSOCref−UCSOC

♥♣t ♥♦r♠st♦♥

③③② ♦ ♦♥tr♦r ♥ ♥♦r♠s ♥♣ts ♦♠♥ ❬ ❪ s ♥ ♥ q

t♦♥s ♥

∆P =∆P ∗

PFCSmax

∆SOC =∆SOC∗

SOCUCrefmax− SOCUCrefmin

speed∗ =speed

speedmax

❯ ②♥♠ rr♥ ❯ ♦♥tr♦

r♥t t♦rs ♣r♦♣♦s t♦ ♥ ②♥♠ rr♥s ♦r t ❯ st♦♥

❲ ♣r♦♣♦s t♦ s rr♥ ♣♥s ♦♥ t s♣ ♦ t

• ❲♥ t s st♦♣♣ tr s ♥♦ ♣♦sst② t♦ r♦r r♥ ♥r② ♥ t

❯ ♦ stt♦r ♠♥s ss ♥r② t♦ rt rr♥

♥r② ♠♥♠♥t strt②

♦r t ❯ s r ts s ♣r♠tr ♦ t strt② ♥ ♦s ♥♦t ♠♣②

tt t ❯ s ♦♠♣t② r

• t s t ♠①♠ s♣ ♥♦ rtr rt♦♥ rqr ♥ r♥

s t ♥①t stt ❯ ♠t t r♦r② ♦ r♥ ♥r②

rr♥ ♦r t ❯ stt♦r s sr ♥ ts s ♣r♠tr ♦ t

strt② ♥ ♦s ♥♦t ♠♣② tt t ❯ s ♦♠♣t② sr

♣r♦♣♦s rt♦♥ t♥ t ❯ ②♥♠ rr♥ ♥ t s♣ s

♥ ♥ qt♦♥ ♥ s strt ♥ r

UCSOCref = SOCUCrefmax− speed∗

(

SOCUCrefmax− SOCUCrefmin

)

r ❯ stt♦r ②♥♠ rr♥

③③② ♦ ♦♥tr♦r s♥

t②♣ ③③② ♦ s②st♠ s s t♦ ♣r♦r♠ t ♥r② ♠♥♠♥t ③③②

♦ ♦♥tr♦r ♠♣s t♦ rs♣ ♥♣ts ♥t♦ ♦♥ rs♣ ♦t♣t s ♥ qt♦♥

∆PFCS = f (∆P , ∆SOC)

♥ ♥r② ♠♥♠♥t sr② s ♦♥t ♠♦♥ ①♣rts ♥ ②r tr

s ♦r ①♣rts r s t♦ ♥ ③③② rs ♥ ③③② ♥trs ②

s♥ s♣ ♥st s ♥srs r s t♦ rt t ③③② ♦ s②st♠

sr②s ③③② ♦ s②st♠ s ♦ t②♣ ③③② ♦ ♠♠rs♣ ♥t♦♥s

♣r♠ts t♦ ♦♥sr ♥ r t t ♦ t ♥rt♥t② ♥ t ♥srs ♦ t ①♣rts

♠t♦♦♦② ♥ rsts ♦ t sr② r ♣rs♥t ♥ ♣♣♥①

③③② rs

♥♣ts ♦ t ③③② s②st♠ ∆P ♥ ∆SOC r r♣rs♥t ② s♥ ♥st

s t t ♠ t ♦ ❩r♦ ❩ P♦st

♦ P P♦st ♠ P ♥ P♦st P

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦t♣t ♦ t ③③② s②st♠ ∆PFCS s r♣rs♥t ② s♥ ♥st s

rs ♠ rs ♦ rs ♦ ♦ ♥rs

♠ ♥rs ♥ ♥rs

①♣rts r s t♦ ♥ t 7·7 rs ♦ t ③③② ♦ s②st♠ ② s♥ t

s♣ ♥st s rs s ♥ ② t ①♣rts r s♠♠rs ♥

s ♥srs r s t♦ ♥ t rs ♦ t ③③② s②st♠ s ①♣♥ ♥ ♣♣♥①

rs r s♠♠rs ♥

③③② ♠♠rs♣ ♥t♦♥s

♥♣t s ♥ st t♦ tr♥r ♦r t s ❩ P ♥

P ♥ tr♣③♦ ♦r t s ♥ P s r st t♦ s②♠♠tr

r♦♥ t ③r♦ ①s s tt r♣rs♥t ∆P r ♣rs♥t ♥ r s

tt r♣rs♥t ∆SOC r s♦♥ ♥ r

③③② ♦ ♦♥tr♦r ①♠♣

♥ ♣tr ♥♠r ①♠♣ s ♣rs♥t t♦ strt ♦ t ③③② ♦ s②st♠

♦♠♣t ♥ ♦t♣t r♦♠ tr♠♥ ♥♣t ♥②ss ♦ t ♥♠r ①♠♣ s

♥♦ ♣rs♥t t♦ ①♣♥ ♦ t ♦♥tr♦r ♦rs

❬∆P ∆SOC❪ ❬ ❪ t♥ ∆PFCS

s rt♦♥s♣ ♦ ①♣♥ s♥ t ♥st s s

t tr♣t♦rs r rt② ♦rr ♦ rt r

♥

t s②st♠ ♣r♦s ♠♦r ♣♦r t♥ rqr ♦ rt ♣♦r

t♥

rs t ♣♦r ♦ t t ♦ ♠①♠ rs rt

s ♦♥ t ♦♣rt♦♥ ♦♥t♦♥s ts s ♦ ♦t♣t t s s♣♣②♥

♠♦r ♣♦r t♥ rqr ♥ t♦♥② t tr♣t♦rs r ♦rr t♥ t s

♥ssr② t♦ r♣② rs t ♣♦r s♣♣ ② t

♥r② ♠♥♠♥t strt②

Pr♦ss sr② rsts ③③② s

♥ ♥ ∆PFCS s

∆P s ∆SOC s

❩

P

P

P

❩

P

P

P

❩

P

P

P

❩

❩

❩

❩ ❩

❩ P

❩ P

❩ P

P

P

P

P ❩

P P

P P

P P

P

P

P

P ❩

P P

P P

P P

P

P

P

P ❩

P P

P P

P P

♥r②♠♥♠♥tstr

t②s♦♥t②♣

③③②♦

③③② s s ♥tr ♦♥s

∆PFCS

∆SOC ↓ ∆P → ❩ P P P

❬❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❩ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

P ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

P ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

P ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

♥r② ♠♥♠♥t strt②

r ♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s t♦ r♣rs♥t e

P P P ❩

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r ♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s t♦ r♣rs♥t ∆SOC

P P P ❩

♥r② ♠♥♠♥t strt②

♥♦r♠s ♦♥tr♦ sr ♥ ② qt♦♥ s ♠♣♣ ♦♥ ♥

s ♣rs♥t ♦♥ r

r ♥r② ♠♥♠♥t t②♣ ③③② ♦ ♥♦r♠s ♦♥tr♦ sr

③③② ♦ ♦♥tr♦r ♦t♣t

③③② ♦♥tr♦r ♦t♣t rt ♥ ♥ t ♦t♣t ♣♦r rr♥ s

♥♦r♠s ♦♠♥ ❬ ❪ s♥ qt♦♥

♥♦r♠s ♦t♣t s t rt ♦ ♥ ♥ t ♦t♣t ♣♦r s ♦♣rt♦♥

♠♣t② trs t rr♥ ♣♦r ② ♦♥sr♥ t ②♥♠ ♠tt♦♥ ♦ t

dPFCSmax

∆PFCS∗ = ∆PFCS dPFCSmax

rt ♥ s ♥trt t♦ ♥ t ♣♦r rr♥ ♦ ♠t t ♦t♣t

♠t ♥tr s ♦♥sr t ♥trt♦♥ t♦♥ s tr♥ ♦ ♥ ♣♣r ♦r ♦r

♠ts r r qt♦♥

PFCS∗ =

∫

limited∆PFCS

∗ dt

♥② t ♦ ♦ s ♣rs♥t ♥ r

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r s②st♠ ♦ ♥r② ♠♥♠♥t strt② ♦ t

♥trt♦♥ ♦ t ♦ ♥t♦ t ♦ strt②

♦ tt t ♦ strts r ♥ t ♥ st♣ s tr ♥trt♦♥ ♦♥ ♦

strt② s strt ♦♥ r

r ♦ s ♠♣♠♥t ♥ t ♠♥ t

r ♦♣rt♦♥ strts

♠st ♥ r ♦♣rt♦♥ ♥② ♦ t s♦rs s st♦♥

s t s ♥♦t ♦♣rt♦♥ t♦t ttrs s t② ♠♣♦s t s ♦t

r ♦♣rt♦♥s r ♦♥② ♦♥sr ♦r ♦r ❯ r t s ♠♣♦rt♥t t♦ t

tt t ♦t s ♥♦t t♦ ♦♣ ♦ ♥ t t♦ tr t r② ♦♣

t st ♠♦t♦♥s

♠t♦♥ t♦♥

r ♦♣rt♦♥ t♦t

rst s ♦♥sr s t ♥ t r ♦♣rts s ♣♥

t ttrs ♣r♦ t ♦ ♠♦♥t ♦ ♥r② ♥t sr ♥ s ♦♥sq♥

t ♦♥tr♦ ♥ ttrs s ♥♦t ♣♦ss ♥②♠♦r rtss t ❯ ♦

st ♦♥tr♦ t ttrs ♣r♦♣♦s s♦t♦♥ s t♦ s t ttrs t♦ s♣♣② t

♣♦r tt t ♥♥♦t s♣♣② s t ttrs r rt② ♦♥♥t ♥ tr ♣♦r

♥♥♦t rt② ♦♥tr♦ ts s ♦♥ ② ♠♦②♥ t ❯ ♥♣t ♣♦r rr♥

tt ♣r♠ts r ♦♣rt♦♥ t♦t s r♣② ♣rs♥t ♥

r ♦s s ♥ ts strt② r t s♠ s ♦♥ ♥♦r♠ ♦♣rt♦♥ s

♣rs♥t ♦♥ r ♦r t ② t ♦s r ♥tr♦♥♥t s ♥♦t t s♠

r r ♦♣rt♦♥ strt② r

r ♦♣rt♦♥ t♦t ❯

s♦♥ s ♦♥sr s t ♥ t ❯ ♥ ts s t ♦♥tr♦ ♦ ttrs

s ♣♦ss ♦r t ❯ ♦♥tr♦ s ♦♦s② ♥♦t ♥ssr② ♥②♠♦r ♣r♦♣♦s

s♦t♦♥ s t♦ s t s♠ ③③② ♦ ♦♥tr♦r t♥ ♥ ♣r♥t st♦♥ ♦r s t

❯ ♦♥tr♦ s ♥♦t rqr t ♥♣t ∆SOC s ♠♣♦s t♦ ③r♦ s s q♥t

t♦ s② tt t s♦♥ ♦t s r② ♥ t♥ t ♦♥② ♦t s t♦

s♣♣② t ♦ ♠♦♥t ♦ ♥r② ♠♦ ♦r t s strt ♥ r

♦r ts r ♦♣rt♦♥ s r♣② ♣rs♥t ♥ r

♠t♦♥ t♦♥

♣r♦♣♦s s t ② ♦♠♣tr s♠t♦♥s ♥rt ♠r♦s♦♣

r♣rs♥tt♦♥ ♥ t ♥r② ♠♥♠♥t strt② r ♠♣♠♥t ♥ t ♠♥

t♦♥s ♥ t♦♥ s t ② ♦♥sr♥ ♥rt♥

ts ♦ ♥ t②♣ ③③② ♦ s♠t♦♥ rsts r r② s♠r ♣♦r

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r r ♦♣rt♦♥ strt② ❯ r ♦ ♦

strt♦♥ stts♦r ②♥♠ s r② s♦ rr♥ t ♦tr ♣♦r

s♦rs ♥ t r♥ ♠♦♥ t ♣♦r strt♦♥ ♦t♥ t t t♦ s r②

r ♦r ts rs♦♥ ♦♥② s♠t♦♥s t ♥rt♥t② r ♣rs♥t

♠t♦♥s r ♣r♦r♠ ♦r ♥♦r♠s ② ♥ ♦r r r♥ ②

• ♦r♠s ② ♦r♠s r♦♣♥ r♥ ② s r ♦♥sr

r ♦r ♦♥② t r♥ s♠② s rt♥ s t ♠①

♠ s♣ ♦ t t♦♥ s ss t♥ ❬♠❪

• r ② s s r♣rs♥tt r ② ♦ t ♠sr

♥ r tst r rt s ② r♣rs♥ts t ttr r② t ♦♣rt♦♥ ♦

t s♣ ♥ ♥r② ♦♥s♠♣t♦♥

♠t♦♥ ♣r♠trs

♠t♦♥s r ♣r♦r♠ s♥ t ♣r♠trs ♥ ♦ ♦ ts ♣

r♠trs s s ♦♥ t t♥ s♣t♦♥s ♦ t ♥ ts s♦rs

♠t♦♥ rsts

rs ♥ ♣rs♥ts t s♠t♦♥ rsts ♦r t ♥♦r♠s ♥ t r

r♥ ② rs♣t② ♥ t s sr ♥ qt♦♥ t ♣♦r s♣♣ ②

s♦r s ♣♦st s s t ♣♦r ♦♥s♠♣t♦♥ ♥ t ♦ s

♠t♦♥ t♦♥

♠t♦♥ ♣r♠trs

Pr♠tr rr♥s ❱

♠①♠ ♣♦r ❬❲❪

♠♥♠ ♣♦r ❬❲❪

♠①♠ ♣♦r rt ♥ ❬❲s❪

rr♥ t ♠①♠ s♣

rr♥ t s♣ ③r♦

❱ ♠①♠ s♣ ❬♠❪

❯ ♠①♠ stt♦r

❯ r ♠tt♦♥ trs♦

❯ ♠♥♠ stt♦r

❯ sr ♠tt♦♥ trs♦

❯ ♠①♠ rr♥t sr ❬❪

❯ ♠♥♠ rr♥t r ❬❪

ttrs ♠①♠ stt♦r

ttrs ♠♥♠ stt♦r

ttrs ♠①♠ rsr ♣♦r ❬❲❪

ttrs ♦t r♥ ❬❱❪

ttrs rr♥ ♦t ❬❱❪

• ❱ s♣ rs ♥ s♦ t ♦♥sr r ②s

rr ♣r♦ ♦r t ♥ ttrs s ♦♥sr t t ♥ ♦ ② t

♥ ♠ts t ♥t s rr ♣r♦ ♣r♠ts t♦ ♦t② ♦♠♣r

t ♦♥s♠♣t♦♥ r t ♥r② s s♣♣ ② t H2

• r♥ P♦r t rr♥ ♣♦r s t t t s ♥ ♥s t

♣♦r ♦ t tr trt♦♥ ♠♦t♦rs ♥ t ♥r② ♦ t ♣♠♣s

♦♠♣rss♦rs ♥ t s t ♥ t ♠♥ s♥ t ♠♦

♥ t r r ② t ♣♦r s ♠sr t t s t ♥s t ♠♦t♦r

rs ♥ ♥rs ♦♥s♠♣t♦♥

• ttr② ♣♦r s ①♣t t ttr② s t rst ♠♥t ts ♥

♥② ♥ ♥ t rr♥ s ♣♣ ttr② ♦t♣t ♣♦r r♠♥s ♠♦st

♦♥st♥t r♥ ♦ rt♦♥s ♦ t s♣ ♥ rt♦♥ ♦r r♥ rs ♥ t

♦♥trt♦♥ ♦ t ttr② s ♦sr

• ❯tr♣t♦r s②st♠ ♣♦r ❯ s♣♣s ♠♦st ♦ t ②♥♠ rs♣♦♥s

♥ tr s ② ss♦t t♦ t rr♥t ♦♥tr♦r t♥ t rr♥

♣♦r ♥ t tr♣t♦r rs♣♦♥s

• s②st♠ ♣♦r t s♣♣s t ♠♥ ♥r② ♥ ♦♥tr♦s t ❯

♥ ttrs ♦t♣t ♣♦r ♣rs♥ts ♦ rq♥② ♦t♦♥ t ③③②

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦ s②st♠ ts s ♦♣ss tr s ♦ t ♦♥srt♦♥ ♦ t ♠①♠

