Paulo Cesar da Silva

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❯◆■❱❊❘❙■❉❆❉❊ ❉❖ ❊❙❚❆❉❖ ❉❊ ❙❆◆❚❆ ❈❆❚❆❘■◆❆ ✲ ❯❉❊❙❈ ❈❊◆❚❘❖ ❉❊ ❈■✃◆❈■❆❙ ❚❊❈◆❖▲Ó●■❈❆❙ ✲ ❈❈❚

▼❊❙❚❘❆❉❖ P❘❖❋■❙❙■❖◆❆▲ ❊▼ ❊◆●❊◆❍❆❘■❆ ❊▲➱❚❘■❈❆

❉■❙❙❊❘❚❆➬➹❖ ❉❊ ▼❊❙❚❘❆❉❖

P■✲▼◗❘ ❆❉❆P❚❆❚■❱❖ ❆P▲■❈❆❉❖ ❆ ❯▼ ▼❖❚❖❘ ❉❊ ■◆❉❯➬➹❖ ❚❘■❋➪❙■❈❖ ❯❚■▲■❩❆◆❉❖ ❆ P▲❆❚❆❋❖❘▼❆ ❉❙P❆❈❊✶✶✵✸

P❆❯▲❖ ❈➱❙❆❘ ❉❆ ❙■▲❱❆

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P❆❯▲❖ ❈➱❙❆❘ ❉❆ ❙■▲❱❆

P■✲▼◗❘ ❆❉❆P❚❆❚■❱❖ ❆P▲■❈❆❉❖ ❆ ❯▼ ▼❖❚❖❘ ❉❊ ■◆❉❯➬➹❖ ❚❘■❋➪❙■❈❖ ❯❚■▲■❩❆◆❉❖ ❆ P▲❆❚❆❋❖❘▼❆

❉❙P❆❈❊✶✶✵✸

❉✐ss❡rt❛çã♦ s✉❜♠❡t✐❞❛ ❛♦ Pr♦✲ ❣r❛♠❛ ❞❡ Pós✲●r❛❞✉❛çã♦ ❡♠ ❊♥✲ ❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ❞♦ ❈❡♥tr♦ ❞❡ ❈✐ê♥❝✐❛s ❚❡❝♥♦❧ó❣✐❝❛s ❞❛ ❯♥✐✈❡rs✐✲ ❞❛❞❡ ❞♦ ❊st❛❞♦ ❞❡ ❙❛♥t❛ ❈❛t❛r✐♥❛✱ ♣❛r❛ ♦❜t❡♥çã♦ ❞♦ ❣r❛✉ ❞❡ ▼❡str❡ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛✳

❖r✐❡♥t❛❞♦r❛✿ Pr♦❢❛✳ ❉r✳ ▼❛r✐❛♥❛

❙❛♥t♦s ▼❛t♦s ❈❛✈❛❧❝❛

❈♦♦r✐❡♥t❛❞♦r✿ Pr♦❢✳ ❉r✳ ❆❞❡♠✐r ◆✐❡❞

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S586p Silva, Paulo César da

PI-MQR Adaptativo Aplicado a um Motor de Indução Trifásico Utilizando a Plataforma DSPACE1103 / Paulo Cesar da Silva. – 2015.

116 p. : il. ; 21 cm

Orientador: Mariana Santos Matos Cavalca Coorientador: Ademir Nied

Bibliografia: 112-114 p.

Dissertação (mestrado) – Universidade do Estado de Santa Catarina Catarina, Centro de Ciências Tecnológicas, Programa de

Pós-Graduação em Engenharia Elétrica, Joinville, 2015.

1. Motor de indução trifásico. 2. Identificação paramétrica. 3. Mínimos quadrados recursivos. 4. Controle adaptativo. 5. dSPACE (DS1103) . I. Cavalca, Mariana Santos Matos. II. Nied, Ademir. III. Universidade do Estado de Santa Catarina. Programa de Pós-Graduação em Engenharia Elétrica. IV. Título.

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❆●❘❆❉❊❈■▼❊◆❚❖❙

❆❣r❛❞❡ç♦ ❛ t♦❞❛ ❛ ♠✐♥❤❛ ❢❛♠í❧✐❛✱ ❡♠ ❡s♣❡❝✐❛❧ ❛♦s ♠❡✉s ♣❛✐s✱ ♣❡❧♦ ✐♥❝❡♥t✐✈♦✱ ❛♣♦✐♦ ❡ ❝❛r✐♥❤♦ ❞✉r❛♥t❡ ♠❛✐s ❡st❛ ❡t❛♣❛ ❞❛ ♠✐♥❤❛ ✈✐❞❛✳ ❆❣r❛❞❡ç♦ à ♠✐♥❤❛ ♦r✐❡♥t❛❞♦r❛✱ Pr♦❢❛✳ ❉r✳ ▼❛r✐❛♥❛ ❙❛♥t♦s

▼❛t♦s ❈❛✈❛❧❝❛ ❡ ❛♦ ♠❡✉ ❝♦♦r✐❡♥t❛❞♦r✱ Pr♦❢✳ ❉r✳ ❆❞❡♠✐r ◆✐❡❞✱ ♣❡❧❛s s✉❣❡stõ❡s ❡ ❝♦♥tr✐❜✉✐çõ❡s ❞❛❞❛s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✱ ❛❧é♠ ❞❛ ♣❛❝✐ê♥❝✐❛ ❡ ✐♥❝❡♥t✐✈♦ à ♣❡sq✉✐s❛ ❞✉r❛♥t❡ t♦❞♦ ♦ ♣r♦❝❡ss♦✳

●♦st❛r✐❛ ❞❡ ❛❣r❛❞❡❝❡r ❛ t♦❞♦s ♦s ✐♥t❡❣r❛♥t❡s ❞♦ ●r✉♣♦ ❞❡ ❈♦♥✲ tr♦❧❡ ❞❡ ❙✐st❡♠❛s ✭●❈❙✮ ❞❛ ❯❉❊❙❈✱ ❡♠ ❡s♣❡❝✐❛❧ ❛ ❉❛♥✐❡❧ ❞♦s ❙❛♥t♦s ▼❛t♦s ❡ ❊❞✉❛r❞♦ ❍❡♥r✐q✉❡ ❈♦✉t♦ ♣❡❧❛ ❣r❛♥❞❡ ❛❥✉❞❛ ♣r❡st❛❞❛ ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞♦ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦✳

❆❣r❛❞❡ç♦ ❛♦s ❞❡♠❛✐s ♣r♦❢❡ss♦r❡s ❞♦ ❉❡♣❛rt❛♠❡♥t♦ ❞❡ ❊♥❣❡✲ ♥❤❛r✐❛ ❊❧étr✐❝❛✱ q✉❡ ❝♦♥tr✐❜✉ír❛♠ ❞❡ ❛❧❣✉♠❛ ❢♦r♠❛ ♣❛r❛ ❛ ❝♦♥❝r❡t✐③❛✲ çã♦ ❞❡st❡ tr❛❜❛❧❤♦✳

