This document must be cited according to its fjnal version which is - - PDF document

This document must be cited according to its fjnal version which is published in a conference as:

• J. Peralez, M. Nadri, P. Dufour, P. Tona, A. Sciarretta,

“Control design for an automotive turbine rankine cycle system based on nonlinear state estimation”, 53rd IEEE Conference on Decision and Control (CDC), Los Angeles, CA, USA,

• pp. 3316-3321, december 15-17, 2014.

DOI : 10.1109/CDC.2014.7039902 You downloaded this document from the CNRS open archives server, on the webpages of Pascal Dufour: http://hal.archives-ouvertes.fr/DUFOUR-PASCAL-C-3926-2008

❈♦♥tr♦❧ ❉❡s✐❣♥ ❢♦r ❛♥ ❆✉t♦♠♦t✐✈❡ ❚✉r❜✐♥❡ ❘❛♥❦✐♥❡ ❈②❝❧❡ ❙②st❡♠ ❜❛s❡❞ ♦♥ ◆♦♥❧✐♥❡❛r ❙t❛t❡ ❊st✐♠❛t✐♦♥

❏♦❤❛♥ P❡r❛❧❡③✶,✷✱ ▼❛❞✐❤❛ ◆❛❞r✐✷✱ P❛s❝❛❧ ❉✉❢♦✉r✷✱ P❛♦❧✐♥♦ ❚♦♥❛✶✱ ❆♥t♦♥✐♦ ❙❝✐❛rr❡tt❛✶

✶ ■❋P ❊♥❡r❣✐❡s ◆♦✉✈❡❧❧❡s ✭❋r❛♥❝❡✮ ✷ ▲❆●❊P✱ ❯♥✐✈❡rs✐t② ♦❢ ▲②♦♥ ✭❋r❛♥❝❡✮

✺✸rd ■❊❊❊ ❈♦♥❢❡r❡♥❝❡ ♦♥ ❉❡❝✐s✐♦♥ ❛♥❞ ❈♦♥tr♦❧ ✭❈❉❈ ✷✵✶✹✮

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t

❖r❣❛♥✐❝ ❘❛♥❦✐♥❡ ❝②❝❧❡ ✭❖❘❈✮ ❢♦r ✇❛st❡ ❤❡❛t r❡❝♦✈❡r② ▼♦r❡ t❤❛♥ ❛ t❤✐r❞ ♦❢ t❤❡ ❡♥❡r❣② ♣r♦❞✉❝❡❞ ❜② ✐♥t❡r♥❛❧ ❝♦♠❜✉st✐♦♥ ❡♥❣✐♥❡s ✐s r❡❧❡❛s❡❞ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❤❡❛t t❤r♦✉❣❤ ❡①❤❛✉st ❣❛s✳ ❘❛♥❦✐♥❡ ❝②❝❧❡ ✐s ❛ s②st❡♠ ❢♦r ✇❛st❡ ❤❡❛t r❡❝♦✈❡r②✳ ❖❘❈ ❢♦r tr❛♥s♣♦rt ❛♣♣❧✐❝❛t✐♦♥ ❚❤❡ ♠❛✐♥ ❞✐✛❡r❡♥❝❡s ✇✐t❤ st❛t✐♦♥❛r② ❛♣♣❧✐❝❛t✐♦♥s ❧✐❡ ✐♥ t❤❡ ❤✐❣❤❧② tr❛♥s✐❡♥t ❜❡❤❛✈✐♦✉r ♦❢ t❤❡ ❤♦t s♦✉r❝❡✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ❞r✐✈✐♥❣ ❝♦♥❞✐t✐♦♥s✳