♣♦r rt ♥ dPfcsmax ♥② ♥ t s st♦♣♣ t

♣♦r ♥rss t♦ r t tr♣t♦r s②st♠ ♥ t ttrs

• ttr② ♦t t ttr② ♦t rs t t ttr② ♦t♣t ♣♦r t

st②s ♥ ss♥ ♠ts

• ttr② stt♦r t ttr② stt♦r ♦s ♥♦t rs ♠ ♥

st② ♥ t ss♥ ♠ts ♥ t ② t ♠♥♠ ttrs rr♥

s

• ❯tr♣t♦r stt♦r t tr♣t♦r s②st♠ stt♦r st② ♥

t ss♥ ♠ts t s♦ rs ♥rs② t t s♣

s s♠t♦♥ rsts r ♥ r♠♥t t ①♣tt♦♥s t ♥①t st♣ s ♥♦ t♦ t

t ♥ r ♦♥t♦♥s

①♣r♠♥t t♦♥

s st♦♥ ♣rs♥ts t ♠♣♠♥tt♦♥ ♥ t♦♥ ♦ t ♦♣ ♥ t

♣r♦s st♦♥s ①♣r♠♥t ♦♥t♦♥s r qt r♥t r♦♠ t♦s ♥ s♠t♦♥

♥ ♣rtr② rr♥ t ♦♥tr♦ ♦ t ♥r② s♦rs ♥ t ♥ t

❯ r ♦♥tr♦ ② tr ♦♥ ♦♥tr♦ s②st♠ ♣r♦ ② tr s♣♣rs ♥ t

♦♥tr♦ strtr ♣r♦♣♦s ♥ t♦♥ ♥♥♦t rt② ①♣r♠♥t② t

♥r② ♠♥♠♥t s②st♠ s♦tr rr s ♠♣♠♥t s♥ P

t♦♦① ♣r♦r♠♠ ♦♥tr♦r s s②st♠ ♥rts rr♥t rr♥s ♦r t ❯

♥ s rqr ② tr ♦♥tr♦ s②st♠s ♦♥tr♦ s♦tr strt♣ srt②

s ♠♣♠♥t ♥ t ♠♥ ♥ t♥ ♣♦ t♦ t P t

♠♥ ♦s r t s♠ t♥ s ♥ s♠t♦♥

①♣r♠♥t t♦♥ s ♣r♦r♠ ♥ t♦ st♣s rst② stt t♦♥

t♦t ♠♦♥ t ♥ s♦♥② r♥ t♦♥

tt t♦♥

tt t♦♥ ♣rs♥ts r② ♥trst♥ rtrsts t♦ t t t ①

♣r♠♥tt♦♥ s s② t♦ ♦♥tr♦ ♥ t♦ st♦♣ ♥② ♣r♦♠ ♦rs ♥ t ♦ ♣♦r

♦♥s♠♣t♦♥ ♥ s② ♠♣♦s ♥ ♦♥tr♦

①♣r♠♥t st♣

r rsst ♦ st ♣♦r rsst♦r s rt② ♦♥♥t t♦ t s

s strt ♥ r ♥♦♠♥ ♦ t ♦ s ❲❱ ♥ st♣s ♦

❲ r strts t ①♣r♠♥t st♣

①♣r♠♥t t♦♥

r s♠t♦♥s rsts r♥ ②

❱ s♣ P♦r strt♦♥ s ♦t ❯

ttrs P♦r strt♦♥ t

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r s♠t♦♥s rsts r♥ ②

❱ s♣ P♦r strt♦♥ s ♦t ❯

ttrs P♦r strt♦♥ t

①♣r♠♥t t♦♥

r tt t♦♥ s♠ t ①♣r♠♥t st♣ rt

tt t♦♥ ♣r♠trs

s ♣♦ ♥t♦ t P t♦♦① s♥ t ♣r♠trs ♥ ♥

s t ②♥♠ ♦♥tr♦ ♦ t ❯ s ♦♥ t s♣ s ♥♦t ♣♦ss t rr♥

♦r t ❯ ♦♥tr♦ s t♥ ♠♣♦s ② t s♦tr ttrs ♦♥tr♦

s ♥♦t ♦♥sr r t s ♠♣♦rt♥t t♦ t tt t ♦t s t♦ t t

r♥t ♦ strts ♦r ts rs♦♥ t rr♥ ♥ t ❯ s r② ♦ ♥

♥sr ♦♥t♦♥ ♥ r ♦♣rt♦♥ ♠st ♦♥sr

①♣r♠♥t stt t♦♥ ♣r♠trs

Pr♠tr rr♥s ❱

♠①♠ rr♥t ❬❪

♠♥♠ rr♥t ❬❪

♠①♠ rr♥t rt ♥ ❬s❪

❯ rr♥

❯ ♠①♠ stt♦r

❯ r ♠tt♦♥ trs♦

❯ ♠♥♠ stt♦r

❯ sr ♠tt♦♥ trs♦

❯ ♠①♠ rr♥t r sr ❬❪

❯ ♠①♠ rr♥t r sr ❬❪

tt t♦♥ rsts ♦

rst t♦♥ ♣r♦r♠ ♦♥sst ♥t♦ ♠♣♦s♥ r♥t rt♦♥s ♦ t r

♥ ♥②s♥ t ♦ ♣♦r strt♦♥ t♥ t r♥t s♦rs ♣r♥♣

♥trst ♦ ♣r♦r♠♥ ts tst s t t t♥ t t ♦ ♥ ♥ r♦♠ ③r♦ t♦ t

♥♦♠♥ ♠ str t♥ ♥ r♥ ♦♥t♦♥s

r ♣rs♥ts t rsts ♦ t rst t♦♥ ♦ rr♥ ♥rs♥ ♦r

rs♥ ♥ r st♣s r♦♠ ❬❲❪ t♦ ❬❲❪ r ♣rs♥ts t ♣♦r str

t♦♥ t♥ t r♥t s♦rs t rr♥t ♥ ♥ ❯ ♥ t s ♦t

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r ①♣r♠♥t rsts tt t♦♥ ♦ trt②

P♦r strt♦♥ s ♦t ❯ rr♥t rr♥t ❯

• ♣♦r rts t ❯ stt♦r ♥ s rt② ♦ rq♥s

• ①♠♠ ♥ ♠♥♠♠ ♠tt♦♥ s ♦ rr♥t r t s s t

♠①♠♠ ♦ t ❯ rr♥t

• ♦t♣t rr♥ts ♦ t s♦rs ♦♦ tr rr♥s

• ❯ s♣♣s t tr♥s♥t ♣♦r t♦ t ♦ ②♥♠s ♥ ♥s ♥r②

r♦r② ♥ ts s r♦♠ t

• ♣♦r ♦♥trt♦♥ s s t ♦t rt♦♥ ♦ t ttrs s ②

♠♥♠s ttrs r♥♦rs t ❯ ♥ rqr r♦♠ t♠ t♦

①♣r♠♥t t♦♥

❬s❪ ♦r r♦♠ t♦ ❬s❪ ♥ ♦ s ♣♣ ♥ t ❯ rr♥t rs

ts ♠①♠♠

tt t♦♥ rsts ❯ ♦

s♦♥ t♦♥ ♣r♦r♠ ♦♥sst ♥t♦ r②♥ t ♦♣rt♦♥ ♦ t ♦rr

♥ sr ♠ts ♥ t ❯ s ♥ ♥ t♦♥ ♥ r②♥ t ♦♣rt♦♥ ♦

t ❯ ♦♥tr♦ ② t s ♥ ♥ t♦♥

r strts t t♦♥ ♦ t ♣♦r rr♥ ②♥♠ ♠tt♦♥ ♦r

t ❯ ♦ t ts ♠tt♦♥ t♦ r♥t tsts r ♣r♦r♠

♦ rsst♦r ♣♦r s st t♦ r t♥ t ♠①♠ ♦t♣t ♣♦r

♦ t t♥ t ❯ ♣♦r rr♥ s ②s ♣♦st PUCS∗∗∗ ♥ qt♦♥

t ♥ ♦sr r♦♠ t♠ t♦ ❬s❪ tt t ❯ r♠♥s ♥

t ♣rtr♠♥ ♠ts sr ♣r♦tt♦♥ t♦♥ s ♦♥sq♥ t

ttrs sr s♣♣②♥ t r ♦♥s♦♠♠ ② t rsst♦r

♦ rsst♦r s st ♦ t s ♠♥② ♦♣rt ♥ ♦rr t♦ s♣♣②

♠①♠ ♣♦r t ♥ ♦sr r♦♠ t♠ t♦ ❬s❪ tt t ❯

r♠♥s ♥ t ♣rtr♠♥ ♠ts ♦rr ♣r♦tt♦♥ ttrs r ♥

ts ♦♣rt♦♥ ♦♥t♦♥s

r strts t t♦♥ ♦ t ❯ ♦♥tr♦ ②♥♠ rr♥

s t♠♣♦rr② ♠♦ t♦ st② ♦ t ❯ ♦♦s t rr♥ t s ♠♣♦rt♥t

t♦ t tt t s♣ ♦ t ❯ ♦♥tr♦r ♥ r② rst② rr♥ t

♦♣rt♥ ♦♥t♦♥s

• ❯ ♥ rt② st sr ♥ t rqst ♦ ♣♦r s ♦r

rt② st r ♥ t rqst ♦ ♣♦r s ♦

• t rqst ♦ ♣♦r s ♦ ♦r ♥ t sr s ♦♥② ♣♦ss ② r♥

t ttrs s ♦♣rt♦♥ s ♦r r② ♠t ② t ♠ts ♥

s ♦t ♠ts ♥ ♠♥♠ rr♥t ♠ts ♥ ttr② ♣♦r s s t

♦♣rt♦♥ ♠♦ strt ♥ r

• t ♦ ♣♦r s r t♥ t ♥♦♠♥ ♣♦r t r s ♦♥②

♣♦ss ② sr♥ t ttrs s ♦♣rt♦♥ s s♦ r② ♠t ② t

tt t♦♥ rsts ♦

tr t♦♥ ♦♥ssts ♥t♦ r②♥ t ♦♣rt♦♥ ♦ t ♠ts ♥ ♠①♠ rr♥t

rt ♥ ♦ t t♦♥ ♦♥ssts ♥t♦ ♣♣②♥ ♦ ♥ t

♣♦r s ♦ ♥ t ❯ rt② sr ♠♣♦ss ♠①♠ rt♦♥

♦ t rr♥ ♣♦r t♦ s♣♣② t ♣♦r ♥ t♦ rr t ❯

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r ①♣r♠♥t rsts tt t♦♥ ❯ ♦ strt②