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✏❖ q✉❡ s❛❜❡♠♦s é ✉♠❛ ❣♦t❛❀ ♦ q✉❡ ✐❣♥♦r❛♠♦s é ✉♠ ♦❝❡❛♥♦✳✑

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❘❊❙❯▼❖

❙■▲❱❆✱ P❛✉❧♦ ❈és❛r✳ ▼♦t♦r ❞❡ ■♥❞✉çã♦ ❚r✐❢ás✐❝♦✳ ✷✵✶✺✳ ✶✶✻❢✳ ❉✐s✲ s❡rt❛çã♦ ✭▼❡str❛❞♦ Pr♦✜ss✐♦♥❛❧ ❡♠ ❊♥❣❡♥❤❛r✐❛ ❊❧étr✐❝❛ ✲ ➪r❡❛✿ ❆✉✲ t♦♠❛çã♦ ❞❡ ❙✐st❡♠❛s✮ ✕ ❯♥✐✈❡rs✐❞❛❞❡ ❞♦ ❊st❛❞♦ ❞❡ ❙❛♥t❛ ❈❛t❛r✐♥❛✳ ❏♦✐♥✈✐❧❧❡✱ ✷✵✶✺✳

❖s ♣❛râ♠❡tr♦s ❡❧étr✐❝♦s ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝♦ ✈❛r✐❛♠ ❝♦♥✲ ❢♦r♠❡ ♦ s❡✉ ♣♦♥t♦ ❞❡ ♦♣❡r❛çã♦✱ ❝♦♠ ❛ t❡♠♣❡r❛t✉r❛ ❡ t❛♠❜é♠ ❝♦♠ ❛ ❞❡❣r❛❞❛çã♦ ♥❛t✉r❛❧ ❞❛ ♠áq✉✐♥❛✳ ❱✐st♦ q✉❡ ♦ ♣r♦❥❡t♦ ❞❡ r❡❣✉❧❛❞♦r❡s sã♦ t✐♣✐❝❛♠❡♥t❡ r❡❛❧✐③❛❞♦s ❝♦♠ ❜❛s❡ ❡♠ ❡q✉❛çõ❡s ❧✐♥❡❛r❡s ❡ s✐♠♣❧✐✜✲ ❝❛❞❛s ❞❛ ♠áq✉✐♥❛✱ ❛ ✈❛r✐❛çã♦ ♣❛r❛♠étr✐❝❛ ♣♦❞❡ ❝❛✉s❛r r❡s♣♦st❛s ✐♥✲ ❞❡s❡❥❛❞❛s✱ ♣♦✐s ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♠♦t♦r é ♥ã♦✲❧✐♥❡❛r ❡ ✈❛r✐❛♥t❡ ♥♦ t❡♠♣♦✳ ❉❡st❛ ❢♦r♠❛ ♣r♦♣õ❡✲s❡ ♥❡st❡ tr❛❜❛❧❤♦ r❡❛❧✐③❛r ❛ ✐❞❡♥t✐✜❝❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❡❧étr✐❝♦s ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦✱ ✉t✐❧✐③❛♥❞♦ ♦ ❡st✐♠❛❞♦r ❞❡♥♦♠✐♥❛❞♦ ❞❡ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❘❡❝✉rs✐✈♦s ✭▼◗❘✮✳ ❆ss✐♠✱ ❝♦♠ ♦s ❞❛❞♦s ♣❛r❛♠étr✐❝♦s ❛t✉❛❧✐③❛❞♦s ❛ ❝❛❞❛ ♣❡rí♦❞♦ ❞❡ ❛♠♦str❛❣❡♠✱ ♣♦❞❡✲s❡ r❡❝❛❧❝✉❧❛r ❡♠ t❡♠♣♦ r❡❛❧✱ ♦s ❣❛♥❤♦s ❞♦s r❡❣✉❧❛❞♦r❡s q✉❡ sã♦ ♣r♦❥❡t❛✲ ❞♦s ♣❛r❛ ♦ ❝♦♥tr♦❧❡ ❞❛ ♠áq✉✐♥❛ ❞❡ ✐♥❞✉çã♦ ❡ t♦r♥❛r ♦s ❞❡s❝❛s❛♠❡♥t♦s ♠❡♥♦r❡s✳ ❖s r❡s✉❧t❛❞♦s ❡①♣❡r✐♠❡♥t❛✐s ❢♦r❛♠ ♦❜t✐❞♦s ❝♦♠ ♦ ♣r♦❝❡s✲ s❛♠❡♥t♦ r❡❛❧✐③❛❞♦ ♣❡❧♦ ❤❛r❞✇❛r❡ ❞❙P❆❈❊ ✭❉❙✶✶✵✸✮✱ q✉❡ ♣♦ss✉✐ ✉♠❛ ✐♥t❡r❢❛❝❡ ❝♦♠ ♦ ▼❛t❧❛❜✴❙✐♠✉❧✐♥❦✱ ❢❛❝✐❧✐t❛♥❞♦ ❛ ✉t✐❧✐③❛çã♦ ♣♦r ♣❛rt❡ ❞♦ ✉s✉ár✐♦ ❡ r❡❞✉③✐♥❞♦ ♦ t❡♠♣♦ ❞✐s♣❡♥❞✐❞♦ ♣❛r❛ ♦s t❡st❡s ❡♠ ❜❛♥❝❛❞❛✳ ❖s r❡s✉❧t❛❞♦s ❞❡ s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s ❡ ♣rát✐❝♦s ❛♣r❡s❡♥t❛♠ ✉♠❛ ❝♦♠✲ ♣❛r❛çã♦ ❡♥tr❡ ❛ ♠❛❧❤❛ ♣r♦♣♦st❛✱ ❝♦♠ ❛ ✐❞❡♥t✐✜❝❛çã♦ ♣❛r❛♠étr✐❝❛ ❡ ❛t✉✲ ❛❧✐③❛çã♦ ❞♦s ❣❛♥❤♦s ❞♦s ❝♦♥tr♦❧❛❞♦r❡s ✭❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦✮ ❡ ❛ ♠❛❧❤❛ ❝♦♠ ❝♦♥tr♦❧❛❞♦r❡s ❝♦♠ ❣❛♥❤♦s ✜①♦s✳