✷ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t

❖r❣❛♥✐❝ ❘❛♥❦✐♥❡ ❝②❝❧❡ ✭❖❘❈✮ ❢♦r ✇❛st❡ ❤❡❛t r❡❝♦✈❡r② ▼♦r❡ t❤❛♥ ❛ t❤✐r❞ ♦❢ t❤❡ ❡♥❡r❣② ♣r♦❞✉❝❡❞ ❜② ✐♥t❡r♥❛❧ ❝♦♠❜✉st✐♦♥ ❡♥❣✐♥❡s ✐s r❡❧❡❛s❡❞ ✐♥ t❤❡ ❢♦r♠ ♦❢ ❤❡❛t t❤r♦✉❣❤ ❡①❤❛✉st ❣❛s✳ ❘❛♥❦✐♥❡ ❝②❝❧❡ ✐s ❛ s②st❡♠ ❢♦r ✇❛st❡ ❤❡❛t r❡❝♦✈❡r②✳ ❖❘❈ ❢♦r tr❛♥s♣♦rt ❛♣♣❧✐❝❛t✐♦♥ ❚❤❡ ♠❛✐♥ ❞✐✛❡r❡♥❝❡s ✇✐t❤ st❛t✐♦♥❛r② ❛♣♣❧✐❝❛t✐♦♥s ❧✐❡ ✐♥ t❤❡ ❤✐❣❤❧② tr❛♥s✐❡♥t ❜❡❤❛✈✐♦✉r ♦❢ t❤❡ ❤♦t s♦✉r❝❡✱ ❞❡♣❡♥❞✐♥❣ ♦♥ ❞r✐✈✐♥❣ ❝♦♥❞✐t✐♦♥s✳

✷ ✴ ✶✺

❈♦♥t❡♥ts

✶

❘❛♥❦✐♥❡ ❝②❝❧❡ ❙②st❡♠ ❞❡s❝r✐♣t✐♦♥ ❈♦♥tr♦❧✲♦r✐❡♥t❡❞ ♠♦❞❡❧

✷

❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❖❜s❡r✈❡r ❞❡s✐❣♥ ❈♦♥tr♦❧ ❞❡s✐❣♥

✸

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥

✹

❈♦♥❝❧✉s✐♦♥

❈♦♥t❡♥ts

✶

❘❛♥❦✐♥❡ ❝②❝❧❡ ❙②st❡♠ ❞❡s❝r✐♣t✐♦♥ ❈♦♥tr♦❧✲♦r✐❡♥t❡❞ ♠♦❞❡❧

✷

❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❖❜s❡r✈❡r ❞❡s✐❣♥ ❈♦♥tr♦❧ ❞❡s✐❣♥

✸

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥

✹

❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❚❤❡r♠♦❞②♥❛♠✐❝ ❝②❝❧❡

✶ ❱❛♣♦r✐③❛t✐♦♥ ✷ ❊①♣❛♥s✐♦♥ ✸ ❈♦♥❞❡♥s❛t✐♦♥ ✹ ❈♦♠♣r❡ss✐♦♥

❙✉♣❡r❤❡❛t✐♥❣ SH ❉❡✜♥✐t✐♦♥✿ SH ✐s t❤❡ ✧❞✐st❛♥❝❡✧ ✐♥ ❦❡❧✈✐♥ ♦❢ t❤❡ ✢✉✐❞ ❢r♦♠ t❤❡ ❡✈❛♣♦r❛t✐♦♥ t❡♠♣❡r❛t✉r❡✳ ❊✛❡❝t✐✈❡ SH ❝♦♥tr♦❧ ✐s ❛ ❦❡② ✐ss✉❡ ❢♦r✿ ❝②❝❧❡ ❡✣❝✐❡♥❝②✱ ❝♦♠♣♦♥❡♥t s❛❢❡t②✳

✹ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❘❛♥❦✐♥❡ ❢♦r ❛✉t♦♠♦t✐✈❡ ❛♣♣❧✐❝❛t✐♦♥