❯ ❯ t

r s♦s tt ♥ t ♣♦r ♦ s ♣♣ t ♣♦r ♥rss t

♠①♠♠ rt ♥t t rs t ♠t ♥ ♠①♠ ♣♦r s ♥ ♥ qt♦♥s

♥

r ①♣r♠♥t rsts tt t♦♥ ♦ strt②

P♦r strt♦♥ rr♥t rr♥ rt♦♥ ③③② ♦ ♦♥tr♦r ♦t♣t

r♥ t♦♥

r♥ t♦♥ s ♣r♦r♠ ♦♥ r rt ♦t ♥ P t ♥tr♠♥

♦r r♥ t♦♥ ♦ t s ♣r♦r♠ t♦ ♥②s t ♦♣rt♦♥ ♥ t

♥r r♦r stt♦♥s s t ② ♦♥sr♥ ♥rt♥ts ♦

♥ t②♣ ③③② ♦ ①♣r♠♥t rsts r s♠r ♣♦r strt♦♥

stts♦r rt♦♥ t r② t t♦ ♦♠♣r ♦t② s s s ♥

r ①♣r♠♥tt♦♥ t s ♠♦st ♠♣♦ss t♦ r♣t ①t② t s♠ ♦♥t♦♥s ♥t

stts♦r s♣ ♣r♦ ♦r ts rs♦♥ ♦♥② t ♥rt♥t② rsts r

♣rs♥t

①♣r♠♥t t♦♥

r r♥ t♦♥ t P ♥tr♠♥

r♥ t♦♥ ♣r♠trs

s ♣♦ ♥t♦ t P t♦♦① s♥ t ♣r♠trs ♥ ♥

①♣r♠♥t t♦♥ ♣r♠trs

Pr♠tr rr♥s ❱

♠♥♠♠①♠ rr♥t ❬❪

♠①♠ rr♥t rt ♥ ❬s❪

❯ rr♥

❯ ♠①♠ stt♦r

❯ r ♠tt♦♥ trs♦

❯ ♠♥♠ stt♦r

❯ sr ♠tt♦♥ trs♦

❯ ♠①♠ rr♥t r sr ❬❪

❯ ♠①♠ rr♥t r sr ❬❪

ttrs ♠♥♠♠①♠ stt♦r

ttrs ♠①♠ rsr ♣♦r ❬❲❪

ttrs ♠♥♠♠①♠ ♦t ❬❱❪

ttrs rr♥ ♦t ❬❱❪

♦♠♥ ♦♣rt♦♥ ♦♥t♦♥s t ❯ ♥ ttrs rsts

rs ♥ ♣rs♥t ①♣r♠♥t rsts ② r stst♦r② ♥ ♥ r♠♥t

t t s♠t♦♥ rsts ♦ts ♦ t s ♥ ♥ t♦♥ r

r ♣rs♥ts t ♣♦r strt♦♥ t♥ t ♥r② s♦rs r

t♦♥② ♣rs♥ts t s♣ t ❯ ♥ ttr② ♥ t s ♦t

• ❱ s♣ t s ♠t t♦ ♦ s ♥ ♦rr t♦ ♠t t ♦ ♣♦r ❲♥

r s♣s r ♦♥sr t ❯ srs st ♥ t ♦t♣t s ♥♦t

♥♦ t♦ ♣r♦♣ t ♥ t ttrs r♦♣s st s t s ♦t

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r ①♣r♠♥t rsts r t♦♥

r♥ ttr ♣♦r ❯ ♣♦r ♣♦r

• r♥ P♦r ♠♦♥t ♦ r♥ ♥r② s ♦r t♥ ①♣t

s t r♥ rt s r② ♦♥str♥ ♥ tr♠s ♦ s♦♣ ♥ rs ♦r

♦r ♥ r♥ ♥ ♥t s♦♣s r t ♥r② s ①♣t t♦ r♦r

t rt s r② r ♥ t ♥r② s s t♦ s♣♣② t ♣♦r str♥

• ttr② ♣♦r ttr② ♦t♣t ♣♦r r♠♥s ♠♦st ♦♥st♥t ①♣t ♥

t ❯ r rt② sr ♥ t ttr② r♥♦rs t

• ❯tr♣t♦r s②st♠ ♣♦r ❯ s♣♣s ♠♦st ♦ t ②♥♠ ♣♦r

s♦tt♦♥s

• s②st♠ ♣♦r t s♣♣s t ♠♥ ♥r② ♥ ♦♥tr♦s t ❯

♥ ttrs ♦t♣t ♣♦r r♠♥s ♥t♦ tr♠♥ ♠ts

• ttr② ♦t t ttr② ♦t rs t t ttr② ♦t♣t ♣♦r t

st②s ♥ ss♥ ♠ts

• ttr② stt♦r ttr② ♦♥tr♦ s r ♦♥trt♦♥ ♦

❲ s ♦sr ♠♦st t t♠ s t s r t♥ t rr♥

• ❯tr♣t♦r stt♦r ❯ ♦♥tr♦ s r t ♦ s♣s

t ❯ s r ② t t s♣s t ❯ srs

①♣r♠♥t t♦♥

r ①♣r♠♥t rsts r t♦♥

♣ P♦r sr♥ s ♦t ❯ ttr②

r ♦♣rt♦♥ t♦t ❯

①♣r♠♥t rsts r ♣rs♥t ♥ r ♦ ♠t t ❯ t ♦t♣t

♦ ts ♠♥t s ♠♣♦s t♦ ③r♦ t♦♥② t s ♠♦ s ①♣♥ ♥

st♦♥ ♥ s♦♥ ♥ r ♥ ts r ♦♣rt♦♥ t ttrs s♣♣②

t ②♥♠ rs♣♦♥s ♥ t t ♦t♣t ♦t s ♥♦t st s ♥ t ♦♥rt♦♥

♥♥ t ❯ ttrs s ♥rtss ♦♥tr♦ ② t

r ♦♣rt♦♥ t♦t

♦ ♠t t t ♦t♣t ♦ ts ♠♥t s ♠♣♦s t♦ ③r♦ strt②

s ♠♦ s ①♣♥ ♥ st♦♥ ♥ s♦♥ ♥ r ①♣r♠♥t rsts

r ♣rs♥t ♥ r ♥ ts ♦♥rt♦♥ t ❯ s♣♣s t ②♥♠ rs♣♦♥s

♥ t ♦t♣t ♦t rt♦♥ s ♠ ♦r t♥ ♥ t r ♦♥rt♦♥ t♦t

❯ ts ♠♥t ♠♥♠ss t s ♦t rt♦♥ ttrs ♦♥tr♦s t ❯

♦r t ttrs ♥♥♦t ♦♥tr♦ ♥ t♥ ♣r♦rss rs ♥

t ttrs ♦t ♥ ♥♦t

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

r ①♣r♠♥t rsts r t♦♥ ❲t♦t t ❯

P♦r strt♦♥ s ♦t

r ①♣r♠♥t rsts r t♦♥ ❱ ❲t♦t t

P♦r strt♦♥ s ♦t

♣tr ♦♥s♦♥

♥♦ ♥r② ♠♥♠♥t strt② s ♣rs♥t ♥ ts ♣tr t s s

♦♥ t ♠ ♥r② s♦rs rtrsts t♦t ♥② ♣r♦s ♥♦ ♦ r♥

♦♥t♦♥s ♦♥② rt♠ ♥♦r♠t♦♥ s s ♣r♥♣ ♦♥trt♦♥ s t s ♦

t②♣ ③③② ♦ s②st♠s ♥ ♠♥ ①♣rts ♥ ♥r② ♠♥♠♥t ♦ ②r s♦rs

• s r s ♥♦ t s t rst ♥str ♣♣t♦♥ ♦ t②♣ ③③② ♦ ♥ r♥

♥ t rst ①♣r♠♥t t♦♥ ♦ ♥ ♥r② ♠♥♠♥t s②st♠ ♦♥ ②r

tr s♥ t②♣ ③③② ♦ ♥ s♥ ①♣r♥ ♦ ♠t♣

①♣rts

♣tr ♦♥s♦♥

• t s ♥ ♣♣t♦♥ ♦r ♠tr② ♣♣t♦♥ t t ♦ s ♥ ♣♣

t♦♥s t ♣r♠trs ♦ t ♥r② ♠♥♠♥t strt② ♣♥s ♦♥② ♦♥ t

rtrsts ♦ t s♦rs ♥ ♥♦t ♦♥ t

• ♥ ts t ♣r♦rt② s♦r s t ❯ s t s t ♠♦st ♣r♦r♠♥ s♦r ♥

tr♠s ♦ ♥② ♣♦r ♥ ②♥♠ rs♣♦♥s ♦r♦r t ♦♥s ♦ ♦♣rt♦♥

r ♥♦t ♠t s ss② ♥ t trtr t strt② ♦♥srs t s♣

t♦ ♥ ②♥♠ rr♥ ♦r t ❯

• strt② ♣r♠ts ♥ s② ♦♣rt♦♥ ♥ r ♠♦ s♥ ♦♥② ♦♥ s♦tr

♣♣t♦♥ t♦♥② t ③③② ♦ ♦♥tr♦r strtr s s tr t♦ ♥

♣♦r rr♥ s♠t♦♥ ♦r t♦ ♥ rr♥t rr♥ ①♣r♠♥tt♦♥

strtr ts ♦s ♥♦t ♥

♦t t s t♦ ♠♣r♦ t ♥r② ♠♥♠♥t strt② r ♥tr t ♦♥

♥♦r ♣rs♥t ♥ ts ssrtt♦♥ rtr rsr r ♥t

• ♦ r♥ t ②♥♠ rr♥s ♦ t stt♦r ♦ ❯ ♥ ttrs r

r♥ t r♦ s♦♣ ♥♦r t tr s♥ P ♥♦r♠t♦♥

• tst ♥ ♦♣rt♦♥ s r② ♦♥str♥ ♥ tr♠s ♦ ♦t rt♦♥

♦r♦r t ttrs s ♦♥ ts r rt② ♥♥t ♥

s♦ ♣rs♥ts rt② ♦ rt② ♦r ts rs♦♥s t s ♦ ttrs ♥

s ♠♥♠s ♦r r♥t ttrs r ♦♥sr s s t♠

♦r ♥s t ♦ ♥trst♥ t♦ r♥ t ttrs

• ❲♥ t ♥r② ♠♥♠♥t sr② s ♣rs♥t t♦ t ①♣rts ♥♦t t ♥

♦r♠t♦♥ ♦t t ♦♥str♥ts ♦♥♥tt② rs♦♥s ♥♦r t ♦ ♠♥

♠♥t strt② r ♣rs♥t ♥♦t ♦r ♣t♦♥ ♥ ♥♦t t

♦♥str♥ts r r② ♥t ♦r ①♣r♠♥t t♦♥ t ♦ ♥

trst♥ t♦ ♦♥t ♥ sr② ♣rs♥t♥ ♠♦r ♥♦r♠t♦♥ ♦t t

• ♥stt♦♥ ♦ ♣t ♥r② ♠♥♠♥t strt② t r♥ st② r♦

♥t♦♥

♥r② ♠♥♠♥t strt② s ♦♥ t②♣ ③③② ♦

♦♥s♦♥

s tss ♣rs♥ts rsr ♦r ♦♣ r♦♥ t♦ ①s ♥ tr ♥♥r♥

♥r② ♠♥♠♥t ♥ ②r tr s ♥ t②♣ ③③② ♦ ♦♥tr♦rs

s ♦r ts ♣rt ♦ t rsr ♦♣ ♥ ♦rt♦r② ♦t t

♠♦♥ ♥ ♦♥tr♦ ♦ ♠t♣②ss s②st♠s t s ♥tr ♦♥t♥t♦♥ ♦ ♣r

♦s rsr ♦♣ ♥ sts s s ♥rt r♦s♦♣ ♣rs♥tt♦♥

♠♦♥ ♥ ♦♥tr♦ ♦ tr s♦rs ♦r t②♣ ③③② ♦ ♦♥tr♦rs ♥ t s♠ ♣r

s♣t ts tss ♠s t♦ ♣rs♥t ♦♥trt♦♥ t♦ t rsr ♦♣ ♥

♦rt♦r② r♦♥ ♥r② ♠♥♠♥t ♥ ②r tr ❱s ❱ ♥ t②♣

③③② ♦ ♦♥tr♦

r

rsr ♣rs♥t ♥ ts tss s rs ♥ t r♠♦r ♦ t ♣r♦t

s ②r tr tt ♥ s s ♠♦ ♦rt♦r② r t

♥trst s t♦ ♦♣ ♥ t♦ t ♥ ♥r② ♠♥♠♥t s②st♠ ♦r ②r s♦r

♦♠♣♦s ② ♥ ♦ ttrs ♥ ❯tr♣t♦r ②st♠ ❯ ♥ ②st♠

♦r♠s♠ s st t♦ r♣rs♥t t ❱ ♥ t♦ ♥t② ts Prt

♦♥tr♦ trtr P ♠♦♥ ♥ t ♣r♠tr ♥tt♦♥ ♦ t ttrs

♥ t ♥ ♦♣ ♥ ♣r♦s rsr t ♦rt♦r② s

tss ♣r♦♣♦s ♥ ♣r♦r t♦ ♥t② t q♥t tr ♣r♠trs ♦ t ❯

s ♣r♦r s ①♣r♠♥t② t

s ♣r♦s ♥♦ ♦ t r♥ ②s s ♥♦t ♦♥sr ♦♥♥ t♥qs r

♥t s t ♠♦st ♣t t♦ ♣r♦r♠ t ♥r② ♠♥♠♥t ♥ ♣r♦♣♦s

♥r② ♥♠♥t trt② ♦♥② ♦♥srs rt♠ ♥♦r♠t♦♥ s s tr

♣♦r rr♥t ♦r ♦t t stt ♦ r ♦ t st♦r s♦rs ♦r t s♣ ♦ t

s ♦♣♥ ♦♥sr♥ t ♥ts ♥ rs ♦ ♦

t s♦rs ttrs r rt② ♦♥♥t t♦ t s ♥ t♥ tr ♣♦r s

♥rt② ♦♥tr♦ ② t ♥ ❯ ❯ s t ♠♦st ♥t s♦r ♥ t♥

s ♦♥sr s t ♣r♦rt② s♦r t♦ s♣♣② t ♣♦r ③③② ♦ ♦♥tr♦r s st

t♦ ♣r♦r♠ t ♦ ♥r② ♠♥♠♥t ♦ t

♦♥s♦♥

s ♥ ♣r♦s ♥♦ ♦ t r♥ ②s s ♥♦t ♦♥sr ♠♥ ①♣rts

s s t♦ s♥ t ③③② ♦ ♦♥tr♦r ♦♥tr♦ t ③③② ♦

s②st♠ s s♥ r♦♠ ♠♥ ①♣r♥ t ♣r♠ts s♥ ♠♥ ♥♦ t♦ ♥

t ③③② rs ♥ ♠♠rs♣ ♥t♦♥s ♦ t ③③② s②st♠ ♥r② ♠♥♠♥t

sr② s ♣r♦r♠ ♠♦♥ ①♣rts ♥ ♥r② ♠♥♠♥t ♦ ❱ ②♣ ③③② ♦

♦♥tr♦rs r rt♥ s t② ♦♥sr t ♥rt♥t② ♥ t ♥srs

♥ t t tt r♥t ①♣rts t♥s r♥t ♥ ♥ r♥t rs

t♦♦♦① s ♦♣ ♥ t t♦ ♠♣ ♥t♦ ♦♥tr♦ srs ♥tr t②♣

③③② ♦ ♦♥tr♦rs r ♦♥sr ♥ ts tss ♦♥tr♦ sr ♥ t r

♠♣♠♥t ♥ t ♠♥ ♥ ♦♠♣tr s♠t♦♥s r ♣r♦r♠ s♥ t

♥ t P ♦ t ♠t♦♥ rsts s♦♥ ♥ s t ♠♣♦s

rqr♠♥ts s s ♥tr♣rt s stst♦r② ♥♦ t♦ ♦♥t♥ t t ①♣r♠♥t

t♦♥

s♦♥r② ♣♣t♦♥ s ♦♥sr t♦ ①♣r♠♥t② t t ♦r

ts ♠♣♠♥tt♦♥ ♥ t r s s t♦ ♦♥tr♦ t ♦t ♥

♣♦r ♦♥rtr ♣r♥♣ ♠♦tt♦♥ t♦ ♣r♦r♠ ts ♥tr♠r② t♦♥

s ts rt② s② ♠♣♠♥tt♦♥ ♥ ♦♥♦♠ ①♣r♠♥t st♣ ♦r♦r t

t♦♥ ♦ ts s ♦♥ ♥r ♦♥tr♦ ♦♥t♦♥s ♥ ♦rt♦r②

s ♦♣ ♠♣♠♥t ♥ ①♣r♠♥t② t t stst♦r② rsts s

s♦♥r② t♦♥ ♦ s ♦♥sr t♦tr t t s♠t♦♥ rsts s

str♦♥ ♠♦tt♦♥ t♦ ♦♥t♥ t♦ t st st ♦ t ♣r♦t t ♠♣♠♥tt♦♥ ♦ t

♥ t ♥r② ♠♥♠♥t s②st♠

♥② ①♣r♠♥t t♦♥ ♦ t ♥r② ♠♥♠♥t s②st♠ s ♣r♦r♠ ♥ t

♠♦ ♦rt♦r② s ①♣t ♥ s♠t♦♥ ♦sr ♥ ♥r② ♠♥♠♥t

s②st♠ t ♦♥tr♦ ♦ts ①♣r♠♥t rsts t ♦t ♦♥tr♦r

♥ t ♥r② ♠♥♠♥t s②st♠ ♥ s♥ s str♦♥ ♥ tt r

♣t ♦r s ♥ tr ♥♥r♥ ♣♣t♦♥s ♦r s t rsr ♣rs♥t

♥ tss ♦s ♥♦t ♦♥sr ♦♣t♠st♦♥ ♦ t ③③② ♦♥tr♦rs t ♦s ♥♦t ♣rs♥t ♥♦

♥ t♦ r♠ tt r ttr ♣r♦r♠♥ t♥ rtss t♥s

t♦ t ♣r♦♣♦s sr② ♥ t s ♦ t②♣ t ♥♦ ♦ r♥t ①♣rts

♠♦♥ t ♦r ♥ s② ♥trt ♥t♦ ♦♥ s♥ ③③② ♦♥tr♦r

sr s♠♠r②

♣trs ♥tr♦s t rsr r♦♣ t ♦♥t①t ♥ ♠♦tt♦♥s ♦ t

♣r♦t ♥ t♦ ♣rs♥t t r♦♥ ♦ t tss ②r tr s ♥r②

♠♥♠♥t t♥qs ♥ t②♣ ③③② ♦

♣tr srs t r♥t s♦rs s ♥ t r♦♠ tr t

♦♣s tr ♣rt ♦♥tr♦ strtr P ② ♦♥sr♥ t t♥ ♥ ♦♥♦♠

♦♥s♦♥

♦♥str♥ts t s♦ ♥tr♦ t ♠♦♥ ♥ ♣r♠tr ♥tt♦♥ ♦ t s♦rs

♣tr ♥tr♦s t②♣ ③③② ♦ s②st♠s ♥ ♣rs♥t ♥ t t ♥

tr t②♣ ③③② ♦ s②st♠s rt♥ ♥ ts rsr s ♣tr ♣rs♥t t rst

①♣r♠♥t t♦♥ ♦ ♦♥tr♦ t ♦t♣t ♦t ♦♥tr♦ ♥ ♦♥rtr

♣tr ♣rs♥ts t s♥ ♠♣♠♥tt♦♥ ♥ t♦♥ ② s♠t♦♥ ♥ ①♣r

♠♥tt♦♥ ♦ t ♥r② ♠♥♠♥t s②st♠

♣♣♥① ♣rs♥ts t s♦tr ♦♣ t♦ ♠♣ ♥trt②♣ ③③② s②st♠s ♥t♦

♦♥tr♦ srs ♣♣♥① ♣rs♥ts t ♥r② ♠♥♠♥t sr② ♣r♦r♠ t♦ s♥

t ♠♣♠♥t ♥

♣trs ♥ ♣rs♥t t♦ ♣♣t♦♥s ♦ t②♣ ③③② ♦ ♥ tr ♥♥r♥

s ♣♣t♦♥s ♣rs♥t r② r♥t s♥r♦s t♦ t t②♣ ③③② ♦ ♦♥tr♦rs

♦t♣t ♦t ♣rs♥t ♥ ♣tr rqrs rt② s② t♦ ♠

♣♠♥t ♥ ♦♥♦♠ ①♣r♠♥t st♣ r t♦♥ s ♦♥ ♥r ♦♥tr♦

♦♥t♦♥s ♥ ♦rt♦r② ♦♥tr♦ ♦ t ♦♥rtr s ①s② ♣r♦r♠

② t s ♣♣t♦♥ s ♣t t♦ t r♥t ③③② ♦ s②st♠s

♥ ♥ s s t♦ st② ♦♣t♠st♦♥ s ♣rs♣t ♦ tr rsr

♥r② ♠♥♠♥t ♣♣t♦♥ ♣rs♥t ♦♥ ♣tr rqrs r② ♦♠♣①

♥ r② ①♣♥s ①♣r♠♥t st♣ t♦♥ ♦ ts ♣♣t♦♥ s ♦♥ ♥r r

str♥ ♥ ss ♦♥tr♦ ♦♥t♦♥s rr ♦♥t♦♥s rs♣♦♥s ♥♦t

♦♥② ♣♥s ♦♥ t t s♦ ♦♥ t ♦♥tr♦ s②st♠s ♦ t ♦tr s♦rs ♠♣

♠♥t ♥ t ①♣r♠♥t t♦♥ ♦ t s ♠ ♠♦r ♦♠♣t ♥

♦♣t♠st♦♥ s ♣r♦t ♦r t ♠♦♠♥t

sr ♦♥trt♦♥s

s ♦♥trt♦♥s ♦ ts tss st

♥ tr♣t♦r rt ♠♦ ♦r ②r tr s♠t♦♥ ♥ t ♣r♦

r t♦ ♥t② ts ♣r♠trs s ♣r♦♣♦s rt ♠♦ ♥ ♣r♠tr ♥tt♦♥

s ①♣r♠♥t② t ♥ ♦rt♦r② ♥ ♥ r ②r tr

s♦tr t♦ ♠♣♠♥t ♥tr t②♣ ③③② ♦ s②st♠s s ♣r♦♣♦s s s♦tr

s s ♦♥ ♦rts ♥ strtr ♣r♦r♠♠♥ ♥ ♦s ♥♦t rqr t s ♦ t

t ③③② ♦ ♦♦♦① s t s♦tr ♣r♦♣♦s ② ♦tr t♦rs

♥♦ ♥r② ♠♥♠♥t strt② s ♣rs♥t ♥ ts tss s

s ♦♥ t ♠ ♥r② s♦rs rtrsts t♦t ♥② ♣r♦s ♥♦ ♦

r♥ ♦♥t♦♥s t ♦♥srs t s♣ t♦ ♥ ②♥♠ rr♥ ♦r t ❯

strt② ♣r♠ts ♦♣rt♦♥ ♥ r ♠♦ r ♦ ♦♥ ♦ t s♦rs

♦♥s♦♥

♣r♥♣ ♦♥trt♦♥ s t s ♦ t②♣ ③③② ♦ s②st♠s ♥ ♠♥ ①♣rts ♥

♥r② ♠♥♠♥t ♥ ❱

rsr ♦♣ ♥ ts tss s ♥ ♣rs♥t ♥ ♥t♦♥ ❬♦❪

❬♦❪ ♥ ♥tr♥t♦♥ ♦♥r♥s ❬♦❪ ❬♦❪ ❬♦❪ ❬♦❪ ♥ s

♥t ♦r♥s t tr ♦♠♠tt ❬♦❪ ❬♦❪ ❬♦❪ ♥ ❬♦❪ s

♣rt ♦ rsr ♦♥trt ♥ r t♥ r♣♦rts ❬♦❪ ❬♦❪ ❬♦❪

♥ ❬♦❪

sr ♦t♦♦s

s ♣rs♣ts ♦ ts tss t ♥ ♥t

♥ t st ♦ ♥r② ♠♥♠♥t t ♦ ♥trst♥ t♦ r♥ t ②♥♠

rr♥s ♦ t stt♦r ♦ t ❯ ♥ t ttrs ② ♦♥sr♥ t r♦ s♦♣

♥♦r ♦rst♥ ♦ t tr s♥ P ♥♦r♠t♦♥ t s ♦♥sr t♦ tr

t ♣r♦♣♦s ♥ s t ♥ t r♥t ♦♥rt♦♥s ♦ t ❱ ♥♥

② s②st♠s ♦r ♥tr♥ ♦♠st♦♥ ♥♥s strts ♥ r ♦♥rt♦♥s

♠st ♠♣r♦ t ♦ s♦ ♥trst♥ t♦ ♦♥sr ♥r② ♠♥♠♥t ♦ ②r

s♦rs r t ♦ ♣r♦ ♥ ♣rt② ♥♦♥ ♥ ♥ s s ♥ stt♦♥r②

♣♣t♦♥s ♦r ♥ rr♦ tr♥s♣♦rt

♥ t ♦ t②♣ ③③② ♦ ♦♥tr♦ ♥♦♥♦♣t♠s ♥tr ♠♠rs♣ ♥

t♦♥s r rt♥ ♥ ts tss rtr rsr t ♦♥sr r♥t

t♦♣s s s t ♠♣♠♥tt♦♥ ♦ ♥r t②♣ t ♥♥ ♦ t ♥rt♥t②

♥ t ♦♣rt♦♥ ♥ ♥ t stt② ♦ t ♦♥tr♦ s②st♠s t ♥t♦♥ ♦ t ♣r♠trs

♦ t ♥② t s ♥trst♥ t♦ st② t ♦♣t♠st♦♥ ♦ t t②♣ ③③② ♦

♦♥tr♦rs

♦♥ér♥ ♥s rrs ♥ é♥ étrq st ♣♣r r ♥str ♥♥♦t♦♥Pr① ♦ ♥ rr ♥ r♥♦♠té r ♦ t Pr① ♦ ♣♥ ♦♠♣tt♦♥ ♦r