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❆❇❙❚❘❆❈❚

❙■▲❱❆✱ P❛✉❧♦ ❈és❛r✳ ■♥❞✉❝t✐♦♥ ▼❛❝❤✐♥❡✳ ✷✵✶✺✳ ✶✶✻❢✳ ❉✐ss❡rt❛t✐♦♥ ✭▼❛st❡r ✐♥ ❊❧❡❝tr✐❝❛❧ ❊♥❣✐♥❡❡r✐♥❣ ✲ ❆r❡❛✿ ❙②st❡♠s ❆✉t♦♠❛t✐♦♥✮ ✕ ❙t❛t❡ ❯♥✐✈❡rs✐t② ♦❢ ❙❛♥t❛ ❈❛t❛r✐♥❛✳ ❏♦✐♥✈✐❧❧❡✱ ✷✵✶✺✳

❚❤❡ ❡❧❡❝tr✐❝❛❧ ♣❛r❛♠❡t❡rs ♦❢ t❤r❡❡✲♣❤❛s❡ ✐♥❞✉❝t✐♦♥ ♠♦t♦rs ✈❛r② ❛❝❝♦r❞✲ ✐♥❣ t♦ t❤❡✐r ♦♣❡r❛t✐♥❣ ♣♦✐♥t✱ ✇✐t❤ t❤❡ t❡♠♣❡r❛t✉r❡ ❛♥❞ ❛❧s♦ ✇✐t❤ t❤❡ ♥❛t✉r❛❧ ♠❛❝❤✐♥❡ ❞❡❣r❛❞❛t✐♦♥✳ ❙✐♥❝❡ t❤❡ ❞❡s✐❣♥ r❡❣✉❧❛t♦rs ❛r❡ t②♣✐❝❛❧❧② ♣❡r❢♦r♠❡❞ ❜❛s❡❞ ♦♥ ❧✐♥❡❛r ❛♥❞ s✐♠♣❧✐✜❡❞ ❡q✉❛t✐♦♥s ♦❢ t❤❡ ♠❛❝❤✐♥❡✱ t❤❡ ♣❛r❛♠❡tr✐❝ ✈❛r✐❛t✐♦♥ ❝❛♥ ❝❛✉s❡ ✉♥✇❛♥t❡❞ r❡s♣♦♥s❡s✱ s✐♥❝❡ t❤❡ ♠♦✲ t♦r ❜❡❤❛✈✐♦r ✐s ♥♦♥✲❧✐♥❡❛r ❛♥❞ t✐♠❡ ✈❛r✐❛♥t✳ ❚❤✉s✱ ✐t ✐s ♣r♦♣♦s❡❞ ✐♥ t❤✐s ✇♦r❦ ❝❛rr② t❤❡ ✐❞❡♥t✐✜❝❛t✐♦♥ ♦❢ t❤❡ ❡❧❡❝tr✐❝❛❧ ♣❛r❛♠❡t❡rs ♦❢ t❤❡ ✐♥❞✉❝t✐♦♥ ♠♦t♦r ✉s✐♥❣ t❤❡ ❡st✐♠❛t♦r ❝❛❧❧❡❞ ▲❡❛st ❙q✉❛r❡s ❘❡❝✉rs✐✈❡ ✭❘▲❙✮✳ ❚❤✉s✱ ✇✐t❤ t❤❡ ♣❛r❛♠❡tr✐❝ ❞❛t❛ ✉♣❞❛t❡❞ ❡✈❡r② s❛♠♣❧✐♥❣ ♣❡✲ r✐♦❞ ❝❛♥ ❜❡ r❡❝❛❧❝✉❧❛t❡❞ ✐♥ r❡❛❧ t✐♠❡ t❤❡ ❣❛✐♥s ♦❢ t❤❡ r❡❣✉❧❛t♦rs ❛r❡ ❞❡s✐❣♥❡❞ ❢♦r ❝♦♥tr♦❧❧✐♥❣ t❤❡ ✐♥❞✉❝t✐♦♥ ♠❛❝❤✐♥❡ ❛♥❞ ♠❛❦❡ ♠✐♥♦r ♠✐s✲ ♠❛t❝❤❡s✳ ❚❤❡ ❡①♣❡r✐♠❡♥t❛❧ r❡s✉❧ts ✇❡r❡ ♦❜t❛✐♥❡❞ ✇✐t❤ t❤❡ ♣r♦❝❡ss✐♥❣ ♣❡r❢♦r♠❡❞ ❜② ❞❙P❆❈❊ ❤❛r❞✇❛r❡ ✭❉❙✶✶✵✸✮✱ ✇❤✐❝❤ ❤❛s ❛♥ ✐♥t❡r❢❛❝❡ ✇✐t❤ ▼❛t❧❛❜✴❙✐♠✉❧✐♥❦✱ ❢❛❝✐❧✐t❛t✐♥❣ t❤❡ ✉s❡ ❜② t❤❡ ✉s❡r ❛♥❞ r❡❞✉❝✐♥❣ t❤❡ t✐♠❡ t❛❦❡♥ ❢♦r t❡st✐♥❣ ❜❡♥❝❤✳ ❚❤❡ r❡s✉❧ts ♦❢ ♥✉♠❡r✐❝❛❧ ❛♥❞ ♣r❛❝t✐❝❛❧ s✐♠✉✲ ❧❛t✐♦♥s s❤♦✇ ❛ ❝♦♠♣❛r✐s♦♥ ❜❡t✇❡❡♥ t❤❡ ♠❡s❤ ♣r♦♣♦s❛❧✱ t❤❡ ♣❛r❛♠❡tr✐❝ ✐❞❡♥t✐✜❝❛t✐♦♥ ❛♥❞ ✉♣❞❛t❡ ♦❢ t❤❡ ❣❛✐♥s ♦❢ t❤❡ ❝♦♥tr♦❧❧❡rs ✭❛❞❛♣t✐✈❡ ❝♦♥✲ tr♦❧✮ ❛♥❞ t❤❡ ♠❡s❤ ✇✐t❤ ❝♦♥tr♦❧❧❡rs ✇✐t❤ ✜①❡❞ ❣❛✐♥s✳

(16)
(17)

▲■❙❚❆ ❉❊ ■▲❯❙❚❘❆➬Õ❊❙

❋✐❣✉r❛ ✶ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ♠áq✉✐♥❛ tr✐❢ás✐❝❛ ✸✷ ❋✐❣✉r❛ ✷ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ tr✐❢ás✐❝♦ ✭❛❜❝✮ ❡ ❞❡

✉♠ s✐st❡♠❛ ❜✐❢ás✐❝♦ ✭❞q✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ❋✐❣✉r❛ ✸ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡s♣❛❝✐❛❧ ❞♦ ♣r✐♥❝í♣✐♦ ❞♦ ❝♦♥tr♦❧❡