✶ ❱❛♣♦r✐③❛t✐♦♥ ✷ ❊①♣❛♥s✐♦♥ ✸ ❈♦♥❞❡♥s❛t✐♦♥ ✹ ❈♦♠♣r❡ss✐♦♥

▼❛✐♥ ❛❝t✉❛t♦rs ❡✈❛♣♦r❛t♦r ❜②✲♣❛ss✿ ❧❡ts ❛ ❢r❛❝t✐♦♥ ♦❢ ❡①❤❛✉st ❣❛s ❢❡❡❞✐♥❣ ❖❘❈✳ ♣✉♠♣✿ ❝✐r❝✉❧❛t❡s t❤❡ ✇♦r❦✐♥❣ ✢✉✐❞✳ ❈♦♥tr♦❧ ♦❜❥❡❝t✐✈❡ ❘❡s♣♦♥❞ t♦ ❛ ♣♦✇❡r ♣r♦❞✉❝t✐♦♥ ❞❡♠❛♥❞ ✇❤✐❧❡ ❡♥s✉r✐♥❣ ❛♥ ❡✛❡❝t✐✈❡ SH ❝♦♥tr♦❧✳

✺ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❖❘❈✿ ❤✐❣❤ ♣r❡ss✉r❡ ♣❛rt

❋✐rst ♠♦❞❡❧ r❡❞✉❝t✐♦♥ ❋❧✉✐❞ ❝♦♥❞✐t✐♦♥s ✐♥ ❧♦✇ ♣r❡ss✉r❡ ♣❛rt ❝❛♥ ❜❡ s❡❡♥ ❛s ❛ ✭s❧♦✇✮ ❞✐st✉r❜❛♥❝❡✳ ❆ ♣♦✇❡r ♣r♦❞✉❝t✐♦♥ ❞❡♠❛♥❞ ✐s t❤❡♥ ❡q✉✐✈❛❧❡♥t t♦ ❛ ❤✐❣❤ ♣r❡ss✉r❡ ❞❡♠❛♥❞✳ ❑♥♦✇♥ ❞✐st✉r❜❛♥❝❡s✿ ❋❧✉✐❞ t❡♠♣❡r❛t✉r❡ ❛t ♣✉♠♣ ✭♠❡❛s✉r❡❞✮✳ ❋❧✉✐❞ ♣r❡ss✉r❡ ❛t t✉r❜✐♥❡ ♦✉t❧❡t ✭♠❡❛s✉r❡❞✮✳ ❊①❤❛✉st ♠❛ss ✢♦✇ ˙ mexh ✭❡st✐♠❛t❡❞✮✳ ❊①❤❛✉st t❡♠♣❡r❛t✉r❡✿ Texh ✭♠❡❛s✉r❡❞✮✳

✻ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

▼♦❞❡❧✐♥❣ ♦❢ ❡✈❛♣♦r❛t♦r✿ ♠♦✈✐♥❣✲❜♦✉♥❞❛r② ✭▼❇✮ ♣r✐♥❝✐♣❧❡

❆ ❧♦✇✲♦r❞❡r✱ ❜✉t r❡❛❧✐st✐❝✱ ♠♦❞❡❧ ♦❢ ❡✈❛♣♦r❛t♦r ❝❛♥ ❜❡ ♦❜t❛✐♥❡❞ ✈✐❛ ▼❇ ✭s❡❡ ❡✳❣ ❬❏❡♥s❡♥✱ ✷✵✵✸❪✮✳ ♠❡t❤♦❞✳ ❚❤❡r♠♦❞②♥❛♠✐❝ ✈❛r✐❛❜❧❡s ✢✉✐❞ ♣r❡ss✉r❡ p ✭❤♦♠♦❣❡♥♦✉s ❛❧♦♥❣ t❤❡ ❡✈❛♣♦r❛t♦r✮ ✢✉✐❞ ❡♥t❤❛❧♣✐❡s hi ✭❢♦r ❡❛❝❤ ③♦♥❡✮ ✇❛❧❧ t❡♠♣❡r❛t✉r❡s✿ Tw,i