②♦♥ rsrrs ♦ t r♦♥ ♦ r♥♦♠té

♣♣♥①

♥tr t②♣ ③③② ♦ s②st♠

s♦tr ♠♣♠♥tt♦♥

s ♣♣♥① ♣rs♥ts t s♦tr t♦ ♠♣♠♥t ♥tr t②♣ ③③② ♦ s②st♠s

s s♦tr s s t♦ ♠♣ ♥tr t②♣ ③③② ♦ s②st♠s r♦♠ tr ♠♠rs♣

♥t♦♥s ♥ tr ③③② rs s ♣rs♥t ♥ ♣♣♥① ♣♣t♦♥ t

♣r♦r♠ s strtr ♥t♦ t ♦♦♥ s♣r♦r♠s t ♠♠rs♣ ♥t♦♥ ♥ t

③③② sts rt♦rs t ③③r t ♥r♥ ♥♥ t t②♣rr ♥ t ③③r

s♣r♦r♠ s ♣rs♥t ♥ ①♣♥ s♥ ①♠♣s

♦ tt t ♠♣♠♥tt♦♥ ♥ ♥② ♦♠♣tt♦♥ ♥ t s♣r♦r♠s r

♦♣ s♥ ♦rts ♥ strtr ♣r♦r♠♠♥ t ♦ s s♦ ♣rs♥t

♦♠♣♠♥tr② ♣♣r♦s t♦ ♠♣♠♥t t②♣ ③③② s②st♠s s♥ t ♥ ♦♥

♥ ❬♥❪ ❬st❪ ♦r ❬③❪

♠rs♣ ♥t♦♥s rt♦♥

rst s♣r♦r♠ s s t♦ rt tr♥r ♥ tr♣③♦ ♠♠rs♣ ♥t♦♥s

♦♠♥ ♦ t ③③② sts s x = [−1, 1]

♥t♦♥ ♦ t ♦♠♥ ♦r t ♥♦r♠s ③③② st srts ♥t♦ p ♣♦♥ts

❳♥s♣ p

♥t♦♥ t♦ rt ♥r ♠♠rs♣ ♥t♦♥s

♥t♦♥ ❬r♣③♦❪ r♣③♦❳

♦r ♥t❳

r♣③♦♠① ♠♥❬❳ ❳❪

♥

♦tr s rr t tt♣s♣s ♠♥s♦tr

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

③③② sts rt♦♥

s s♣r♦r♠ s s t♦ rt t ③③② sts ♦ t ③③② s②st♠ t rqrs t

♣r♦s ♥t♦♥ ♦ t ♣r♠trs ♥ t ♠♠rs♣ ♥t♦♥s

• ♥♣ts ♦ t s♣r♦r♠ r t ♦♠♥ ♦ t st x ♥ t ♣r♠trs tt

♥ t s

• ♦t♣t ♦ t s♣r♦r♠ s ③③② st ♦ 2 · n s ♦r ♥♣t r n

r♣rs♥ts t ♥♠r ♦ s ♣r ♥♣t ♥ t t♦r ♦s ♦♥sr♥ tt

♥tr t②♣ s ♥ ② ♦♥ ❯ ♥ ♦♥

③③② sts ♠♣♠♥tt♦♥ s♥ t

♦r ♥♣ts ♠r ♦ ♥♣ts

♦r s ♠r ♦ ♠♠rs♣ ♥t♦♥s ♦ ♥♣t

♦r ❯

r♣③♦❳

♥

♥

♥

♥tr♦ ♦ t②♣ ③③②

s s♣r♦r♠ ♦♠♣ts t ♥tr♦ ♦ ♥ ♥tr t②♣ ③③② srts ♥t♦ p

♥tr t②♣ s s strt ♦♥ r s s ♦♠♣t ② s♥ t r♥

♥ ♦rt♠ s t♦ ♦♠♣t t t ♣♦♥t ♦ t ♥tr♦ s s♦♥ ♥

r t ♦rt♠ t♦ ♦♠♣t t rt ♣♦♥t s s♦♥ ♥ r

♥tr♦ ♦♠♣tt♦♥ s♥ t

♥tr♦

♦r ♥♣ts

♦r

♦r ♣

①❳

❲❬❪ ❩❬①①❪

♥

♠ s r♥♥ ♦rt♠

♥tr♦❬②②r❪

♥

♥

③③r

t ♣♦♥t ♦ t ♥tr♦

①①

t♦r

①①

♥

♥♠

t♦rt♦r

♦r ♣

① > t♦r r rt♦r t♦ ♦♠♣t t rt ♣♦♥t

tt❲ r ❲ t♦ ♦♠♣t t rt ♣♦♥t

s

tt❲ r ❲ t♦ ♦♠♣t t rt ♣♦♥t

♥

♥♠♥♠①tt

♥♥tt

♥

t♦r♥♠♥r rt♦r t♦ ♦♠♣t t rt ♣♦♥t

t♦rt♦rr rt♦r ♥ rt♦r t♦ ♦♠♣t t rt ♣♦♥t

①①

♥

♥

②t♦rr ②r ♥ rt♦r t♦ ♦♠♣t t rt ♣♦♥t

♥tr♦ ①♠♣

r s♦s ♥ ①♠♣ ♦ t ♥tr♦ ♦ t②♣ s♥ ♥ srtst♦♥ ♦

p = 501 ♣♦♥ts

♣rs♥ts t rst ♦ t ♦r t ③③② ♠♠rs♣ ♥t♦♥s ♣rs♥t

♥ r ♥ r♥t srtst♦♥s r ♦♥sr

③③r

③③r ♦♥rts rs♣ ♥♣t ♥t♦ t②♣ ③③② sts s♠ ③③r s ♥

t②♣ ③③② s s s ♥ ♥tr t②♣ ③③② s ♦r ③③t♦♥ s ♣r♦r♠

t♦ t♠s ♦♥ ♦r t ❯ ♥ ♦♥ ♦r t

r s♦s t ♦rt ♦ t ③③r ♦s ♥ s② ♠♣♠♥tt♦♥ ♥

♥② ♦♠♣tr ♥

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

r ♦rt t♦ ♦♠♣t t rt ♣♦♥t ♦ t ♥tr♦

r t②♣ ♠♠rs♣ ♥t♦♥s ♥ ts ♥tr♦

♥tr♦s ♦ t ③③② s ♦r ∆P

p ❩ P P P

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

❬ ❪ ❬ ❪ ❬ ❪ ❬ ❪

♥r♥ ♥♥

③③r ♠♣♠♥tt♦♥ s♥ t

♦r ♥♣ts

♦r s

♠♥♣t

♠❯♥♣t

♥

♥

❲t t ♦♦♥ ♥t♦♥s

♥t♦♥ ❬❪ ①

♥tr♣❳①♥r ♥tr♣♦t♦♥

♥t♦♥ ❬❯❪ ❯①

♥tr♣❳①♥r ♥tr♣♦t♦♥

r ③③t♦♥ ♦rt

♥r♥ ♥♥

♥r♥ ♥♥ ♠♣s t②♣ ③③② sts ♥t♦ t②♣ ③③② sts s♠ ♥r♥

♥♥ s ♥ t②♣ ③③② ♦ s s ♦r ♥tr t②♣ ③③② ♦

r s♦s t ♦rt srs t ♥r♥ ♥♥ ♦ ♦♦♣s r

s ♦♥ ♦r ♥♣t t♦ rt t♦r ♦♥t♥♥ t r♥ r ♦r r

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

♥r♥ ♥♥ ♠♣♠♥tt♦♥ s♥ t

♦r s

♦r s

♠♠

♠♠

♥

♥

r ♥r♥♥♥ ♦rt

t♣t ♣r♦ss♦r

♦t♣t ♣r♦ss♦r ♦♠♥s t②♣ ③③② sts t♦ ♦t♥ t rs♣ ♦t♣t ♦ t ③③②

♦ s②st♠ t s t ♣r♥♣ r♥ t♥ ♥ s②st♠s ♦r

t ♦t♣t ♣r♦ss♦r ♦ s②st♠ ♥ s ♥ s②st♠s ♥♦t rs

t♣t ♣r♦ss♦r ♠♣♠♥tt♦♥ s♥ t

s

♦r s

♦r s

∼||∼

ss

❲s❬❪

❩s❬❨❨❪ ❨ ♦♥t♥s t s ♦ t ③③② rs s ♥

♥

♥

♥ ♠ s r♥♥ s♣r♦r♠

♥tr♦❬②②r❪♦t♣t② ②r ③③t♦♥

t♣t ♣r♦ss♦r

t ♣♦♥t ♦ t t②♣rt♦r

①①t♦r

①①

♥ ♥♠ t♦rt♦r

♦r r t ♦ srtst♦♥ p ♦ t ♥ ②♣ ♥tr♦

❩ > rt♦r r ❩ t♦ ♦♠♣t t rt ♣♦♥t

tt❲ r ❲ t♦ ♦♠♣t t rt ♣♦♥t

s

tt❲ r ❲ t♦ ♦♠♣t t rt ♣♦♥t

♥

♥♠♥♠❩tt r ❩ t♦ ♦♠♣t t rt ♣♦♥t

♥♥tt

♥

rt♦r♥♠♥

rt♦rrt♦r

①①

♥

♥

②rrt♦r

r ♦rt t♦ ♦♠♣t t t ♣♦♥t ♦ t t②♣r st

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

③③② ♦ ♦♥tr♦ s♦tr ♠♣♠♥tt♦♥

②♣ ③③② ♦ ③③t♦♥ s ♥♦♥ s t ♦t♥ ♥ t②♣ ③③② s②st♠s

♦♠♣tt♦♥ ♦st ♦ ts ss②st♠ s rt t t t② t♦ ♠♣♠♥t r

t♠ t②♣ ③③② ♦♥tr♦r r ♦♦s ♥♦t t♦ ♠♣♠♥t rt♠ ③③② ♦♥tr♦r

t t♦ ♦ ♦♥ ♠♣♣♥ ♦ t s②st♠ s s♦ ♣r♦♣♦s ② ❬tt❪

♦tr ♠♣♠♥tt♦♥ ❱t♦♥

♦ t t s♦tr ♠♣♠♥tt♦♥ t♦ r♥t t♦♥s r ♣r♦r♠

♥tr t②♣ ③③② ♦ s②st♠s ♣rs♥t ♥ ❬♥❪ ♥ ❬♥❪ ♣rs♥t

t ♣r♠trs ♦♠♣t② ♥ t ③③② ♦ s②st♠s s ③③② s②st♠

r ♠♣♠♥t ♥ ♦r ♣♣t♦♥ ♥♣t♦t♣t rsts ♦ ♦r ♣♣t♦♥

♠ts t♦s ♥ t ♣t♦♥s

③③② ♦ s②st♠s t ♥t ♠♠rs♣ ♥t♦♥s ♥ rs r rt ♥ t

t ③③② t♦♦♦① ♥ ♥ ♦r ♣♣t♦♥ ♦t ③③② ♦ s②st♠s r ♠♣♣

♥ t r♥ s ♦♠♣t s♠ rsts r ♦t♥ ♥ t t t♦♦♦①

♥ ♥ ♦r ♣♣t♦♥ s t♦♥ s♦ ts tt ♦r ♣♣t♦♥ ♥ s

tr t♦ rt t②♣ ♦r t②♣ ③③② ♦ s②st♠s ♦s② t ♥rt♥t② s

st t♦ ③r♦ t ♠t t♦♦♦① ♦♥② ♥ ♦r t t②♣ ③③② s②st♠s

t r♣ sr ♥trs ③③② ♦ ♦♥tr♦r

♣♣t♦♥s ♥ t s ♥ ♦♣ t♦ t♦♠t② ♠♣ ③③② ♦ ♦♥tr♦r

sr r♦♠ tr ③③② ♠♠rs♣ ♥t♦♥s ♥ rs ♣r♠trs t rsts ♦

t sr② s ♣rs♥t ♥ ♣♣♥①

♣♣t♦♥ rqrs

♥♠r ♦ ♣♦♥ts t♦ rt t s rs♦t♦♥

♥rt♥t② ♥ t s

♦t♣t ♠♣ srtst♦♥ ♦r r s③ ♥ s♠ r s③ ♠♣r♦s t rs♦t♦♥

♦ t ♠♣ t ♦ s ♣r♦♠s ♥ ♠♠♦r② ♦ t ♦♥tr♦r

t r♣ sr ♥trs ③③② ♦ ♦♥tr♦r

r ♣rs♥ts t r♣ sr ♥tr ♦♣ ♥ t t♦ ♠♣ t s

s ♥ t ♥r② ♠♥♠♥t s ♣tr ♥ ♣♣♥① ③③②

s②st♠s r ♠♣♣ ♦♥t♦ ♦♥tr♦ srs r r ♦ ♣♦♥ts s st t♦

♦♠♦♥s sr tt ♥ s② ♥ ② t P ♥ tr♠s ♦ ♠♠♦r②

s ♦♠♣♠♥tr② ①♠♣ ♦ t ♣♣t♦♥ r strts t r♥

t♥ t t②♣ ♥ t t②♣ s♥ r♦♠ t sr②

③③② ♦ ♦♥tr♦ s♦tr ♠♣♠♥tt♦♥

r t ♣♣t♦♥ t♦ ♦♠♣t t ③③② ♦ sr

r ②♣ t t②♣ ♠♠ ③③② ♠♣s ♥ tr r♥s rt

♥tr t②♣ ③③② ♦ s②st♠ s♦tr ♠♣♠♥tt♦♥

♣♣♥①

r②s ③③② ♦ s②st♠ ♦r

♥r② ♠♥♠♥t

s ♣♣♥① ♣rs♥ts t s♥ ♦ t t②♣ ③③② ♦ ♦♥tr♦r s ♥ ♣tr ❱

t②♣ ③③② ♦ ♦♥tr♦r s s t♦ ♣r♦r♠ t ♥r② ♠♥♠♥t ♥ t

②r tr ♦♥tr♦r s s t♦ ♥ rr♥ ♦r t ♣♦r r

② t s②st♠ s♥ ♦ t ③③② s②st♠ rs ♥ ♠♠rs♣ ♥t♦♥s

s ♦♥ s♥ t ♥♦♠♥♥ ♦r ♥♦ ♥♥r♥ t♥q ♣r♦♣♦s ②

♥ ❬♥❪ s t♥q s ♦♥ sr②s ♦s ①trt♥ ♥♦r♠t♦♥ r♦♠

①♣rts ♥ t ♦r♠ ♦ rs

♥r② ♠♥♠♥t sr②

♥ ♥r② ♠♥♠♥t sr② s ♦♥t ♠♦♥ ①♣rts ♥ ②r tr

s ♦r sr② s ♠♥② ♣r♦r♠ ♠♦♥ t ♣rt♣♥ts ♦ t

❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ♣t♠r ♥ r♥ ♣r

t♣♥ts ♦ ts sr② r t t t ❯♥rst② ♦ r♥♦♠t t r♥

t♦r ♦♥ ②r tr ❱s ❱ ♥ t r♥ ♥sttt ♦r r♥s♣♦rt

♥ t② sr ♥ r♥ t ♦♥t♦♥ ♦r t ♦♣♠♥t ♦

②r♦♥ ♥♦♦s ♥ ♣♥ t ❯♥rst② ♦ P♦rt♦ ♥ P♦rt t ❯♥rst② ♦

r♥ ♥ ♥ t P P♦t trö♥ r♦♣ ♥ r♥ t ❯♥rst② ♦ Pr♦r♥

♥ r♠♥② ♥ t ❯♥rst② ♦ r♦sèrs ♥ ♥ sr② s s♥ t

t ♥tr ♦r ♦♠♣tt♦♥ ♥t♥ t str ❯

♥r② ♠♥♠♥t sr② s♠♣

①♣rts r s t♦ ♥sr ③③② ♥r② ♠♥♠♥t sr② ♥ tr

st♦♥s st♦♥ ♣rs♥t ①♠♣s t♦ ①♣♥ ♦ t♦ ♥sr t qst♦♥♥r

rs ♥ ♣rs♥t s♠♣ ♦ t sr② s ♣rs♥t t♦ t ①♣rts

r②s ③③② ♦ s②st♠ ♦r ♥r② ♠♥♠♥t

HEV Fuzzy Energy Management Survey

My name is Javier Solano and I am a Ph.D. student at Femto Laboratory - University of Franche Comte in Belfort, France. My current research focuses on the use of human expert knowledge in energy management of Hybrid Electrical Vehicles (HEVs). This is a joint project between the Femto Laboratory and the Centre for Computational Intelligence at De Montfort University in Leicester, UK. As an expert in HEVs you have been selected to participate in this survey that aims to design a Fuzzy Logic System (FLS) for energy management in a HEV. All the information you provide will be treated confidentially and you will be notified of the results of this research as soon as possible. If you have any question or comment please feel free to contact me at: Email: jsolanom@univ-fcomte.fr Address: FC LAB Belfort, 90000 France Tel: +33 3 84 58 36 25

Section I. Contact details Name __________________________________________________________ Affiliation __________________________________________________________ Email __________________________________________________________

Section II. Expert knowledge

Section II aim to extract expert knowledge to design the energy management system for the HEV shown in Figure 1.

Figure 1. Energy configuration of the Vehicle

The objectives of the management strategy for this HEV are: In steady state the reference power is provided by the Fuel Cell System (FCS) In transitory the Supercapacitor System (SCS) reinforces the FCS The battery regulates the bus voltage and reinforces the SCS if required The SCS State of Charge(SOC) is maintained at optimal levels

r ❱ ③③② ♥r② ♥♠♥t r② P

♥r② ♠♥♠♥t sr②

A fuzzy controller is used to find the FCS output power. Figure 2 presents the fuzzy logic controller, and Table 1 explains its inputs and outputs.