✈❡t♦r✐❛❧ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✵ ❋✐❣✉r❛ ✹ ✲ ❉✐❛❣r❛♠❛ ❞❡ ❜❧♦❝♦s ❞♦ ❝♦♥tr♦❧❛❞♦r ✈❡t♦r✐❛❧ ✐♥❞✐✲

r❡t♦ ❝♦♠ ✐♥✈❡rs♦r ❛ ❡♥tr❛❞❛ ❡♠ t❡♥sã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✻✷ ❋✐❣✉r❛ ✺ ✲ ▼❛❧❤❛ ❞❡ ❝♦♥tr♦❧❡ ❞❡ ❝♦rr❡♥t❡ ❞❡ ❡✐①♦ ❞✐r❡t♦ ✳ ✳ ✳ ✻✹ ❋✐❣✉r❛ ✻ ✲ ▼❛❧❤❛ ❞❡ ❝♦♥tr♦❧❡ ❞❡ ❝♦rr❡♥t❡ ❞❡ ❡✐①♦ ❡♠ q✉❛❞r❛t✉r❛ ✻✹ ❋✐❣✉r❛ ✼ ✲ ▼❛❧❤❛ ❞❡ ❝♦♥tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✻✻ ❋✐❣✉r❛ ✽ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ♠♦❞❡❧♦ ❆❘❳ ✳ ✳ ✳ ✼✵ ❋✐❣✉r❛ ✾ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ♠♦❞❡❧♦ ❆❘▼❆❳ ✳ ✼✶ ❋✐❣✉r❛ ✶✵ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❡ ♠♦❞❡❧♦ ❞❡ ❡rr♦ ♥❛

s❛í❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✷ ❋✐❣✉r❛ ✶✶ ✲ ❊st✐♠❛çã♦ ❞❛s ✐♥❞✉tâ♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ❋✐❣✉r❛ ✶✷ ✲ ❊st✐♠❛çã♦ ❞❛ r❡s✐stê♥❝✐❛ r♦tór✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ❋✐❣✉r❛ ✶✸ ✲ ❱❡❧♦❝✐❞❛❞❡ s✐♠✉❧❛❞❛ ❡ r❡❢❡rê♥❝✐❛ s❡❣✉♥❞♦ ✭❙❚❖P❆✱

✶✾✾✼✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ❋✐❣✉r❛ ✶✹ ✲ ❱❡❧♦❝✐❞❛❞❡ s✐♠✉❧❛❞❛ ❡ r❡❢❡rê♥❝✐❛ s❡❣✉♥❞♦ ✭▼❆❨❆❀

▲❊❖◆❆❘❉■✱ ✷✵✶✶✮ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✼ ❋✐❣✉r❛ ✶✺ ✲ ❚❡♥sã♦ tr✐❢ás✐❝❛ s❡❣✉♥❞♦ ✭❙❚❖P❆✱ ✶✾✾✼✮ ✳ ✳ ✳ ✳ ✳ ✽✽ ❋✐❣✉r❛ ✶✻ ✲ ❚❡♥sã♦ tr✐❢ás✐❝❛ s❡❣✉♥❞♦ ✭▼❆❨❆❀ ▲❊❖◆❆❘❉■✱ ✷✵✶✶✮ ✽✽ ❋✐❣✉r❛ ✶✼ ✲ ❆çã♦ ❞❡ ❝♦♥tr♦❧❡ s❡❣✉♥❞♦ ✭❙❚❖P❆✱ ✶✾✾✼✮ ✳ ✳ ✳ ✳ ✳ ✽✾ ❋✐❣✉r❛ ✶✽ ✲ ❆çã♦ ❞❡ ❝♦♥tr♦❧❡ s❡❣✉♥❞♦ ✭▼❆❨❆❀ ▲❊❖◆❆❘❉■✱ ✷✵✶✶✮ ✽✾ ❋✐❣✉r❛ ✶✾ ✲ ❈♦rr❡♥t❡ ❜✐❢ás✐❝❛ ✭❞q✮ s❡❣✉♥❞♦ ✭❙❚❖P❆✱ ✶✾✾✼✮ ✳ ✳ ✾✵ ❋✐❣✉r❛ ✷✵ ✲ ❈♦rr❡♥t❡ ❜✐❢ás✐❝❛ ✭❞q✮ s❡❣✉♥❞♦ ✭▼❆❨❆❀ ▲❊❖◆❆❘❉■✱

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✶✻

❋✐❣✉r❛ ✷✾ ✲ ❇❛♥❝❛❞❛ ❞❡ t❡st❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✾ ❋✐❣✉r❛ ✸✵ ✲ ▼■❚ ❡ ❡♥❝♦❞❡r ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✵ ❋✐❣✉r❛ ✸✶ ✲ ❉❡t❛❧❤❡s ❞♦ ✐♥✈❡rs♦r ❈❋❲✵✻ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ❋✐❣✉r❛ ✸✷ ✲ ❊❧❡♠❡♥t♦s ❞❛ ❜❛♥❝❛❞❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✶ ❋✐❣✉r❛ ✸✸ ✲ ■♥❞✉tâ♥❝✐❛s ❡st✐♠❛❞❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ❋✐❣✉r❛ ✸✹ ✲ ❘❡s✐stê♥❝✐❛ ❡st✐♠❛❞❛ ❝♦♠ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✳ ✳ ✶✵✸ ❋✐❣✉r❛ ✸✺ ✲ ❱❡❧♦❝✐❞❛❞❡ ❡ r❡❢❡rê♥❝✐❛ ❝♦♠ ❝♦♥tr♦❧❡ ♥ã♦✲❛❞❛♣t❛t✐✈♦✶✵✹ ❋✐❣✉r❛ ✸✻ ✲ ❚❡♥sã♦ tr✐❢ás✐❝❛ ❝♦♠ ❝♦♥tr♦❧❡ ♥ã♦✲❛❞❛♣t❛t✐✈♦ ✳ ✳ ✶✵✹ ❋✐❣✉r❛ ✸✼ ✲ ❚❡♥sã♦ ❜✐❢ás✐❝❛ ✭❞q✮ ❝♦♠ ❝♦♥tr♦❧❡ ♥ã♦✲❛❞❛♣t❛t✐✈♦ ✶✵✺ ❋✐❣✉r❛ ✸✽ ✲ ❈♦rr❡♥t❡ tr✐❢ás✐❝❛ ❝♦♠ ❝♦♥tr♦❧❡ ♥ã♦✲❛❞❛♣t❛t✐✈♦ ✳ ✶✵✺ ❋✐❣✉r❛ ✸✾ ✲ ❱❡❧♦❝✐❞❛❞❡ ❡ r❡❢❡rê♥❝✐❛ ❝♦♠ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✳ ✶✵✻ ❋✐❣✉r❛ ✹✵ ✲ ❚❡♥sã♦ tr✐❢ás✐❝❛ ❝♦♠ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ❋✐❣✉r❛ ✹✶ ✲ ❚❡♥sã♦ ❜✐❢ás✐❝❛ ✭❞q✮ ❝♦♠ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✳ ✳ ✶✵✼ ❋✐❣✉r❛ ✹✷ ✲ ❈♦rr❡♥t❡ tr✐❢ás✐❝❛ ❝♦♠ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✶✵✼ ❋✐❣✉r❛ ✹✸ ✲ ●❛♥❤♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ❋✐❣✉r❛ ✹✹ ✲ ■♥❞✉tâ♥❝✐❛ ❞❡ r♦t♦r ✲Lr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ❋✐❣✉r❛ ✹✺ ✲ ❘❡s✐stê♥❝✐❛ ❞❡ r♦t♦r ✲Rr ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✾ ❋✐❣✉r❛ ✹✻ ✲ ❘❡♣r❡s❡♥t❛çã♦ ❞♦s s✐st❡♠❛s ❞❡ ❝♦♦r❞❡♥❛❞❛s ❡st❛✲