✼ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

▼❛ss ❛♥❞ ❡♥❡r❣② ❜❛❧❛♥❝❡s

❙❡❝♦♥❞ ♠♦❞❡❧ r❡❞✉❝t✐♦♥✿ t✇♦ t✐♠❡ s❝❛❧❡ s❡♣❛r❛t✐♦♥ ❆ss✉♠❡ ✇♦r❦✐♥❣ ✢✉✐❞ ❛t st❡❛❞②✲st❛t❡✳ ❚❤❡♥ ▼❛ss ✢♦✇ ✐s ❤♦♠♦❣❡♥❡♦✉s✳ ❊♥❡r❣② ❜❛❧❛♥❝❡✿ ✵ = ˙ m(hin,i − hout,i) + ˙ Qf ,i Li✱ ✇❤❡r❡ ˙ Qf ,i = Sf αi (Tw,i − Tf ,i) ❉②♥❛♠✐❝s ♦❢ t❤❡ r❡❞✉❝❡❞ ♠♦❞❡❧✿ ✇❛❧❧ ❡♥❡r❣② ❜❛❧❛♥❝❡ mw cw d

dt Tw,i = ˙

Qexh,i − ˙ Qf ,i✱ ✇❤❡r❡ ˙ Qexh,i = ˙ mexh cexh

• ✶ − exp(− αexh Sexh

˙ mexh cexh )

• (Texh − Tw,i)

✽ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❊①♣❧✐❝✐t ♠♦❞❡❧

❆ss✉♠✐♥❣ t❤❛t SH ✐s ♣❡r❢❡❝t❧② r❡❣✉❧❛t❡❞✶ ❛t ❛ ❝♦♥st❛♥t ✈❛❧✉❡ ❜② t❤❡ ♣✉♠♣ ♠❛ss✲ ♦✇ ✭u✶✮✱ t❤❡ r❡❞✉❝❡❞ ♠♦❞❡❧ ❝❛♥ ❜❡ ✇r✐tt❡♥ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ s❡♠✐✲❡①♣❧✐❝✐t ❢♦r♠✿

• ˙

x = f (x, p) + u✷ g(x, t), ϕ(x, p) = ✵. ✭✶✮ Pr♦♣♦s✐t✐♦♥ ❚❤❡r❡ ❡①✐sts ǫ > ✵ s✉❝❤ t❤❛t ∂ϕ ∂p ❤❛s ❛ ❢✉❧❧ r❛♥❦ ♦♥ t❤❡ t✉❜✉❧❛r ♥❡✐❣❤❜♦✉r❤♦♦❞ Ωǫ = {(x, p) ∈ R✸+✶; ϕ(x, p) < ǫ}. ❚❤❡♥✱ s②st❡♠ ✭✶✮ ❝❛♥ ❜❡ ✇r✐tt❡♥ ✐♥ t❤❡ ❢♦❧❧♦✇✐♥❣ ❡①♣❧✐❝✐t ❢♦r♠✿    ˙ x = f (x, p) + u✷ g(x, t) ˙ p = − ∂ϕ ∂p |x,p −✶ ∂ϕ ∂x |x,p

• × (f (x, p) + u✷g(x, t)) .

✭✷✮

✶❬P❡r❛❧❡③ ❡t ❛❧✳✱ ✷✵✶✸❪ s❤♦✇❡❞ ❡①♣❡r✐♠❡♥t❛❧❧② t❤❛t s✉❝❤ ❛ss✉♠♣t✐♦♥ ✐s r❡❛❧✐st✐❝✱ ❡✈❡♥

✐♥ tr❛♥s✐❡♥t ❞r✐✈✐♥❣ ❝♦♥❞✐t✐♦♥s✮

✾ ✴ ✶✺

❈♦♥t❡♥ts

✶

❘❛♥❦✐♥❡ ❝②❝❧❡ ❙②st❡♠ ❞❡s❝r✐♣t✐♦♥ ❈♦♥tr♦❧✲♦r✐❡♥t❡❞ ♠♦❞❡❧

✷

❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❖❜s❡r✈❡r ❞❡s✐❣♥ ❈♦♥tr♦❧ ❞❡s✐❣♥