Figure 2. Fuzzy logic controller

Definition Description

ΔP Pref is the reference power and

PFCS is the actual FCS power

ΔSOC SOCref is the reference value and

SOC is the actual value in the SCS

ΔPFCS ΔPFCS is an increment in PFCS

Table 1. FLS input–output description

Section II.1 Linguistic label localisation The purpose of this part of the survey is to locate linguistic labels to determine intervals. This information will be used to construct the fuzzy sets. The following example demonstrates how to complete this section. Example 1: Table 2 summarises the assigned values to four linguistic labels representing the speed of a vehicle with maximum speed of 150 (km/h). Obviously these values could be different for different people.

Speed (km/h) Start End

Zero to Very Slow 0 20

Slow 15 50

Medium 35 85

Fast 70 150

Table 2. Linguistic labels to describe speed It can be inferred from Table 2 that the person completing this table thinks that: A slow speed is between 15 and 50 (km/h) A speed of 40 (km/h) could be considered slow as well as medium

r ❱ ③③② ♥r② ♥♠♥t r② P

r②s ③③② ♦ s②st♠ ♦r ♥r② ♠♥♠♥t

Question 1. Power of the Fuel Cell System Please use your own experience, thoughts and preferences to complete Table 3 using percentage values of the FCS nominal power to represent ΔP as defined in Table 1.

ΔP Start End

Almost Zero 0 %

Low

Medium

High 100 % Table 3. Linguistic labels to describe ΔP

Question 2. State of Charge of the Supercapacitor System Please use your own experience, thoughts and preferences to complete Table 4 using percentage of the maximal SOC to represent ΔSOC in the SCS as defined in Table 1.

ΔSOC Start End

Almost Zero 0 %

Low

Medium

High 100 % Table 4. Linguistic labels to describe ΔSOC

Section II .2 Rules definition The FLS presented on Figure 3 and described in Table 1 takes the inputs and processes them to produce outputs using the fuzzy rules and the linguistic labels in Table 5. These rules are summarized in Table 6.

ΔP – ΔSOC

Linguistic Label Abbreviation

Negative High NH

Negative Medium NM

Negative Low NL

Zero Z

Positive Low PL

Positive Medium PM

Positive High PH

ΔPFCS

Linguistic Label Abbreviation

High Decrease in output power DH

Medium Decrease in output power DM

Low Decrease in output power DL

Hold the output power H

Low Increase in output power IL

Medium Increase in output power IM

High Increase in output power IH

Table 5. Linguistic labels to locate the speed

r ❱ ③③② ♥r② ♥♠♥t r② P

♥r② ♠♥♠♥t sr②

The following examples demonstrate how to complete this section. However, they are only examples. Please feel free to modify your answers. Example 2: If ΔP is NH and ΔSOC is NH then ΔPFCS is _____________? The FCS system supplies more power than required and the SCS are relatively overcharged. It is necessary to rapidly decrease the FCS output power: If ΔSOC is NH and ΔP is NH then ΔPFCS is DH Example 3: If ΔP is Z and ΔSOC is Z then ΔPFCS is _____________? The actual values meet the reference It is necessary to hold the output power in the FCS If ΔSOC is Z and ΔP is Z then ΔPfc is H Question 3. Fuzzy rules definition Please use your own experience, thoughts and preferences to complete Table 6 using the linguistic labels in Table 5. Please remember! A positive ΔSOC is less charge than required. A negative ΔP is more power than required.

ΔPFCS

ΔSOC ΔP NH NM NL Z PL PM PH

NH

NM

NL

Z

PL

PM

PH

Table 6. Fuzzy rules

This is the end of the survey. Thank you very much

r ❱ ③③② ♥r② ♥♠♥t r② P

r②s ③③② ♦ s②st♠ ♦r ♥r② ♠♥♠♥t

r② ♣r♦ss♥

♣r♦s rsts ♦ t sr② r s t♦ ♥ t ③③② sts t♦ ♥♣ts s♥

s ♣r ♥♣t ♥ t ♦rt②♥♥ rs ♦♥ ♣r r

s ♥ ♣rs♥t t ♣r♦ss rsts ♦r st♦♥s ♥ ♦ t sr②

♠♥ s ♥ st♥r t♦♥ ♦ t ♥srs s ♥♦r♠t♦♥ s s t♦ ♥

t ♣r♠trs rqr t♦ rt t ♠♠rs♣ ♥t♦♥s ♦r t ♥♣ts ♦ t ③③②

s②st♠ ♣rs♥ts t ♣r♦ss rsts ♦r st♦♥ ♦ t sr② s♠♠rss

t rs ♥ ② t ①♣rts s ♥♦r♠t♦♥ s s t♦ ♥ t ③③② rs

Pr♦ss sr② rsts ∆P ♥st s

♥ t t♦♥

♥ strt a ♥ b strt σa ♥ σb

❩r♦

♦

♠

Pr♦ss sr② rsts ∆SOC ♥st s

♥ t t♦♥

♥ strt a ♥ b strt σa ♥ σb

❩r♦

♦

♠

③③② sts s♥ ♠♠rs♣ ♥t♦♥s

s ♥r② ♦♥ ♥ trtr t s s ♥ st t♦ tr♥r ♦r t s

t ♠ t ♦ ❩r♦ ❩ P♦st ♦ P ♥ P♦st

♠ P ♥ tr♣③♦ ♦r t s t ♥ P♦st P

s r st t♦ s②♠♠tr r♦♥ ③r♦ ♥ s r

♦♠♣t② ♥ ② t P P ♥ P s rs♣t②

r♣③♦ ♠♠rs♣ ♥t♦♥s ♥t♦♥ P

s r ♥ s♥ t ♦♦♥ rt♦♥s ❬♥❪ ♥ t♦♥

• ♣♣r tr♣③♦s ❯ r ♥ ♦r t r♣♦♥ts

a− (1 + ρ)σa a− ρ σa b+ ρ σb ♥ b+ (1 + ρ)σb

• ♦r tr♣③♦s r ♥ ♦r t ♦♦♥ r♣♦♥ts

a− (1− ρ)σa a+ ρ σa (b− ρ σb ♥ b+ (1− ρ)σb

r② ♣r♦ss♥

rt♦♥ ♦ t②♣ s t ρ = 0.5 ♦r t ∆P P s ♣rs♥t s ①♠♣

rsts ♦ t sr② r s♠♠rs ♥

a = 0.565 b = 1 σa = 0.17 σb = 0

r♣♦♥ts ♦ t ♣♣r tr♥ r ♦t t

a− (1 + ρ)σa = 0.3099 a− ρ σa = 0.48 b+ ρ σb = 1 ♥ b+ (1 + ρ)σb = 1

r♣♦♥ts ♦ t ♦r tr♥ r ♦t t

a− (1− ρ)σa = 0.48 a+ ρ σa = 0.65 b− ρ σb = 1 ♥ b+ (1− ρ)σb = 1

s r♣rs♥t♥ ∆P P r s♦♥ ♥ r

s r♣rs♥t♥ ∆P strt ♥ r r ♦♥strt s♥ t

♥t s ♦ t r♣♦♥ts ♦ t ∆P P

r♥r ♠♠rs♣ ♥t♦♥s ♥t♦♥ ❩ P P

• ♣♣r tr♥s ❯ r ♥ ♦r t r♣♦♥ts

a− (1 + ρ)σa (a+ b)/2 ♥ b+ (1 + ρ)σb

• ♦r tr♥s r ♥ ♦r t r♣♦♥ts

a+ (1 + ρ)σa (a+ b)/2 ♥ b− (1 + ρ)σb

rt♦♥ ♦ t②♣ s t ρ = 0.5 ♦r t ∆P P s ♣rs♥t s ①♠♣

rsts ♦ t sr② r s♠♠rs ♥

a = 0.225 b = 0.63 σa = 0.092 σb = 0.137

r♣♦♥ts ♦ t ♣♣r tr♥ r ♦t t

a− (1 + ρ)σa = 0.0869 (a+ b)/2 = 0.4275 ♥ b+ (1 + ρ)σb = 0.8275

r♣♦♥ts ♦ t ♦r tr♥ r ♦t t

a− (1− ρ)σa = 0.1790 (a+ b)/2 = 0.4275 ♥ b+ (1− ρ)σb = 0.6958

s r♣rs♥t♥ ∆P P r s♦♥ ♥ r

s r♣rs♥t♥ ∆P strt ♥ r r ♦♥strt s♥ t

♥t s ♦ t r♣♦♥ts ♦ t ∆P P

♠rs♣ ♥t♦♥s sts

s tt r♣rs♥t ∆P r ♣rs♥t ♥ r s tt r♣rs♥ts ∆SOC

r s♦♥ ♥ r

♠rs♣ ♥t♦♥s ♥tr♦s

♥tr♦s ♦ t s ∆P r t s♥ t r♥♥ ♦rt♠ ②

r ss♦t t♦ t ∆PFCS ♦r t sr ♥ ♥ t ♣♦r s strt

♥ r

♦r♣②

s ♥ ♥ t sr② t ♥st s r rs ♠ rs

♦ rs ♦ ♦ ♥rs ♠ ♥rs ♥

♥rs

r ♥tr♦s ♦ t ♥tr t②♣ ③③② s r♣rs♥t♥ ∆P

③③② rs s♥

sr② s t ①♣rts t♦ ss♦t s t♦ r s s♠♠rs ♥

♦ ts s s ♥♦ ss♦t t ∆PFCS s ♣rs♥t ♦♥ r

s r♥t ①♣rts ♥ r♥t rs ♥ ❵r r s rt♥ r s

t♥ ss♦t t s t r ♦ t s ♥ ② t ①♣rts

③③② rs s♥ ①♠♣

♦ ①♣♥ ♦ t ♣r♦r ♦rs t rt♦♥ ♦ t ♦r t r s ①♣♥

❵ ∆P s ♥ ∆SOC s P t♥ ♦ s① ①♣rts ♣rrr ♠♠ rs tr

♦ rs ♥ ♦♥ ①♣rt ♣rrr t♦ ♦ t ♣♦r s s♠♠rs ♥

r ♥tr♦ s t

C5avg =

6[−0.4781,−0.4034] + 3[−0.2271,−0.1755] + [−0.0160, 0.0160]

10= [−0.3566,−0.2931]

s r♣rs♥ts t ③③② r s strt ♥ r

r ∆P s ♥ ∆SOC s P t♥ ∆PFCS s ❬ ❪

rs♠s t ♣r♠trs tt ♥ t s s t♦ r♣rs♥t t rs

③③② ♦ ♦♥tr♦ sr

③③② ♦ s②st♠ s ♦♠♣t② ♥ ② ts ♠♠rs♣ ♥t♦♥s ♥ ③③② rs

♥ ♥rt♥t② ♦ p s rt♥ s rst ♣♣r♦ r s♦s t ③③②

♦ sr r♣rs♥t♥ t ③③② ♦ ♦♥tr♦r s♥ r♦♠ t sr②

♦r♣②

❬❪ Pér ss èrs r♣♥ ♥ ♦♠

t♣②ss s♠t♦♥ ♦ P tr♦②sr ♥rt r♦s♦♣ ♣rs♥

tt♦♥ ♣♣r♦ ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r② ❱♦ ♦

♣♣ r ♥♥ ♦r❯ ♦♥t ②♠♣♦s♠ ♦♥ ②

r♦♥ ♥♦♦s

❬❪ ♦♥♣t♦♥ s②stè♠q ♥ ♦♦♠♦t ②r é♠♦strt♦♥ t

♥stt♦♥s ♥ é♥rtq ② é♦♣♣é ♣r P tss

♥sttt t♦♥ P♦②t♥q ♦♦s

❬❪ r ♦s②r♦ ♥ r ♥♥ ♦ ♦♥tr♦ strts ♦♥

ttr②s♣r♣t♦r ②r ♥r② st♦r s②st♠s ♦r trt♦♥ ♣♣t♦♥s

♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬❪ èr st♦♥ st♦ ♠①t é♥r ♣♦r é ②r é

trq P tss ❯♥rsté ♥s t ♥♦♦s

❬♠❪ ♠rs ♦♥ ♦♣♥ ♥ ♦♣♦♦ ♠ srs ♦rst♥

s♥ ③③② s②st♠ t♥ t s♠t ♥♥♥ ♥ ③③② ②st♠s

❯❩❩ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬♠❪ ♠ ♥ ③③ Prt rr♥ s♥ ♥rt♦r ♦r ②r

tr s ❱r ♥♦♦② r♥st♦♥s ♦♥ ❱♦ ♦

♣♣

❬s♥❪ s♥s♦ ♦ést♦♥ t s♠t♦♥ ♥ strtr♥rt♦r ♦♥t♦♥♥♥t

sr ♥ s t♥s♦♥ ♦♥t♥ ♠ts♦r ♣♦r ♣♣t♦♥ é♦♣tèr ♥s

rrs ♥ é♥ trq ❱♦ ♣♣ ♦rt

❬♣❪ ♣♥r② r♥ ♥ r ②♣ ③③② st ♥②ss ♥

♠♥♠♥t sr②s ♥ Pr♦ ❯❩❩ ♦♥ ♣♣

❬r❪ rt ♠ ♠♥ ss ♥ ♦♥ ③♥ ♦ ②r

♦♦♠♦t ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

♦r♣②

❬r❪ rt P♦t ss ♥ Pér ♥rt r♦s♦♣ ♣r

s♥tt♦♥ ♦ ②r ② P♦rtr♥ ♥ ❱ P♦r ♥ Pr♦♣s♦♥

♦♥r♥ ❱PP

❬❪ P ② P ❱ ♦③ ♥ P r♦♣♦♦s ♠ t♦ ♠rt ♣rt♦♥

s♥ t②♣ ③③② sts ♦r♥ ♦ ♥tr♥ ♥♦♦② ♥♠♥t

❱♦ ♦ ♣♣

❬❪ P ♥ r♥s♥ ②♣ ③③② ♦ s r♥ tr ♠♥

♠♥t ♥♥r♥ ♣♣t♦♥s ♦ rt ♥t♥ ❱♦ ♣

❬r❪ rt r♦ ♥ ♦rt ♣♣t♦♥ ♦ t②♣ ③③② ♦ ♦♥

tr♦r t♦ ♥ ♥t♦♥ ♠♦t♦r r t s♥ ♦♠♣ ♥rtr ♥

♦♥tr♦ ♥ tr ♥♥r♥ r r tr♦t♥ ❱♦

♦ ♣♣

❬r❪ rt ♦r ♥ ♠♥ ♦♥♥trt♥ ♣t ♦♥tr♦ ♦

P ❯s♥ ♥tr ②♣ ③③② ♦ ②st♠s ③③② ②st♠s

r♥st♦♥s ♦♥ ❱♦ ♦ ♣s ♦ ♣♣

❬rt❪ ❾ rt③ ♥ t♦s ♥♦ss t t②♣ ③③② s♦♥

trs ♦♠♣trs ♥ tt② ❱♦ ♣♣

❬❪ r ♥ ss PP ♦ P s ♦♥ r s♣♣② ♦♥tr♦ ♦

t ♠♦t♦♦♠♣rss♦r r♦♣ ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r② ❱♦

♦ ♣♣

❬♥♦❪ ♥♦ ♦♠♣s♦♥ ♥ ♥r ② ttrs ♦r s ♥

t♦♥♦♠♦s ❯♥rtr ❱s Pr♦♥s ♦ t ❲♦rs♦♣ ♦♥

♣♣

❬♥❪ ♥♠ ♦ést♦♥ t rtérst♦♥ ①♣ér♠♥t s♣r♦♥♥s

trs éés à s ♣♣t♦♥s tr♥s♣♦rts strs tss ❯♥rsté

❬♥❪ ♥♠ t ♥ rés ♦r ♥ é♦♣tèr sé sr ♣rés♥

tt♦♥ ♥rétq r♦s♦♣q ♥s rrs ♥ é♥ trq

❱♦ ♣♣ ♦rt

❬♥❪ ♥♠ rs Pér st♥ rt♦♥ ♥ ♦♣♥♥

♥rt ♠r♦s♦♣ r♣rs♥tt♦♥ ♦ ♥ tr ♥t♦r ♠ ♥

♦♣tr ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

❬r❪ P r♥ ♥ r ♦♠♣rs♦♥ ♦ ②♣ ♥ ②♣ ③③② ♦♥

tr♦rs ♥ ♠r♦r♦♦t ♦♥t①t ♥ ③③② ②st♠s ❯❩❩

♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

♦r♣②

❬♦❪ ♦♦♥ ♦ést♦♥ ♠t♣②sq s éé♠♥ts st♦ t ♦♥rs♦♥

é♥r ♣♦r s és étrqs ②rs ♣♣r♦ s②sté♠q ♣♦r

st♦♥ é♥r P tss ❯♥rsté r♥ ♦♠té

❬♦❪ ♦♦♥ ss ♦s②r♦ P♣ ♥ Pr ♠t♦♥ ♦ ♦

tr② ❱ ❲t ② ♥♥t rttr ❱r ♥♦♦②

r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬♦❪ ♦♦♥ ss ♦s②r♦ ♥ Pr r♦♠ ♦♥ t♦ ♦♥tr♦