(19)

▲■❙❚❆ ❉❊ ❚❆❇❊▲❆❙

(20)
(21)

▲■❙❚❆ ❉❊ ❆❇❘❊❱■❆❚❯❘❆❙ ❊ ❙■●▲❆❙ ❆❉ ❆♥❛❧ó❣✐❝♦✲❉✐❣✐t❛❧

❆❘▼❆ ❆✉t♦r❡❣r❡ss✐✈❡ ▼♦✈✐♥❣ ❆✈❡r❛❣❡

❆❘▼❆❳ ❆✉t♦r❡❣r❡ss✐✈❡ ▼♦✈✐♥❣ ❆✈❡r❛❣❡ ✇✐t❤ ❊①♦❣❡♥♦✉s ■♥♣✉ts ❆❘❳ ❆✉t♦r❡❣r❡ss✐✈❡ ✇✐t❤ ❊①♦❣❡♥♦✉s ■♥♣✉ts

❈❆ ❈♦rr❡♥t❡ ❆❧t❡r♥❛❞❛ ❈❈ ❈♦rr❡♥t❡ ❈♦♥tí♥✉❛ ❉❆ ❉✐❣✐t❛❧✲❆♥❛❧ó❣✐❝♦

▼■❚ ▼♦t♦r ❞❡ ■♥❞✉çã♦ ❚r✐❢ás✐❝♦ ▼◗ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s

▼◗❘ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❘❡❝✉rs✐✈♦s

◆❊▼❆ ◆❛t✐♦♥❛❧ ❊❧❡❝tr✐❝❛❧ ▼❛♥✉❢❛❝t✉r❡rs ❆ss♦❝✐❛t✐♦♥ P❲▼ P✉❧s❡ ❲✐❞t❤ ▼♦❞✉❧❛t✐♦♥

❚❚▲ ❚r❛♥s✐st♦r✲❚r❛♥s✐st♦r✲▲♦❣✐❝

(22)
(23)

✷✶

▲■❙❚❆ ❉❊ ❙❮▼❇❖▲❖❙

a P♦❧♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦

ˆ

a P♦❧♦ ❡st✐♠❛❞♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦

B ❈♦❡✜❝✐❡♥t❡ ❞❡ ❛tr✐t♦ ✈✐s❝♦s♦ ♥♦ ❡✐①♦ ❞♦ ♠♦t♦r ❬N ms❪ b0 ❩❡r♦ ❞♦ ♠♦❞❡❧♦ ❞✐s❝r❡t♦

b1 ❩❡r♦ ❞♦ ♠♦❞❡❧♦ ❞✐s❝r❡t♦ d0 ❩❡r♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦

ˆ

d0 ❩❡r♦ ❡st✐♠❛❞♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦ d1 ❩❡r♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦

ˆ

d1 ❩❡r♦ ❡st✐♠❛❞♦ ❞♦ ♠♦❞❡❧♦ ❝♦♥tí♥✉♦ f P♦❧♦ ❞♦ ♠♦❞❡❧♦ ❞✐s❝r❡t♦

IIIabcr ❱❡t♦r ❞❡ ❝♦rr❡♥t❡ ❞❡ r♦t♦r

IIIabcs ❱❡t♦r ❞❡ ❝♦rr❡♥t❡ ❞❡ ❡st❛t♦r

IIIs

dqr ❱❡t♦r ❞❡ ❝♦rr❡♥t❡ ❜✐❢ás✐❝❛ ❞❡ r♦t♦r ♥♦ ❢r❛♠❡ ❡st❛❝✐♦♥ár✐♦ ❬A❪

IIIs

dqs ❱❡t♦r ❞❡ ❝♦rr❡♥t❡ ❜✐❢ás✐❝❛ ❞❡ ❡st❛t♦r ♥♦ ❢r❛♠❡ ❡st❛❝✐♦♥ár✐♦ ❬A❪

J ▼♦♠❡♥t♦ ❞❡ ✐♥ér❝✐❛ ❞♦ s✐st❡♠❛

JM Q ❋✉♥çã♦ ❝✉st♦ ♠✐♥✐♠✐③❛❞❛ ♣❡❧♦s ♠í♥✐♠♦s q✉❛❞r❛❞♦s

KKK ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ tr✐❢ás✐❝❛✲❜✐❢ás✐❝❛ KKKe

r ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s tr✐❢ás✐❝♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❜✐❢ás✐❝♦ ♥♦ ❢r❛♠❡ sí♥❝r♦♥♦ ❛♦ ❝❛♠♣♦ ❣✐r❛♥t❡ ♣❛r❛ ✈❛r✐á✈❡✐s r♦tór✐❝❛s

KKKe

s ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s tr✐❢ás✐❝♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❜✐❢ás✐❝♦ ♥♦ ❢r❛♠❡ sí♥❝r♦♥♦ ❛♦ ❝❛♠♣♦ ❣✐r❛♥t❡ ♣❛r❛ ✈❛r✐á✈❡✐s ❡st❛tór✐❝❛s

Ki ●❛♥❤♦ ✐♥t❡❣r❛❧ ❞♦s ❝♦♥tr♦❧❛❞♦r❡s ❞❡ ❝♦rr❡♥t❡

Kiω ●❛♥❤♦ ✐♥t❡❣r❛❧ ❞♦ ❝♦♥tr♦❧❛❞♦r ❞❡ ✈❡❧♦❝✐❞❛❞❡

Kp ●❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ ❞♦s ❝♦♥tr♦❧❛❞♦r❡s ❞❡ ❝♦rr❡♥t❡