✸

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥

✹

❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❆♥ ✐♠♣❧✐❝✐t ❡①t❡♥❞❡❞ ❑❛❧♠❛♥ ✜❧t❡r

❆♥ ✐♠♣❧✐❝✐t ❡①t❡♥❞❡❞ ❑❛❧♠❛♥ ✜❧t❡r✷ ✭❊❑❋✮ ❢♦r s②st❡♠ ✭✶✮ ✐s ❣✐✈❡♥ ❜②✿            ˙ ˆ Tw = f ( ˆ Tw, ˆ p) + u✷ g( ˆ Tw, ˆ p) − SC TR−✶(ˆ p − p) Φ( ˆ Tw, ˆ p) = ✵ ˙ S = AS + SAT − SC TR−✶C TS + Q S(✵) = S(✵)T > ✵, ✭✸✮ ✇❤❡r❡ Q ✐s ❛ ❝♦♥st❛♥t s②♠♠❡tr✐❝ ♣♦s✐t✐✈❡ ❞❡✜♥✐t❡ ✭❙P❉✮ ♠❛tr✐①✱ R ✐s ❛ r❡❛❧ ♣♦s✐t✐✈❡ ❝♦♥st❛♥t ❛♥❞ A = ∂(f + u✷ g) ∂x |( ˆ

Tw,ˆ p),

C = ϕ−✶

p ϕT Tw .

✷s❡❡ ❬➴s❧✉♥❞ ❛♥❞ ❋r✐s❦✱ ✷✵✵✻❪

✶✵ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❖❜s❡r✈❡r ✈❛❧✐❞❛t✐♦♥

❙✐♠✉❧❛t✐♦♥ r❡s✉❧ts ✉♥❞❡r ✈❛r②✐♥❣ ✐♥❧❡ts✿ r❡❢❡r❡♥❝❡ ♠♦❞❡❧ ✭Twi✮✱ ♦❜s❡r✈❡r ✭ ˆ Twi✮✱ r❡❢❡r❡♥❝❡ ♠♦❞❡❧ ✇✐t❤ ♦❜s❡r✈❡r ✐♥✐t✐❛❧ ❝♦♥❞✐t✐♦♥s ✭ ¯ Twi✮✳

✶✶ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

Pr❡ss✉r❡ ❝♦♥tr♦❧ ❞❡s✐❣♥

Pr♦♣♦s✐t✐♦♥ ▲❡t k > ✵ t❤❡♥✱ t❤❡ ❝♦♥tr♦❧ u✷(Tw, p, pSP) = −ϕT

Tw f (Tw, p) + k(pSP − p)

ϕT

Tw g(Tw, t)

, ✭✹✮ ❛s②♠♣t♦t✐❝❛❧❧② st❛❜✐❧✐③❡s p t♦ t❤❡ s❡t♣♦✐♥t pSP✳ ▼♦r❡♦✈❡r✱ t❤❡ ✐♥♣✉t u✷ ❛♥❞ t❤❡ st❛t❡s ♦❢ s②st❡♠ ✭✷✮ r❡♠❛✐♥ ❜♦✉♥❞❡❞✳

✶✷ ✴ ✶✺

❈♦♥t❡♥ts

✶

❘❛♥❦✐♥❡ ❝②❝❧❡ ❙②st❡♠ ❞❡s❝r✐♣t✐♦♥ ❈♦♥tr♦❧✲♦r✐❡♥t❡❞ ♠♦❞❡❧

✷

❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❖❜s❡r✈❡r ❞❡s✐❣♥ ❈♦♥tr♦❧ ❞❡s✐❣♥

✸

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥

✹

❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❘❡❛❧✐st✐❝ ❞r✐✈✐♥❣ ❝♦♥❞✐t✐♦♥s

❊①♣❡r✐♠❡♥t❛❧ ❞❛t❛ ❢♦r ❡①❤❛✉st ❣❛s ❝♦♥❞✐t✐♦♥s t❤❛t ❛r❡ r❡♣r❡s❡♥t❛t✐✈❡ ♦❢ ❛ ❧♦♥❣✲❤❛✉❧ tr✉❝❦ ♠✐ss✐♦♥ ✇❡r❡ ✉s❡❞✿