♦ P ❯s♥ ♥rt r♦s♦♣ ♣rs♥tt♦♥ ♥str

tr♦♥s r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬♦❪ ♦♦♥ Pér P r ♦s②r♦ ♥ ss s

s②st♠ ♠♦ st ♦r tr♥s♣♦rtt♦♥ s♠t♦♥ ♣♣t♦♥s ♦r♥ ♦

♥ ♥ ♥♦♦② ❱♦ ♣

❬♦s❪ ♦s②r♦ ♦r♠s♠s r♣rés♥tt♦♥ t ♦♠♠♥ s s②stè♠s

étr♦♠é♥qs ♠t♠♥s ♠t♦♥rtssrs ❯♥rsté

♥s t ♥♦♦s ♣

❬♦s❪ ♦s②r♦ P r ♥ ❳ P♦r strts ♦r ♠①♠♠

♦♥tr♦ strtr ♦ ♥ ♥r② ♦♥rs♦♥ s②st♠ t s②♥r♦♥♦s ♠

♥ ♥ ♥r② ❱♦ ♦ ♣♣

❬♥❪ P ♥ r♥♥r ♥ ♥ Prs Prt♦♥s ♦♣t♠

♣♦r ♠♥♠♥t ♥ ttr② ♣♥ ②r ♦r♥ ♦

P♦r ♦rs ❱♦ ♣♣

❬st❪ st♥ rr♥ P♦ ♥ r♥ ♦♥strt♦♥ ♦

♥tr t②♣ ③③② ♠s t♦ r♣rs♥t ♠s ♥ r②s s s ♥

③③② ②st♠s ♦♥r♥ ❯❩❩ ♥tr♥t♦♥ ♣♣

❬♥❪ ♥ss♦ èr ♥ ♦t♥ ②r ♣♦r s♦r ♦r

s♠ tr ♥r ♥ P♦r ♥♥r♥ ❱♦ ♦

♣♣

❬♦❪ ♦ P ♥ r♦♥ ♣t ③③② ♦ ♦♥tr♦r ♦r

t ss♣♥s♦♥s t ♥tr t②♣ ③③② ♠♠rs♣ ♥t♦♥s ♥ ③③②

②st♠s ❯❩❩ ❲♦r ♦♥rss ♦♥ ♦♠♣tt♦♥ ♥

t♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬st❪ st♦ ♥ P ♥ ♥ ♣♣r♦ ♦r ♣♥t ♠♦♥t♦r♥ s♥ t②♣

③③② ♦ ♥ rt t♦r② ♥tr♥t♦♥ ♦r♥ ♦ ♥r ②st♠s

❱♦ ♦ ♣♣

♦r♣②

❬st❪ st♦ P ♥ ♥ str♦ ♦♠♣tt♦♥ ♥t♥ s♦tr ♦r

♥tr t②♣ ③③② ♦ ♦♠♣tr ♣♣t♦♥s ♥ ♥♥r♥ t♦♥

❱♦ ♣

❬①❪ ① ❲ ♥ ♥ ss ♥♥ ③③② ♥r② ♠♥

♠♥t ♦r ②r s②st♠s ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r②

❱♦ ♦ ♣♣

❬❪ ②♠③ rs♥ t ♥♥ ③③② s②st♠ ♠♦s t ♠

♣r♦ ③③② str♥ ♦rt♠ ③③② ②st♠s r♥st♦♥s ♦♥

❱♦ ♦ ♣♣

❬r❪ r♦♦ ②♥♠ ♠♦s ♦ ttrs P♦r ②st♠s

r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬r❪ r♦♦ ♦♥t♦ ♥ r♥s ♥r ♣♣r♦ t♦ ♥r②

♦♣t♠③t♦♥ ♦ ②r tr s ❱r ♥♦♦② r♥s

t♦♥s ♦♥ ❱♦ ♦ ♣♣

❬♥❪ ♥ stt ♦ t rt ♦ tr ②r ♥ s Pr♦

♥s ♦ t ❱♦ ♦ ♣♣

❬♣❪ P ♣♦ ♦ést♦♥ s②sté♠q ♣♦r ♦♥♣t♦♥ és é

trqs ♠ts♦rs ♣♣t♦♥ ① és éq♣és é♥értrs ♣♦t♦

♦tïqs ♦ s♣r♦♥♥strs P tss ♥sttt t♦♥ P♦②t

♥q ♦♦s

❬♥❪ ♥ ♦♠♠♦♥ ♥rt ♠r♦s♦♣ r♣rs♥tt♦♥ ♥ ♥ ♦♥tr♦

strtr ♦r r♥t ②r tr s P tss ❯♥rsté s

♥s t t♥♦♦s ❯♥rsté r♥♦♠té

❬♥❪ ♥♥ ♦ést♦♥ ♠r♦s♦♣q ♣s P t ♣♦r ét

r ♦♣ P tss ❯♥rsté r♥♦♠té ❯♥rsté

♥♦♦ ♦rt♦♥tr

❬r❪ r♥♦ ♥rt r♦s♦♣ ♣rs♥tt♦♥ ♦♥ ♥ ♦♥tr♦ ♦

♦ ♠♣rtr ②st♠ ② ②r♦r♦♥s P tss ❯♥rsté

r♥♦♠té

❬r❪ r♥♦ ♦q r ss ♥ Pér tt ♥ ②♥♠

♠♦♥ ♦ s ♣♦r s♣♣② ♥tr♥t♦♥ ♦r♥ ♦ ②

r♦♥ ♥r② ❱♦ ♦ ♣♣

❬r❪ ❲ rst♥ ♥ rs ♦ ♠t♦s ♦r t s♥ ♦ ♥r t②♣

③③② sts s ♦♥ rtrsts ♥ ♥st s sr②s ♥

❯ ♣♣

♦r♣②

❬♦♣❪ ♦♣♥ ②♣ ③③② ♦♥tr♦ ♦ ♠♦ ♦♦t ♥tr ♦r ♦♠♣t

t♦♥ ♥t♥ ♦♥t♦rt ❯♥rst② ❯ ❱♦ ♣

❬♦♣❪ ♦♣♥ ❲r ♥ ♦♥♦r ♥rs t②♣ ③③② ♦

s②st♠ ♠ ♦r ♥ ♥trt ♦♣♠♥t ♥r♦♥♠♥t ♥ ③③②

②st♠s ❯❩❩ ❲♦r ♦♥rss ♦♥ ♦♠♣tt♦♥ ♥

t♥ ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬♥❪ ♥♦t P ♦r Pr ♥ ss ♣rè ♣♦r ♣

à ♦♠st ♥ é♥♦♥ P ♥ ♥ts r♥

❬s♣❪ P s♣r③ rr P r r♥ ♦t

♥ t ♣r♣t♦rs s ♥ ttrs Pr♦ P

❱♦ ♣♣

❬❪ rs ♠ ♥♠ Pér ♥ st♥ r

tr③t♦♥ ♦r s♣r♣t♦r ♠♦♥ ♠tt t♦ r♥st♦♥s ♦♥

♥str tr♦♥s ❱♦ ① ♣ ①①

❬ ❪ s♦ s♦ ♥ ♣♣ r♥t ♥♦ss tr♦

t②♣ ③③② sts ♥ ③③② ②st♠s ❯❩❩ t ♥tr

♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬♦♣❪ ♦♣ ♦♥trt♦♥ st♦♥ é♥r ♥ é ②r sr P

tss ❯♥rsté r♥♦♠té

❬♦t❪ ♦t♦r rs ♦rts ♥ ❱ ♥ t②♣ ③③② s

s②st♠ ♦r ♥♥ t ♥rt♥ts ♥ r♦♣ s♦♥s ♦r r♥♥ ♦ ♣

♣♥ts t♥ ♠♥ rs♦rs s②st♠s ♥ ③③② ②st♠s ❯❩❩

❲♦r ♦♥rss ♦♥ ♦♠♣tt♦♥ ♥t♥ ♥

tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬♦s❪ ♦s ♥ r ①♠♥♥ t ♠♣t ♦ r♥ t② ♦♥ t Pr

tt② ♥ s♣♦♥s♥ss ♦ t rr ♦r ♥ ♠t♦r ♥

②ss ♥ ♥t♥t ❱s ②♠♣♦s♠ ❯♥rst② ♦ ♦r♥

♥ ♦ ❯ ♥ ♣♣

❬❪ s ♦♥♣t♦♥ ♥ ♠♦tr r♣ à ♠♥ts ♣r♠♥♥ts ♣♦r

♥tr♥♠♥t ♦♠♣rssrs ♣s ♦♠st P tss ❯♥rsté

r♥♦♠té ♦rt r♥

❬ ❪ ♦♠♥s ♥ ❱♦♥ ②♣ ③③② ♠①tr ♦ ss♥s

♠♦ ♣♣t♦♥ t♦ r♦♥ ♠♦♥ ♥s ♥ ❱s ♦♠♣t♥

❱♦ ♣♣

♦r♣②

❬ ❪ r ♦♥trt♦♥ ♦♥♣t♦♥ ♥ é♥értr ②r é♥r

étrq ♣♦r é ♠♦ést♦♥ s♠t♦♥♠♠♥s♦♥♠♠♥t P

tss ❯♥rst t♥♦♦ ♦rt♦♥tér

❬♠❪ ♠s ♣r♦ ♥ ②♥ ♣t ③③② ♦ ♦♥tr♦r ♦r

♦♥rtrs ①♣rt ②st♠s t ♣♣t♦♥s ❱♦ ♦ ♣♣

❬r♥❪ ❨ r♥ r♥ ♦r♥ ❯③♥♦ ♥ ❱r ③③② ♦

s s♣rs♦r② ♦♥tr♦r ♦r ♥ ❯ ②r r ♣♦r s②st♠

♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r② ❱♦ ♦ ♣♣

❬s♣❪ s♣♥t ♠♥♥ ♥ r♥r ♦♠♣rs♦♥ ♦ ♦ ♥❲

Pr♠♥♥t ♥t ♦t♦rs ♦r tr② ♣♣t♦♥s ♥ ❱ P♦r ♥

Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬❪ r③ ♥ ③③② ♣♣r♦①♠t♦♥ s♥ t②♣

③③② ♦ s②st♠s ♥ ts ♣♣t♦♥ t♦ ♠♦♥ ♣♦t♦♦t rr② ♥

♠r♥ ♦♥tr♦ ♦♥r♥ ♣♣

❬❪ ♦ P ♥ ❱ ♥ ❳ ♥r ♥t ♥ ♥ ♣r

♣t♦rs ♦r t ♥r② ♠♥♠♥t ♦ tr s ♦r♥ ♦ P♦r

♦rs ❱♦ ♦ ♣♣

❬③❪ ③ ❩r♥ ❩r♥ ♥ ③ ②st♠t ♠ ♣r♦ss♥ ♦r

♥♦s♥ r♥ t♠♦rs ②♣ ③③② ①♣rt s②st♠ ♣♣r♦ ♣♣

♦t ♦♠♣t♥ ❱♦ ♣

❬rr❪ rrr P♦♠♦ ♣③③ ♥ r♦ ♥r② ♠♥

♠♥t ③③② ♦ s♣rs♦r② ♦r tr ♣♦r s♣♣s s②st♠

r♥st♦♥s ♦♥ P♦r tr♦♥s ❱♦ ♦ ♣♣

❬❪ r♦ P♦s ♦r♥♦ r♦ ♥ ♦s t②♣ ③③②

♦♥tr♦r ♦r tr♥ ♠♦ ♦ts ♥ t ♦♥t①t ♦ r♦♦t s♦r ♠s

♥ ③③② ②st♠s ❯❩❩ t ♥tr♥t♦♥ ♦♥r♥

♦♥ ♣♣

❬s❪ P sr ❲t s ❲r ②♣ ③③② ts ♦r ♦r♣ ♥♦r♠t♦♥

♦♠♣tt♦♥ ♥t♥ ③♥ ❱♦ ♦ ♣♣

❬♦r❪ ❲ ♦rs ♦♠♦ r♥ ♥ tt ♥♦ ♦rt♠ ♦r

t ♥♦sts ♦ ♣♦r tr♥s♦r♠rs s♥ t②♣ ③③② ♦ s②st♠s ♥

r♥s♠ss♦♥ ♥ strt♦♥ ♦♥r♥ ♥ ①♣♦st♦♥ ①

P ♣♣

♦r♣②

❬♦❪ ♦ ❩ ♥ ♥ ♥r② ♠♥♠♥t strt② s ♦♥ ③③② ♦

♦r ②r s ♦r♥ ♦ P♦r ♦rs ❱♦ ♦ ♣♣

❬②❪ ② ss ♥③tt Pr ♥ t ♥rt r♦s♦♣

♣rs♥tt♦♥ ♦ ♦ ① ♦r tr♥ ♥♥ ♦♠♥ ② ♥

♥t ♣♦rtr♥s ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥

❱PP ♣♣

❬②❪ ② ss ♥③tt Pér ♥ t ♥rt r♦

s♦♣ ♣rs♥tt♦♥ ♦ s♦ ① ♦r tr♥ ♥♥

♦♠♥ ② ♥ ♥♠♥ts ♥ ♦♣♠♥ts ♦ s ♦♥

r♥ r♥♦

❬②❪ ② ♥③tt ss ♥ t ♣rés♥tt♦♥ ♥rétq

r♦s♦♣q ♥ ♠♦tr tr♥ ♥ ♥ ②rt♦♥ tr

♠q ♥ ♦♥rès ♥♥ ♦été r♥çs r♠q

Pr♣♥♥ r♥

❬t❪ t♥r ♥ ❲ ♦♠♥♥ ♥ ♣♦r ♦ ♦r♥t ♠♦♥ ♦ ②

♥♠ s②st♠s ss ♥ P♦r tr♦♥s ♥ ♣♣t♦♥s P

t r♦♣♥ ♦♥r♥ ♦♥ ♣♣

❬♥r❪ ♥rr♥♣rr ♠♥tt♦♥ ♥ r ♥ ♣ à ♦♠st ♦♥♣

t♦♥ s②stè♠ rtérst♦♥ ♠♦ést♦♥ strs tss ♦♥srt♦r

t♦♥ s rts t étrs ♥tr ré♦♥ r♥♦♠té

❬r♥❪ r♥♠♥ ♠♥ ss r② ♥ r♥ r

♠ ♠♦♥ ♦ ♥♦s s ♥ t♦♠♦t ♣♣t♦♥s ♥ ❱ P♦r

♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬r♥❪ r♥♠♥ ♠♥ r② ♥ ss ♠♣t② ♦ ♣♦r

s rs ♦r ②rtr ♦r tr ❱s ♥ ❱ P♦r ♥ Pr♦♣

s♦♥ ♦♥r♥ ❱PP ♣♣

❬❪ ♦s ♥ ② ♣♣t♦♥s s s♣r♦♥♥strs ♥qs

♥é♥r é♥ étrq ❱♦ ♦ ♣

❬♣t❪ ♣t ❯ Pr ♥ r ♦t ♦♠♣tt♦♥ ♦ tr♥ ♥t t♠♣rtr

♦ s tr♥ ♣♦r ♣♥t s♥ t②♣ ③③② ♦ s②st♠s ♥ ③③② ②st♠s

♦♥r♥ ❯❩❩ ♥tr♥t♦♥ ♣♣

❬r❪ rs rr t②♣ ③③② ♦ ♦♥tr♦ rttr ♦r

t♦♥♦♠♦s ♠♦ r♦♦ts ③③② ②st♠s r♥st♦♥s ♦♥ ❱♦ ♦

♣♣

♦r♣②

❬❪ ♠r ♥ ♠s ③③② ♥r② ♠♥♠♥t strt② ♦r srs

②r tr t ♣rt ♦♥tr♦ ♥ rt② ①t♥s♦♥ ♦ t

ttr② ♥ tr ♥ ②r ❱s ❱ ♦♥r♥

♦♥ ♣♣

❬❪ r r P♦r♦ r② sérs ❳P ①♣♦tt♦♥ rr②

❬②❪ ②♥ r ♥t♦rs ♦♠♣r♥s ♦♥t♦♥ Pr♥t P

❯♣♣r r ❯

❬❪ r♠♥ tt♦r ♦♥ r♥♥ t ②s♥ ♥t♦rs ♥♥♦t♦♥s

♥ ②s♥ t♦rs ❱♦ ♣♣

❬r♥❪ r♥♥③ ♥♦st ♥ ♣ à ♦♠st t②♣ P P tss

❯♥rsté ♥♦♦ ♦rt ♦♥tr

❬ss❪ ss ♥ss♦ ♥ r ③③②str♥ rt② ♥♦ss ♦

♣♦②♠r tr♦②t s t t♦ tr♥s♣♦rtt♦♥ ♣♣t♦♥s ❱

r ♥♦♦② r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬ss❪ ss P ♦s②r♦ ♥ r♥♦ ♣rés♥tt♦♥ é♥ré