Kpω ●❛♥❤♦ ♣r♦♣♦r❝✐♦♥❛❧ ❞♦ ❝♦♥tr♦❧❛❞♦r ❞❡ ✈❡❧♦❝✐❞❛❞❡

KKKr

r ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s tr✐❢ás✐❝♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❜✐❢ás✐❝♦ ♥♦ ❢r❛♠❡ ❞❡ r♦t♦r ♣❛r❛ ✈❛r✐á✈❡✐s r♦tór✐❝❛s

KKKr

s ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ ❞♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s tr✐❢ás✐❝♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❜✐❢ás✐❝♦ ♥♦ ❢r❛♠❡ ❞❡ r♦t♦r ♣❛r❛ ✈❛r✐á✈❡✐s r♦tór✐❝❛s

Ks ●❛♥❤♦ ❞❛ ♣❧❛♥t❛ ✭♠♦t♦r ✲ ❝❛♣✳ ✸✮

KKKs

(24)

✷✷

K K Ks

s ▼❛tr✐③ tr❛♥s❢♦r♠❛çã♦ ❞♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ♣❛r❛ ♦ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s ❜✐❢ás✐❝♦ ❡st❛❝✐♦♥ár✐♦ ♣❛r❛ ❛s ✈❛r✐á✈❡✐s ❞❡ ❡st❛t♦r

L L

L ●❛♥❤♦ ❞♦ ✜❧tr♦ ❞❡ ❑❛❧♠❛♥ ♦✉ ❣❛♥❤♦ ❞♦ ❡st✐♠❛❞♦r Labcr ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ♣♦r ❢❛s❡ ❞❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦

❬H❪

Labcs ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ♣♦r ❢❛s❡ ❞❡ ❡st❛t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

λ ❋❛t♦r ❞❡ ❡sq✉❡❝✐♠❡♥t♦

Lar ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡a ❞❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Las ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡a❞❡ ❡st❛t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Lbr ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡b ❞❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Lbs ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡b❞❡ ❡st❛t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Lcr ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡c ❞❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Lcs ■♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❛ ❢❛s❡c❞❡ ❡st❛t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Lrσ ■♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ r♦t♦r ❬H❪

Lsσ ■♥❞✉tâ♥❝✐❛ ❞❡ ❞✐s♣❡rsã♦ ❞♦ ❡st❛t♦r ❬H❪

Mr ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❞✉❛s ❢❛s❡s ❞❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Ms ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❞✉❛s ❢❛s❡s ❞❡ ❡st❛t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

Msr ■♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❡st❛t♦r ❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

M M

Msr ▼❛tr✐③ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❡st❛t♦r ❡ r♦t♦r ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❬H❪

np ◆ú♠❡r♦ ❞❡ ♣❛r❡s ❞❡ ♣♦❧♦s

ν(k) ❱❛r✐á✈❡❧ ❛❧❡❛tór✐❛

P P

P ▼❛tr✐③ ❞❡ ❝♦✈❛r✐â♥❝✐❛ ❞♦ ❡st✐♠❛❞♦r ❞❡ ♠í♥✐♠♦s q✉❛❞r❛❞♦s

r❡❝✉rs✐✈♦s

φ φ

φabcr ❱❡t♦r ❞❡ ✢✉①♦ ❡♥❧❛ç❛❞♦ ❝♦♠ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞❡ r♦t♦r ❬W b❪

φ φ

φabcs ❱❡t♦r ❞❡ ✢✉①♦ ❡♥❧❛ç❛❞♦ ❝♦♠ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞❡ ❡st❛t♦r ❬W b❪

Pm P♦tê♥❝✐❛ ♠❡❝â♥✐❝❛ ❬W❪

q−1 ❖♣❡r❛❞♦r ❞❡ ❛tr❛s♦ R

R

(25)

RRRabcs ▼❛tr✐③ r❡s✐stê♥❝✐❛ ❞❡ ❡st❛t♦r ❬Ω❪

Rr ❘❡s✐stê♥❝✐❛ ❞❡ r♦t♦r ♣♦r ❢❛s❡ ❬Ω❪

Rs ❘❡s✐stê♥❝✐❛ ❞❡ ❡st❛t♦r ♣♦r ❢❛s❡ ❬Ω❪

τc ❘❡♣r❡s❡♥t❛ ♦ t♦rq✉❡ r❡s✐st❡♥t❡ ❞❡ ❝❛r❣❛ ❬N m❪

τm ❘❡♣r❡s❡♥t❛ ♦ t♦rq✉❡ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❬N m❪

θr P♦s✐çã♦ ❛♥❣✉❧❛r ❞♦ r♦t♦r ❬rad❪

Tp ❈♦♥st❛♥t❡ ❞❡ t❡♠♣♦ ❞❛ ♣❧❛♥t❛ ✭❝❛♣✳ ✸✮ ❬s❪

Ts P❡rí♦❞♦ ❞❡ ❛♠♦str❛❣❡♠ ❬s❪

VVVabcr ❱❡t♦r ❞❡ t❡♥sã♦ ❞❡ r♦t♦r ❬V❪

VVVabcs ❱❡t♦r ❞❡ t❡♥sã♦ ❞❡ ❡st❛t♦r ❬V❪

VVVs

dqr ❱❡t♦r ❞❡ t❡♥sã♦ ❜✐❢ás✐❝♦ ❞❡ r♦t♦r ♥♦ ❢r❛♠❡ ❡st❛❝✐♦♥ár✐♦ ❬V❪

VVVs

dqs ❱❡t♦r ❞❡ t❡♥sã♦ ❜✐❢ás✐❝♦ ❞❡ ❡st❛t♦r ♥♦ ❢r❛♠❡ ❡st❛❝✐♦♥ár✐♦ ❬V❪

ωe ❱❡❧♦❝✐❞❛❞❡ ❞❛ ❢r❡q✉ê♥❝✐❛ ❡❧étr✐❝❛ ❬rad/s❪

ωr ❱❡❧♦❝✐❞❛❞❡ ♠❡❝â♥✐❝❛ ❞♦ r♦t♦r ❬rad/s❪

ωsl ❱❡❧♦❝✐❞❛❞❡ ❞❡ ❡s❝♦rr❡❣❛♠❡♥t♦ ❬rad/s❪

ξ ❈♦♥st❛♥t❡ ❞❡ ❛♠♦rt❡❝✐♠❡♥t♦

(26)
(27)

❙❯▼➪❘■❖

✶ ■♥tr♦❞✉çã♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✷✼ ✷ ▼♦❞❡❧❛❣❡♠ ❞♦ ▼♦t♦r ❞❡ ■♥❞✉çã♦ ❚r✐❢ás✐❝♦ ✸✶ ✷✳✶ ▼♦❞❡❧♦ ❚r✐❢ás✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✶ ✷✳✷ ❚r❛♥s❢♦r♠❛çã♦ ❞❡ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ✳ ✳ ✳ ✸✽ ✷✳✷✳✶ ❚r❛♥s❢♦r♠❛çã♦ ●❡r❛❧ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s