✶✸ ✴ ✶✺

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥✿ ♣❡r❢♦r♠❛♥❝❡s

❆ t✐❣❤t ♣r❡ss✉r❡ s❡t✲♣♦✐♥t tr❛❝❦✐♥❣ ✐s ❞❡♠♦♥str❛t❡❞ ❛s ❧♦♥❣ ❛s ❡①❤❛✉st ❣❛s ❤❡❛t ✢♦✇ ✐s s✉✣❝✐❡♥t✳

✶✹ ✴ ✶✺

❈♦♥t❡♥ts

✶

❘❛♥❦✐♥❡ ❝②❝❧❡ ❙②st❡♠ ❞❡s❝r✐♣t✐♦♥ ❈♦♥tr♦❧✲♦r✐❡♥t❡❞ ♠♦❞❡❧

✷

❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❖❜s❡r✈❡r ❞❡s✐❣♥ ❈♦♥tr♦❧ ❞❡s✐❣♥

✸

❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥

✹

❈♦♥❝❧✉s✐♦♥

❈♦♥t❡①t ❘❛♥❦✐♥❡ ❝②❝❧❡ ❈❧♦s❡❞✲❧♦♦♣ ❞❡s✐❣♥ ❈❧♦s❡❞ ❧♦♦♣ ❡✈❛❧✉❛t✐♦♥ ❈♦♥❝❧✉s✐♦♥

❈♦♥❝❧✉s✐♦♥

❙✉♠♠❛r② ❚❤❡ ♣r♦♣♦s❡❞ s❝❤❡♠❡ ❝♦♠❜✐♥❡s ❛ s✉♣❡r❤❡❛t ❝♦♥tr♦❧❧❡r✱ ❛♥ ❛❞❞✐t✐♦♥❛❧ ♥♦♥❧✐♥❡❛r ❝♦♥tr♦❧❧❡r✱ ❛❧❧♦✇✐♥❣ ♣r❡ss✉r❡ s❡t✲♣♦✐♥t tr❛❝❦✐♥❣ ♦r ❡q✉✐✈❛❧❡♥t❧② ❛ tr❛❝❦✐♥❣ ♦❢ ♣♦✇❡r ♣r♦❞✉❝t✐♦♥ ❞❡♠❛♥❞✳ ❛♥ ✐♠♣❧✐❝✐t ❡①t❡♥❞❡❞ ❑❛❧♠❛♥ ❋✐❧t❡r ❢♦r ✇❛❧❧ t❡♠♣❡r❛t✉r❡ ❡st✐♠❛t✐♦♥s✳ ❚❤❡ ♣r♦♣♦s❡❞ ❛♣♣r♦❛❝❤ ❤❛s ❜❡❡♥ ✐❧❧✉str❛t❡❞ ✇✐t❤ s✉❝❝❡ss ✐♥ ♣r❡s❡♥❝❡ ♦❢ ♠❡❛s✉r❡♠❡♥t ♥♦✐s❡✱ ♠♦❞❡❧ ✉♥❝❡rt❛✐♥t✐❡s ❛♥❞ st❛t❡ ✐♥✐t✐❛❧ ❡rr♦rs✳ ❖♥✲❣♦✐♥❣ ✇♦r❦ ❊①♣❡r✐♠❡♥t❛❧ ✐♠♣❧❡♠❡♥t❛t✐♦♥✳ ❚❤❡♦r❡t✐❝❛❧ ♣r♦♦❢ ♦❢ t❤❡ ❛s②♠♣t♦t✐❝ st❛❜✐❧✐t② ♦❢ t❤❡ ❝❧♦s❡❞✲❧♦♦♣ ✉s✐♥❣ t❤❡ ♦❜s❡r✈❡r✳

✶✺ ✴ ✶✺