tq ♠r♦s♦♣q ♥ ♣ à ♦♠st ♥tr♥t♦♥ é♥

étrq ❱♦ ♦ ♣♣

❬ss❪ ss ♦♥trt♦♥ à ♦♠♠♥ s♣♦sts étr♦t♥qs ♣r

♦q ♦ Pr♦érs ré sr st ♣r ♣♥s ①♣ér♥s t ♠ét♦♦♦

♣♣t♦♥ à ♥ r é♦tr t à ♥ ♠♥ s②♥r♦♥

P tss ♥sttt t♦♥ P♦②t♥q ♦♦s ♦rr

❬♦♠❪ ♦♠ ♦♥ ♥ ♦♣t♠st♦♥ ♦ ♣r♠♥♥t ♠♥t ♠♥ ♥

② P tss ♥s ❯♥rstt t

❬♦♠❪ ♦♠r ❨ ♥ ♥ t ❱rt♦♥ ♦♥tr♦ ♦ ♣t strtrs s♥

P❩ tt♦rs ♥ t②♣ ③③② ♦ ♥ ♠r♥ ♦♥tr♦ ♦♥r♥

Pr♦♥s ♦ t ♣♣

❬r❪ r♥ ♥ ❨ t②♣ ③③② t♠ srs ♠♦ ♦r st♦ ♥①

♦rst♥ P②s ttst ♥s ♥ ts ♣♣t♦♥s ❱♦

♣♣

❬♥❪ ♥ ♥ ❯♥rt♥ ③③② str♥ ♥tr t②♣ ③③②

♣♣r♦ t♦ ♠♥s ③③② ②st♠s r♥st♦♥s ♦♥ ❱♦ ♦

♣♣

♦r♣②

❬♥♥♦❪ P ♥♥♦♥t ♦♥ t♦♥ ♥ ♥② ②♣ ③③② r♣rs♥tt♦♥s

♦ ♥ s♥s t♦ ♣rt ♣♠♦♥r② ♠♦ ♥ ❲♦r ♦♥rss ♥ t

P ♥tr♥t♦♥ ♦♥r♥ ♦♥t t ♣♣

❬♥♥♦❪ P ♥♥♦♥t ♥ ♦♥ ②♣ ③③② ♥♦ss ♥ ③③② ②st♠s

❯❩❩ Pr♦♥s ♦ t ♥tr♥t♦♥ ♦♥r♥ ♦♥

♣♣

❬♦♦s❪ ♦♦ss ♦♥trt♦♥s trt♠♥t s ♥rtts ♥ ♠♦ést♦♥

♥♠érq é♠♦r ❯♥rsté ♦♦s ❱♦ ♣

❬❪ r③ t③♠♦ ♥ ②♣ ♥ t②♣

③③② ♠♦♥ ♦ s♦r rt♦♥ ♦r P❱ ♣♦r ♥rt♦♥ ♥ ♦rt

♠r♥ P♦r ②♠♣♦s♠ P ♣♣ s♣t

❬♠❪ ♠ë ♦ést♦♥ ♥ ♣ à ♦♠st t②♣ P ♣r rés① ♥

r♦♥s P tss ❯♥rsté r♥♦♠té t ❯♥rsté ♥♦♦

♦rt♦♥tr ♥ ♦rr

❬♦♥❪ ♦♥ ♥stt ❱ ♥ ♠♥ ♥ ♦♥ s♥♥ ♦

t②♣ ③③② ♦ tr ♦r ♠♣r♦♥ ♣rsr♥ rst♦rt♦♥ ♦ ♥tr

t♦♣r♦rss ♦♥rs♦♥ ♥♦r♠t♦♥ ♥s ❱♦ ♦ ♣♣

❬❪ r② r ♦t ss ♦ ❱ r ♥ ♦t

s②st♠ ♥trt♦♥ ♦♥ ②t② ♥ ♦♣♠♥t ♦

♦♥tr♦ strt② t r t♠ s♠t♦♥ ♥ ❱ P♦r ♥ Pr♦♣s♦♥

♦♥r♥ ❱PP ♣♣

❬♦❪ ♦♥♥ss♦♥ s♦r ♥ rt ssss♥ t ♣♦t♥t ♦ ♣r

t ♦♥tr♦ ♦r ②r ♣♦rtr♥s s♥ st♦st ②♥♠ ♣r♦r♠

♠♥ ♥t♥t r♥s♣♦rtt♦♥ ②st♠s r♥st♦♥s ♦♥ ❱♦ ♦

♣♣

❬♦♥❪ ♦♥ ♥ ②♣ ③③② sts ♦r ♠♦♥ ♥rs♥ ♥tt♦♥ ♥

❲♦r ♦♥rss ♥ t P ♥tr♥t♦♥ ♦♥r♥ ♦♥t

t ♣♣

❬♦♥❪ ♦♥ ♥ ♦♣♥ ②♣ ③③② ♦ st♦r

♦♠♣tt♦♥ ♥t♥ ③♥ ❱♦ ♦ ♣♣

❬♦♥❪ ♦♥ P ♥♥♦♥t ♥ r♥s ②♣ ③③② sts ♥ ♥r♦③③② s

tr♥ ♦ r♦r♣ t ♠s ♥ ③③② ②st♠s Pr♦♥s

❲♦r ♦♥rss ♦♥ ♦♠♣tt♦♥ ♥t♥ ♥tr♥t♦♥

♦♥r♥ ♦♥ ♣♣

♦r♣②

❬r♥❪ r♥ ♥ ♥ ♥tr♦ ♦ t②♣ ③③② st ♥♦r♠t♦♥ ♥s

❱♦ ♦ ♣♣

❬r♥❪ r♥ ♥ ♥ ♥tr♦t♦♥ t♦ t②♣ ③③② ♦ s②st♠s ♥

③③② ②st♠s Pr♦♥s ❲♦r ♦♥rss ♦♥ ♦♠♣tt♦♥ ♥

t♥ ♣♣ ♦ ♠②

❬r♥❪ r♥ ♥ ♥ ♣♣t♦♥s ♦ t②♣ ③③② ♦ s②st♠s ♥

♥ t ♥rt♥t② ss♦t t sr②s ♥ ③③② ②st♠s ♦♥r♥

Pr♦♥s ❯❩❩ ♥tr♥t♦♥ ♣♣

❬r❪ r ♥ ❲s♦♥ rst t♦♥ t♥ t②♣ ③③② ♦ r♠

♦r ♥ ③③② ②st♠s Pr♦♥s ♥tr♥t♦♥ ♦♥r

♥ ♦♥ ♣♣

❬②❪ ②♥ ❨ ♥③ rs ②♥ ♥ ② r♦ ②st♠

♦♥tr♦ t ♠r②♥ ♥ ♦♥♥r ♦ ♦♥t♦♥s ❯s♥ ②♣

③③② r ②st♠ ♣♣ ♦t ♦♠♣t♥ ❱♦ ♦ ♣s ♣

❬r♠❪ r♠♥ ♣rt r ♥ rr Prt ♥r② ♠♥

♠♥t ♦ ②r ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥

❱PP ♣♣

❬r❪ r ♥ ❨♥ ③③② sts ♥ ③③② ♦ t♦r② ♥ ♣♣t♦♥s Pr♥

t P ❯♣♣r r ❯

❬♦❪ ♦r r ♥ r③♦ ♥stt♦♥ ♦ ♦♥tr♦ strts ♦r

②r ♥r② st♦r s②st♠s ♥ ②r tr s ♥ ❱ P♦r

♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬❪ ② ♦st♦♥ ♥ P ♦♠st ②♣ P ♥tr♥t s

P♥♦♠♥s ❱ss♠♥t P tss ❯♥rsté r♥ ♦♠té

❬r♠❪ r♠♥ ♦r② ♥ trr② tr t♥♦♦② ①♣♥

❲② ♥♥ rr②

❬❪ ❲♥ ♥ rs t②♣ ③③② ♦♥t♦♦② ♥ ts ♣♣t♦♥

t♦ ♣rs♦♥ tt r♦♠♠♥t♦♥ ③③② ②st♠s r♥st♦♥s

♦♥ ❱♦ ♦ ♣♣

❬♦♥❪ ♦♥ ♥ ❱ r♥ t♥♥ t ♦♠♣tt② t♥ s♥s ❯s♥

♦t ♦♠♣t♥ ♥♦r♠t♦♥ Pr♦ss♥ ♥ ♥♠♥t ♦ ❯♥rt♥t② ♥

♥♦s ②st♠s ♣♣t♦♥s ❱♦ ♣♣

♦r♣②

❬♦♠❪ ❲ ♦♠♠ st♦♥ é♥r és étrqs ②rs sé sr

r♣rés♥tt♦♥ é♥rétq ♠r♦s♦♣q P tss ❯♥rsté s ♥s

t ♥♦♦s

❬♦♠❪ ❲ ♦♠♠ r P r ♥♥rt ♦s②r♦ ♥ ♥

t s ♠♦♥ ♦ tr♥s♠ss♦♥ t t ♥ ②r tr

s ❱r ♥♦♦② r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬❪ ❲ ♥ ♥ ②♣ ③③② ♦ ♣♣r♦ ♦r s♦rttr♠ tr

♦rst♥ Pr♦ ♥t r♥s♣ ②st ❱♦ ♦ ♣♣

❬❪ ❲ ❳ ❩ ❲♥ ♥ ❨ ❳ ②♥♠ ♥r② ♠♥♠♥t ♦r ②r

tr s ♦♥ ♣♣r♦①♠t ②♥♠ ♣r♦r♠♠♥ ♥ ♥t♥t

♦♥tr♦ ♥ t♦♠t♦♥ ❲ t ❲♦r ♦♥rss ♦♥ ♣♣

❬❪ ♥ ♣t♠ ③③② ♣♦r ♦♥tr♦ ♥ ♠♥♠♥t ♦

ttr② ②r s ♦r♥ ♦ P♦r ♦rs ❱♦ ♦ ♣♣

❬❪ ❳ ❳ ❳ ♥ ♥ ②♥ P♦r ♠♥♠♥t

strt② ♦r r♣♣ ②r ttr② ♣♦r s②st♠ ♦r♥

♦ P♦r ♦rs ❱♦ ♦ ♣♣

❬♥❪ ♥ r♥ ♥ ♥ ♦♥♥t♦♥ ♠ss♦♥ ♦♥tr♦ ♥

♥t♦rs s♥ sr②s t②♣ ③③② ♦ s②st♠s ②st♠s ♥ ♥

②r♥ts Prt ♣♣t♦♥s ♥ s r♥st♦♥s ♦♥ ❱♦

♦ ♣♣

❬♠❪ ♠ ó ③③② ♦ t♣♦ ♠ st♦ s♦ ♣♦ ♦ ♦♥tr♦

trá♦ ér♦ strs tss ❯♥rs r rs

❬♥❪ ♥ P♥ r③③ ♥ ♥ P♦r ♠♥♠♥t strt② ♦r

♣r ②r tr tr ♦♥tr♦ ②st♠s ♥♦♦② r♥st♦♥s

♦♥ ❱♦ ♦ ♣♣

❬♥❪ P ♥ s ♥ ②♣ ③③② ♦ ♦♥tr♦r s♥ ♦r

♦♥rtrs ♥ ③③② ②st♠s ❯❩❩ t ♥tr♥t♦♥

♦♥r♥ ♦♥ ♣♣

❬♥❪ ♥ ♥ ❲ ♦ ♦ ♦ ❨ ♥ ♥ ♥ r

♥ t② sst♦♥ ② ♥②③♥ s♣♦♥ss t♦ ❯♥①♣t st

♦♥ ss ♥ ②st♠s ♥ ♥ ②r♥ts ♥

tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

♦r♣②

❬♦❪ ♦♦ ♦s ❨ ♥ s♣♥t ♥ s ③♥ ♥

①♣r♠♥t rtr③t♦♥ ♦ tr♣t♦rs ♦r s♠ r♥ ②r tr

♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

♣♣

❬②♥❪ ②♥ rs ♥ ❱ ♥ ♠ t②♣ ♦r rt♠

s♣ ♦♥tr♦ ♦ ♠r♥ ♥ trt♦♥ s ♥♥s ♥ ③③② ②st♠s

❯❩❩ t ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬②♥❪ ②♥ rs ♥ ❱ ♥ ❯s♥ ♥rt♥t② ♦♥s ♥ t

s♥ ♦ ♥ ♠ rt♠ t②♣ ♥r♦③③② s♣ ♦♥tr♦r ♦r ♠r♥

s ♥♥s ♥ ③③② ②st♠s ♥tr♥t♦♥ ♦♥r♥ ♦♥

♣♣

❬❪ tt♦ ♥ ❱♥ r♦ tr ♥ tr ②r t♥♦♦②

sr② ♥ tr ②r ♥ ❱s ♦

♠♥r ♣♣

❬❪ s ♠♥ ♥ s♣♥t ♣t♠ s♥ ♦ sr

♠♦♥t ♣r♠♥♥t ♠♥t ♥ ♠♦t♦r ♦r ♥ r♥ ②r ♥

❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬❪ r♥r P ♦t s ♠♥ ♥ s♣♥t ♦♥

srt♦♥ ♦ r ♠♥t ♦rs ♥ rsss ♠♦t♦rs ♥ tr

♥s ♥ ②st♠s ♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬r❪ r♦♣♦♦s ♥ tr ③③② ♦ s♣t s♦♥ s♣♣♦rt s②st♠ ♦r

r♥ tr ♠♥♠♥t ♦r♥ ♦ tr rs♦rs ♣♥♥♥ ♥ ♠♥

♠♥t ❱♦ ♣

❬♠❪ ♠♥ t ♣♣t♦♥ ♦ ③③② ♦rt♠s ♦r ♦♥tr♦ ♦ s♠♣ ②

♥♠ ♣♥t Pr♦ ❱♦ ♦ ♣♣

❬rt❪ rt♥③ ♥ ② tr♥tr ♥rt à srr éé ♣♦r é

étrq ♦♠t ❱♦ ♦ ♣♣

❬rt❪ rtí♥③ st♦ ♥ r ♣t♠③t♦♥ ♦ ♥tr t②♣

③③② ♦ ♦♥tr♦rs ♦r ♣rtr t♦♥♦♠♦s ♠♦ r♦♦t s♥

♥t ♦rt♠s ♥♦r♠t♦♥ ♥s ❱♦ ♦ ♣♣

♣ t♦♥ ♦♥ rr ③③② ts

❬tt❪ P tt ♦sstt♦ ♣③③ ♥ P ♥t ♥r♣r♣♦s ③③②

♦♥tr♦r ♦r ♦♥rtrs P♦r tr♦♥s r♥st♦♥s ♦♥

❱♦ ♦ ♣♣

♦r♣②

❬❪ ♦② ♥s s②♥r♦♥s à ♠♥ts ♣r♠♥♥ts ♠♥tés ♣r ♦♥

trs t♥s♦♥ ♦ést♦♥ ♦♠♠♥ t s♠♥tt♦♥ ♣ss♥

P tss ♥sttt t♦♥ P♦②t♥q ♦rr♥

❬❪ r♦ ♥ P♥②s ♠♣♠♥t♥ ♥tr ②♣ ③③② Pr♦

ss♦rs ❬♦♣♠♥t ♦♦s❪ ♦♠♣tt♦♥ ♥t♥ ③♥

❱♦ ♦ ♣♣

❬❪ P ♥ ♥ st♦ ♥ ♥t♥t ②r ♣♣r♦ ♦r ♥str qt②

♦♥tr♦ ♦♠♥♥ ♥r ♥t♦rs ③③② ♦ ♥ rt t♦r② ♥♦r♠t♦♥

♥s ❱♦ ♦ ♣♣

❬♥❪ ♥ ❯♥rt♥ rs ③③② ♦ s②st♠s ♥tr♦t♦♥ ♥ ♥

rt♦♥s Pr♥t ❯♣♣r r

❬♥❪ ♥♦③ P í♥ ♥ st♦ ♥tr t②♣ ③③② ♦ ♥ ♠♦r

♥r ♥t♦rs ♦r r♦♥t♦♥ ♣♣t♦♥s ♣♣ ♦t ♦♠♣t♥

❱♦ ♦ ♣♣

❬♥❪ é♥③ ③♠ ♦s r♦Pér③ ♠ír③r

♥ ó♣③ ♣♣t♦♥ ♦ ♥tr ②♣ ③③② ♦ ②st♠s ♦r ♦♥

tr♦ ♦ t ♦♥ ♥tr② ♠♣rtr ♥ ♦t tr♣ ②r rt

♥t♥ ②st♠s ❱♦ ♣♣

❬❪ r ♥ ♦♥ ♥ ♥tr t②♣ ③③② ♠t♣ ♦♥ s♣♣② ♥

♠♦ ♥♦s ②st♠s ❱♦ ♦ ♣♣

❬♦❪ ♦t r ♦t ss ♦ ♦t ♥ ♠t

s②st♠ ♥trt♦♥ ♥t♦ ②t② ②r ♣r♠♥r② ①

♣r♠♥t rsts ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

♣♣

❬♦❪ ♦t ♦♥♦ rt♥③ r ss Pér ♦ ♦s

♦t ♥ ♠t ♠♣♠♥tt♦♥ ♦ ttr② tr♣t♦r

♦♥rt♦♥ ♥t♦ ②t② ♥ s ♥♦♥trs ♥

tqs P ♥rs ♥♦s ♥tr♥t♦♥ ♥t ♦♥r♥ ♦♥ ②r

♥ tr s ❱ ♣

❬r♣❪ ❨ r♣② t♦♥ ♥ rs rrs st② sst♦♥ s♥ r

♥②ss ♥ ♦♠♣tt♦♥ ♥t♥ ♥ ❱s ♥ ❱r ②st♠s

❱❱ ❲♦rs♦♣ ♦♥ ♣♣

❬r❪ rss ♥♦st ♦♥♥trs ♥ P à ♦♠st P râ

♦♥rtssr ttq P tss ❯♥rsté r♥♦♠té

♦r♣②

❬❪ ♦♦ ❨ ♥ ♥ ❨ s ♥♥ ♦♦♠ ♦♥t♥ ♠t♦ ♦r

st♠t♥ stt♦r ♥ stt♦t ♦ t♠♦♥ ttrs ♣♣

♥r② ❱♦ ♦ ♣♣

❬♥❪ ♥ r♥♦ ❱ ♥és ♦♥s♦ rí ♥ Pér③

t♦♠t tr ♦♥tr♦ ♦r ♥♠♥♥ s ♥t ♦rt♠s ♣♣

♦t ♦♠♣t♥ ❱♦ ♦ ♣♣

❬③❪ ③ ♥ ❩ ♣♦t s♦tr t♦♦ ②♣ ③③② ♦ t♦♦♦① ♦♠

♣tr ♣♣t♦♥s ♥ ♥♥r♥ t♦♥ ❱♦ ♦ ♣♣

❬③♥❪ ③♥ ♥ r ♥stt♥ ♣tt♦♥ ♥ t②♣ ③③② ♦ s②s

t♠s ♣♣ t♦ ♠ s ssss♠♥t ♥ Pr♦♥s ♦

r♦♣♥ ②♠♣♦s♠ ♦♥ ♥t♥t ♥♦♦s ❯ ♥♥

♣♣

❬P❪ ❱ P♥ ♦♥t♦ s ♥ ♦r ♣r♣t♦rs

②r tr ♦♣t♠③t♦♥ ♥ ♦♥tr♦ strt② ♦♣♠♥t ♥r②

♦♥rs♦♥ ♥ ♠♥♠♥t ❱♦ ♦ ♣♣

❬P♥❪ P♥♦♦ ♥ ♦♥♠♣ r♦♥ ♣r♦♣rts ♥ tr r♦ ♥ s♣r

♣t♦rs ♦r♥ ♦ ♣♦r s♦rs ❱♦ ♦ ♣♣

❬Pr❪ ❯ Pr ♥ r st♠t♥ ♦♠♣rss♦r sr ♣rssr ♦ s tr♥

♣♦r ♣♥t s♥ t②♣ ③③② ♦ s②st♠s ♥ ③③② ②st♠s

♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬P②♠❪ P②♠♥ Prr ♥ ♦②r ♥r② ♦♥tr♦ ♦ s♣r