❚r✐❢ás✐❝♦✲❇✐❢ás✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✸✾ ✷✳✷✳✷ ❚r❛♥s❢♦r♠❛çã♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❚r✐❢ás✐❝♦

♣❛r❛ ♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❇✐❢ás✐❝♦ ❊st❛✲ ❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✷ ✷✳✷✳✸ ❚r❛♥s❢♦r♠❛çã♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❚r✐❢ás✐❝♦

♣❛r❛ ♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❇✐❢ás✐❝♦ ❙í♥❝r♦♥♦ ❛♦ ❈❛♠♣♦ ●✐r❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✸ ✷✳✷✳✹ ❚r❛♥s❢♦r♠❛çã♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❚r✐❢ás✐❝♦

♣❛r❛ ♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❇✐❢ás✐❝♦ ❞❡ ❘♦t♦r ✹✹ ✷✳✸ ▼♦❞❡❧❛❣❡♠ ❇✐❢ás✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✹✹ ✷✳✸✳✶ ▼♦❞❡❧♦ ♥♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❙í♥❝r♦♥♦ ❛♦

❈❛♠♣♦ ●✐r❛♥t❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✶ ✷✳✹ ❘❡♣r❡s❡♥t❛çã♦ ♥♦ ❊s♣❛ç♦ ❞❡ ❊st❛❞♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✳✹✳✶ ❘❡♣r❡s❡♥t❛çã♦ ♥♦ ❊s♣❛ç♦ ❞❡ ❊st❛❞♦s ♣❡❧❛s ❈♦r✲

r❡♥t❡s ❡ ❋❧✉①♦s ❊st❛tór✐❝♦s ♥♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r✲ ❞❡♥❛❞❛s ❊st❛❝✐♦♥ár✐♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✺✷ ✷✳✹✳✷ ❘❡♣r❡s❡♥t❛çã♦ ♥♦ ❊s♣❛ç♦ ❞❡ ❊st❛❞♦s ♣❡❧❛s ❈♦r✲

(28)

✷✻

✹✳✺ ❋❛t♦r ❞❡ ❊sq✉❡❝✐♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✼✾ ✹✳✻ ■❞❡♥t✐❢✐❝❛çã♦ ❞♦s P❛râ♠❡tr♦s ❊❧étr✐❝♦s ❞♦ ▼♦✲

t♦r ❞❡ ■♥❞✉çã♦ ❚r✐❢ás✐❝♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✵ ✹✳✻✳✶ ❉✐s❝r❡t✐③❛çã♦ ❞❡ ❙✐st❡♠❛s ❈♦♥tí♥✉♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✶ ✹✳✻✳✷ ❆♣❧✐❝❛çã♦ ❞❛ ❉✐s❝r❡t✐③❛çã♦ ❡♠ ✉♠❛ P❧❛♥t❛ ❈♦♥✲

tí♥✉❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✷ ✹✳✻✳✸ ■❞❡♥t✐✜❝❛çã♦ ❞♦ ▼♦t♦r ❞❡ ■♥❞✉çã♦ ❯t✐❧✐③❛♥❞♦ ♦

❈♦♥❝❡✐t♦ ❞❡ ❈❧❛ss❡ ❞❡ ▼♦t♦r❡s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✸ ✺ ❙✐♠✉❧❛çã♦ ◆✉♠ér✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✶ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❘❡❝✉rs✐✈♦s ✭▼◗❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✽✺ ✺✳✷ P■ ♥ã♦✲❛❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✽✻ ✺✳✸ P■✲▼◗❘ ❆❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✶ ✻ ❆♣❧✐❝❛çã♦ Prát✐❝❛ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✻✳✶ P❧❛t❛❢♦r♠❛ ❞❡ ❆❝✐♦♥❛♠❡♥t♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✾✹ ✻✳✷ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❘❡❝✉rs✐✈♦s ✭▼◗❘✮ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✷ ✻✳✸ P■ ♥ã♦✲❛❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✸ ✻✳✹ P■✲▼◗❘ ❆❞❛♣t❛t✐✈♦ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✻ ✻✳✺ ❚❡st❡s Prát✐❝♦s ❞❡ ✶✺ ♠✐♥✉t♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✵✽ ✼ ❈♦♥❝❧✉sõ❡s ❡ ❈♦♥s✐❞❡r❛çõ❡s ❋✐♥❛✐s ✳ ✳ ✳ ✳ ✳ ✶✶✵ ✼✳✶ Pr♦♣♦st❛s ♣❛r❛ ❚r❛❜❛❧❤♦s ❋✉t✉r♦s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✶ ❘❡❢❡rê♥❝✐❛s ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✷ ✽ ❆♣ê♥❞✐❝❡ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✳ ✶✶✺ ✽✳✶ ❚r❛♥s❢♦r♠❛çã♦ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❚r✐✲

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✷✼

✶ ■◆❚❘❖❉❯➬➹❖

❉✉r❛♥t❡ ♠✉✐t♦s ❛♥♦s✱ ❣r❛♥❞❡ ♣❛rt❡ ❞❛s t❛r❡❢❛s ❡♥✈♦❧✈✐❞❛s ♥♦s ♣r♦❝❡ss♦s ♣r♦❞✉t✐✈♦s ❡r❛♠ ❞♦ t✐♣♦ r✉❞✐♠❡♥t❛r✱ ♦♥❞❡ ❛s ♠áq✉✐♥❛s ❡r❛♠ ♦♣❡r❛❞❛s ❡♠ ✈❡❧♦❝✐❞❛❞❡s ❛♣r♦①✐♠❛❞❛♠❡♥t❡ ❝♦♥st❛♥t❡s✱ ♥ã♦ ♥❡❝❡ss✐✲ t❛♥❞♦ ♥❡♥❤✉♠❛ ❛çã♦ ❞❡ ❝♦♥tr♦❧❡ s♦❜r❡ ♦s ♠♦t♦r❡s ♦✉ ❛❝✐♦♥❛♠❡♥t♦s✱ t❛✐s ❝♦♠♦ ❞❡ ♣♦s✐çã♦✱ ✈❡❧♦❝✐❞❛❞❡ ♦✉ t♦rq✉❡ ✭❙❖◆❈■◆■✱ ✷✵✵✶✮ ❡ ✭❋❊❘✲ ❘❆❘■✱ ✷✵✵✻✮✳