♣t♦r ②r ♣♦r s♦r ♥r② ♦♥rs♦♥ ♥ ♥♠♥t

❱♦ ♦ ♣♣

❬P②♥❪ P②♥tr ♥②ss ♥ s♥ ♦ ♥♥r♥ s②st♠s ♣rss

❬Pr❪ Pr Pr♦st rs♦♥♥ ♥ ♥t♥t s②st♠s ♥t♦rs ♦ ♣s

♥r♥ ♦r♥ ♠♥♥

❬Pt❪ Pt♥ r♥s ♥ ♣ ♦s ♥ rts ♥ r♦♥trs ♦

s♥ ♣r♥r ❱r

❬Pr❪ Pr ♥ss♦ ss ♥ ♠♥♥ P♦r ♥rt♦♥ ②

s ♥str tr♦♥s ③♥ ❱♦ ♦ ♣♣

❬Pr❪ Pér③ ♦ss♦ ♦tr ♥ rí ♣t♠③t♦♥ ♦ ♣♦r ♠♥

♠♥t ♥ ♥ ②r tr s♥ ②♥♠ ♣r♦r♠♠♥ t♠ts

♥ ♦♠♣trs ♥ ♠t♦♥ ❱♦ ♦ ♣♣

♦r♣②

❬P❪ Pr Prr♥ ♥ ♦ss♥ t♦s ♦r stt♦r tr♠♥t♦♥

♥ tr ♣♣t♦♥s ♦r♥ ♦ P♦r ♦rs ❱♦ ♦ ♣♣

❬Prs❪ ❲ Prss P♥ ♥ ❲♦♥ ♣r♦ss♥♦ ♠♥♠♥t ♣♣r♦

♦r ssss♠♥t ♥ ♠tt♦♥ ♦ r♥ rss ♦r♥ ♦ Ptr♦♠ ♥

♥ ♥♥r♥ ❱♦ ♦ ♣♣

❬Ps❪ Ps ❨ t♠rt rt♦♥ ♥ ♠♥♥ ♦♥ ♥ s♠

t♦♥ ♦ trt♦♥ ♦♥tr♦ ♦rt♠ ♦r ♥ tr t ♦r s♣rt

rs ♥ ❱r ♥♦♦② ♦♥r♥ Pr♦♥s ❱

t ♣♣

❬Ps❪ Ps ❨ ♠rt ♥ rt♦♥ ③③② ♦ s♣ st♠t♦r t♦ r

♦r tr s tr ♥ P♦r tr♦♥s ♥ ♦t♦♥ ♦♥tr♦ ♦♥r

♥ P t ♥tr♥t♦♥ ♣♣

❬❪ ♦s ② rs③ ♥ rt♦♥ rq♥②

tr♠ ♥ ♦t s♣r♣t♦r rtr③t♦♥ ♥ ♠♦♥ ♦r♥ ♦

♣♦r s♦rs ❱♦ ♦ ♣♣

❬♦❪ ♦♥ ♦ ttr② s②st♠s ♦r tr② ♣♦r s ♦t②

♦ t♦♠♦t ♥♥rs

❬❪ P♦ P ♥ ♥ ♦t②♥ rst ♥ ♦t♦♥ ♥r♦♥

♠♥t ③③② ♥♠r ♣♣r♦ ♥ Pr♦♥s ♦ t ♥tr♥t♦♥ ♦♥t

♦♥r♥ ♦♥ t♦♥♦♠♦s ♥ts ♥ t ♥t ②st♠s❲♦rs♦♣ rst

♥ ♥t ♦ts ♣♣ tsr

❬♦❪ ♦♥ ♥ rs♠ s♥ ♦ ♥tr t②♣ ③③② ♦ s ♣♦r

s②st♠ st③r ♥ Pr♦ ♦ ♦r ♠② ♦ s♥ ♥♥r♥ ♥ t

♥♦♦② ♣♣

❬♦♠❪ ♦♠s t♠♥♥ ♥ ♦r ♣t♠ ♥r② ♠♥♠♥t ♦r

②r ♥r② st♦r s②st♠ ♦r tr s s ♦♥ t♦st ②♥♠

Pr♦r♠♠♥ ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

♣♣

❬♦♠❪ ♦♠r♦ ♥ ❱rs t♥ ♥t♦♥s ♦ ♥tr t②♣ ③③② ♥♠

rs ♦r t rr♥t ♥②ss ③③② ②st♠s r♥st♦♥s ♦♥ ❱♦

♦ ♣♣

❬②❪ ② ❨ Pr ♥ ♥♦♦ tr ♣♦rtr♥ ♠♦♥ ♦

②r tr ♥ ♦♣♠♥t ♦ ♣♦r strt♦♥ ♦rt♠

s ♦♥ r♥ ♠♦ r♦♥t♦♥ ♦r♥ ♦ P♦r ♦rs ❱♦ ♦

♣♣

♦r♣②

❬r❪ r s♣♥t ♥ ss Prt sr♠ ♦♣t♠③t♦♥ ♣♣ t♦ t

♦s♥ ♦ r rt ♦r♥ ♦ P♦r ♦rs ❱♦ ♦

♣♣

❬❪ r ♦♥ ♦♥r r ♥ ♥ ♣t♠③ ♥r②

♠♥♠♥t ♦r s♣r♣ ②r tr s ♥ ❱ P♦r

♥ Pr♦♣s♦♥ ♦♥r♥ ♣♣

❬❪ ❨ s♦ ♥ s♦ ②♣ ③③② r♦t ♦ ♠♦

♥ ♥ ③③② ♥♦r♠t♦♥ Pr♦ss♥ ♦t② P ♥♥ t♥

♦ t ♦rt ♠r♥ ♣♣

❬❪ t♥ ♥ ♠♥ s♦♥ ♠♥ ♦r ♥rt♥ t ♥

②♥♠ ♥r♦♥♠♥t s♥ ②r ♠t♦ ♥ ♦♥tr♦ ♥ t♦♠t♦♥

♥tr♥t♦♥ ♦♥r♥ ♦♥ ♣♣

❬♥❪ ♥♦r ss♥ ♥ ♥ tr♦♠ ♦

②r ♣t♦rs ❯s♥ r♦♥ ♥♦t tr♦ trtrs Pr♦♥s

♦ t ❱♦ ♦ ♣♣

❬♦❪ ♦♥♦ rtí♥③ ♦♦♥ ss Pr ♥ ♠t ♥rt

♠r♦s♦♣ r♣rs♥tt♦♥ ♦ ♠t♣ rttr ② t② ②r

♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP

♣♣

❬♦❪ ♦♥♦ rtí♥③ ss ♥ Pr é♦♣♣♠♥t ♥ ♠♦è

é♥rétq ♥ ♣

❬♦❪ ♦♥♦ rtí♥③ ss ♥ Pr t té♦rq ♣♦t

é♥rétq ♥ t rr s ♣r♠ètrs ♣rt♥♥ts ♣

❬♦❪ ♦♥♦ rtí♥③ ss Pr ♥ ♠t ♣rés♥tt♦♥ ♥

rétq r♦s♦♣q ♥ é ②r ♦r rttr ♠♦

♦♥ér♥ tr♦t♥q tr ❱♦ ♣♣

❬♦❪ ♦♥♦ rtí♥③ ss ♥ Pr ②♣ ③③② ♦ sts ♥ s②st♠s

♦r♣ r♣♦rt ♣

❬♦❪ ♦♥♦ rtí♥③ ss Pr ♥ ♠t Prt ♦♥tr♦

trtr ♦ ② t② ②r tr ❱ ♥ ❱ P♦r ♥

Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬♦❪ ♦♥♦ rtí♥③ st♦♥ é♥r ♥ é étrq ②r sé

sr ♦q ♦ ♦rr ♥s rrs ♥ é♥ trq ♦rt

❱♦ ♣♣

♦r♣②

❬♦❪ ♦♥♦ rtí♥③ ss ♥ Pr trté st♦♥ é♥r

♥ ♣

❬♦❪ ♦♥♦ rtí♥③ ss Pr ♥ ♠t Prt ♦♥tr♦

trtr ♥ ♥r② ♥♠♥t ♦ st ②r tr ❱

❱r ♥♦♦② r♥st♦♥s ♦♥ ❱♦ ss ♦ ♦

♣♣

❬♦❪ ♦♥♦rt♥③ ss ♥ Pér ②♣ ③③② ♦ ♦♥tr♦ ♦

♦♥rtr ♥ P♦r P♥t ♥ P♦r ②st♠s ♦♥tr♦ s②♠♣♦

s♠ ♦♦s ♠tt

❬♦❪ ♦♥♦ rtí♥③ st♦♥ é♥r ♥ é ②r ♣♣r♦ ♣r

♥t♥ rt Pr① ♦ ♥ rr ♥ r♥♦♠té

❱♦ ♣

❬♦❪ ♦♥♦ rtí♥③ ss ♥ Pr ①♣r♠♥t t♦♥ ♦ t②♣

③③② ♦ ♦♥tr♦r ♦r ♥r② ♠♥♠♥t ♥ ②r tr s

③③② ②st♠s r♥st♦♥s ♦♥ ❱♦ ①① ♦ ①① ♣ ①① s♠tt ♥

♣r

❬♦❪ ♦♥♦ rtí♥③ ♦♥ ss ♥ Pér sr②s

t②♣ ③③② ♦ s②st♠ ♦r ♥r② ♠♥♠♥t ♥ ②r tr s

♥♦r♠t♦♥ ♥s ❱♦ ♦ ♣♣

❬♦❪ ♦ ♣r♥t s ♦♠ ♥ s♣♥t P ♥

♥rtr s③♥ ♦♠♣r♦♠s ♣♣ t♦ ② ♦r r② ♣♣t♦♥ ♥

❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣ s♣t

❬♥❪ ❲ ♥ t s♠♣ t②♣ ③③② ♦ ♦♥tr♦r ♦r rt♠ ♦♥tr♦

tr♥st♦♥s ❱♦ ♦ ♣♣

❬❪ ♥ ♦♥trt♦♥ à ♦♣t♠st♦♥ é♥rtq ♥ s②stè♠ ♣ à ♦♠

st ♠rqé P tss ❯♥rsté r♥ ♦♠té

❬❪ ♥ ss Pr ♥ ♠♥♥ ♥r②♠♥♠♥t strt②

♦r ♠ s②st♠s s♥ ③③② ♦ ♥str tr♦♥s

r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬♦❪ P ♦♥t♦♥ ♥ t ♥r② ♠♥♠♥t ♦

ttr②s♣r♣t♦r ②r ♣♦r s♦r ♦r ♣♣t♦♥s ♦r

♥ ♦ P♦r ♦rs ❱♦ ♦ ♣♣

❬r❪ r ♥♥rt ♥ ♥ ②st♠ ♠♦♥ ♦ ②r s

♥ ♦rr t♦ ♣rt ②♥♠ ♣r♦r♠♥ ♥ ♥r② ♦♥s♠♣t♦♥ ♥ t

♦r♣②

❱ rr② ♦ ♠♦s r r♥s♣♦rts rt ❱♦ ♦

♣♣

❬❯r❪ ❯r♥ ♦ést♦♥ étrq t é♥rétq s ♠trs t♠

♦♥ st♠t♦♥ ♥ ♥ t P tss tt t♦♥ P♦②

t♥q ♦rr♥

❬❱♥♦❪ ❱♥♦t r ♥ ♥♥rt ♣t♠ ♠♥♠♥t ♦ tr s

t ②r st♦r s②st♠ ♥ ❱ P♦r ♥ Pr♦♣s♦♥ ♦♥r♥

❱PP ♣♣

❬❲♥❪ ❲♥ ss Pér t♥r rr ♦rr♥t♥♦ P♥s

♦♥tr P r♦♥ ♥ r♥♥ ♦♥ s♦ ♦①

♠♦s ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r② ❱♦ ♦ ♣♣

❬❲st❪ ❲str♥ ♣♣r♦s ①♣ér♠♥ts t ♥②s ♣r♦st ♣♦r

♥♦st ♣s ♦♠st t②♣ P P tss ❯♥rsté r♥

♦♠té

❬❲♦♥❪ ❲♦♥ ♥r ♥ s♥ ♥ ♥r② ♠♥♠♥t ♥ r ss

t♥♥ strt② ♦r ♣r ②r t ❱ ♦♥tr♦ ②st♠s

♥♦♦② r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬❲❪ ❲ ♥ ❲ ♥ t②♣ ③③② ♦ ♦♥tr♦r ♦r t q ♣r♦ss

♥ ③③② ②st♠s Pr♦♥s ♥tr♥t♦♥ ♦♥r♥ ♦♥

♣♣

❬❲❪ ❲ ♥ ♥ sst♦♥ ♦ tt r♦♥ s s♥ ♦st

trs ♥ ③③② ♦ rs ssrs ③③② ②st♠s r♥s

t♦♥s ♦♥ ❱♦ ♦ ♣♣

❬❲❪ ❩ ❲ ♣r♥t r s ss ♥ s♣♥t tr

♠♦t♦r s♥ ♦r ②r ②t② tr ♣♦rtr♥ ♥ ❱ P♦r

♥ Pr♦♣s♦♥ ♦♥r♥ ❱PP ♣♣

❬❲❪ ❩ ❲ ♣r♥t ♥ s♣♥t ♣t♠ s♥ ♦ tr r ♥

♣♦r ♦♥rtr ♦r ②r tr ♣♦rtr♥ ♥ ❱ P♦r ♥ Pr♦♣

s♦♥ ♦♥r♥ ❱PP ♣♣

❬❳❪ ❳ ❳ ♥ ②♥ ♣t♠ ♦♥tr♦ strt② ♦

ttr② ②r t② s ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r②

❱♦ ♦ ♣♣

❬❨♥❪ ❨♥ ❳ ♥ ♥ ❨ ❳ ♦st tt ♦ r st♠t♦♥ ♦r

②r tr ❱s r♠♦r ♥ ♦rt♠s ♥rs ❱♦ ♦

♣♣

♦r♣②

❬❨r❪ ❨r♠ ♦t ♦♠♣t♥ ♥ ♠♥ ♣♣ ♦t ♦♠♣t♥ ❱♦

♦ ♣♣

❬❨♦♥❪ ❨♦♥ ❲t t♦r② ♥ ts ♣♣t♦♥s ♣r♥r

❬❨♦s❪ ❨♦s t♥r ss P ♦ç♦té② ♥ ♥ss♦ ♥♦ss ♦

♣♦②♠r tr♦②t s r ♠♦s ♦♦♥ r②♥ ♦t ② ♥r

♥t♦rs ♠♦♥ ♥tr♥t♦♥ ♦r♥ ♦ ②r♦♥ ♥r② ❱♦ ♦

♣♣

❬❨♦s❪ ❨♦s t♥r P ♦ç♦té② ss ♥ss♦ ♣♣

rr P♥s ♦rr♥t♥♦ ② ♥ ❩ ♣

♣t♦♥ ♦ t tr ♥②ss t♦ ♥♦ss ♥ ♥♠♥ts ♥

♦♣♠♥ts ♦ s ♦♥r♥ r♥♦

❬❩❪ ❩ ③③② sts ♥♦r♠t♦♥ ♥ ♦♥tr♦ ❱♦ ♦ ♣♣

❬❩❪ ❩ ♦♥♣t ♦ ♥st r ♥ ts ♣♣t♦♥ t♦ ♣♣r♦①

♠t rs♦♥♥ ♥♦r♠t♦♥ s♥s ❱♦ ♦ ♣♣

❬❩♥❪ ❩♥ ♥ ❩ ②♣ ③③② ♥ r♦ ♠♦s ♥ tr ♣♣t♦♥

t♦ s♣ r♦♥t♦♥ ③③② ②st♠s r♥st♦♥s ♦♥ ❱♦ ♦

♣♣

❬❩♦❪ ❩♦ r ♦♥ ♥ ♥ ♥ ♦♥strt♥ ♣rs♠♦♥♦s

t②♣ ③③② ♦ s②st♠s ♥♥t r st♦♥ ③③② ②st♠s

r♥st♦♥s ♦♥ ❱♦ ♦ ♣♣

❬❩❪ ❩t ♥ ♦♥rt rtr③t♦♥ ♦ ♦②r ♣t♦rs ♦r ♣♦r

tr♦♥s ♣♣t♦♥s ♥str② ♣♣t♦♥s r♥st♦♥s ♦♥ ❱♦

♦ ♣♣