❆té ❛s ❞é❝❛❞❛s ✜♥❛✐s ❞♦ sé❝✉❧♦ ♣❛ss❛❞♦✱ ❛s ♠áq✉✐♥❛s ❞❡ ❈♦r✲ r❡♥t❡ ❆❧t❡r♥❛❞❛ ✭❈❆✮ t❡♥❞✐❛♠ ❛ s❡r ❡♠♣r❡❣❛❞❛s ❜❛s✐❝❛♠❡♥t❡ ❝♦♠♦ ❞✐s✲ ♣♦s✐t✐✈♦s ❞❡ ✈❡❧♦❝✐❞❛❞❡ ú♥✐❝❛✳ ❚✐♣✐❝❛♠❡♥t❡✱ ❡❧❛s ❢✉♥❝✐♦♥❛✈❛♠ ❛ ♣❛rt✐r ❞❡ ❢♦♥t❡s ❞❡ ❢r❡q✉ê♥❝✐❛ ✜①❛ ✭♥❛ ♠❛✐♦r✐❛ ❞♦s ❝❛s♦s✱ ✺✵ ♦✉ ✻✵ ❍③ ❞❛ r❡❞❡ ❡❧étr✐❝❛✮✳ ◆♦ ❝❛s♦ ❞♦s ♠♦t♦r❡s✱ ♦ ❝♦♥tr♦❧❡ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ♥❡❝❡ss✐t❛✈❛ ❞❡ ✉♠❛ ❢♦♥t❡ ❞❡ ❢r❡q✉ê♥❝✐❛ ✈❛r✐á✈❡❧✱ ❡ t❛✐s ❢♦♥t❡s ♥ã♦ ❡st❛✈❛♠ ❢❛❝✐❧♠❡♥t❡ ❞✐s♣♦♥í✈❡✐s✳ ❆ss✐♠✱ ❛s ❛♣❧✐❝❛çõ❡s q✉❡ ❡①✐❣✐❛♠ ❝♦♥tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❡r❛♠ ❛t❡♥❞✐❞❛s ♣♦r ♠áq✉✐♥❛s ❞❡ ❈♦rr❡♥t❡ ❈♦♥tí♥✉❛ ✭❈❈✮✱ q✉❡ ♣♦❞❡♠ ❢♦r♥❡❝❡r ✉♠ ❝♦♥tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❛❧t❛♠❡♥t❡ ✢❡①í✈❡❧ ✭❋■❚❩●❊❘❆▲❉❀ ❑■◆●❙▲❊❨❀ ❯▼❆◆❙✱ ✷✵✵✻✮✳ P♦ré♠ ❛ ✉t✐❧✐③❛çã♦ ❞❡ ♠♦t♦r❡s ❈❈ ❛♣r❡✲ s❡♥t❛ ✐♥ú♠❡r❛s ❞❡s✈❛♥t❛❣❡♥s ❞❡✈✐❞♦ ❛ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ❝♦♥str✉t✐✈❛s✱ q✉❡ ❡❧❡✈❛♠ ♦ ❝✉st♦ ❞❡ ❢❛❜r✐❝❛çã♦ ❡ ♠❛♥✉t❡♥çã♦ ❞♦s ♠❡s♠♦s✳

❖s ♠♦t♦r❡s ❞❡ ✐♥❞✉çã♦ ♣♦ss✉❡♠ ♠✉✐t❛s ✈❛♥t❛❣❡♥s ❛tr❛t✐✈❛s ♣❛r❛ ❛ ❛♣❧✐❝❛çã♦ ♥♦ s❡t♦r ✐♥❞✉str✐❛❧✱ ❞❡♥tr❡ ❡st❛s ❞❡st❛❝❛♠✲s❡✿ ❢♦r♠❛ ❝♦♥str✉t✐✈❛ s✐♠♣❧❡s ❝♦♠ ❜❛✐①♦ ❝✉st♦ ❞❡ ❢❛❜r✐❝❛çã♦✱ ❣r❛♥❞❡ r♦❜✉st❡③ ❡❧❡tr♦♠❡❝â♥✐❝❛✱ ♠❡♥♦s ♥❡❝❡ss✐❞❛❞❡ ❞❡ ♠❛♥✉t❡♥çã♦✱ ✐♥❡①✐stê♥❝✐❛ ❞❡ ❝♦✲ ♠✉t❛❞♦r❡s ❡ ❡s❝♦✈❛s q✉❡ ❣❡r❛♠ ❢❛✐s❝❛♠❡♥t♦s✱ ♠❛✐♦r ♣♦ss✐❜✐❧✐❞❛❞❡ ❞❡ s❡r ❡♠♣r❡❣❛❞♦ ❡♠ ❛♠❜✐❡♥t❡s ❝❧❛ss✐✜❝❛❞♦s s♦❜ r✐s❝♦ ❞❡ ❡①♣❧♦sã♦ ❡ ♠❛✐♦r r❡❧❛çã♦ ♣♦tê♥❝✐❛✲♣❡s♦✳ P♦ré♠✱ ♠❡s♠♦ ❝♦♠ ❡st❛s ✈❛♥t❛❣❡♥s✱ ❛ ❝♦♠♣❧❡✲ ①✐❞❛❞❡ ❡♥✈♦❧✈✐❞❛ ♥♦ s❡✉ ❝♦♥tr♦❧❡✱ ❡♠ ❢✉♥çã♦ ❞❡ ❝❛r❛❝t❡r✐③❛r✲s❡ ❝♦♠♦ ✉♠❛ ♣❧❛♥t❛ ♥ã♦ ❧✐♥❡❛r✱ ❢♦rt❡♠❡♥t❡ ❛❝♦♣❧❛❞❛ ❡ ♠✉❧t✐✈❛r✐á✈❡❧✱ ❢♦✐ ❛ ♣r✐♥✲ ❝✐♣❛❧ ❞✐✜❝✉❧❞❛❞❡ q✉❛♥t♦ à s✉❛ ✉t✐❧✐③❛çã♦ ❡♠ ❛❝✐♦♥❛♠❡♥t♦s ❝♦♥tr♦❧❛❞♦s✳ ❆ ❞✐✜❝✉❧❞❛❞❡ ❡st❛✈❛ ❛ss♦❝✐❛❞❛ ❛♦ ♣♦❜r❡ ❞❡s❡♠♣❡♥❤♦ ❞✐♥â♠✐❝♦ ❞❛s té❝✲ ♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ❛té ❡♥tã♦ ❡①✐st❡♥t❡s ✭❋❊❘❘❆❘■✱ ✷✵✵✻✮✳

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✷✽

♥❛s ♠áq✉✐♥❛s ❞❡ ✐♥❞✉çã♦ ♥ã♦ ❡①✐st❡ ✉♠ ❝✐r❝✉✐t♦ ❢ís✐❝♦ ❡①❝❧✉s✐✈♦ ♣❛r❛ ♦ ❝❛♠♣♦ ❡ ✐ss♦ t♦r♥❛ ♦ s❡✉ ❝♦♥tr♦❧❡ ♠❛✐s ❝♦♠♣❧❡①♦✱ q✉❛♥❞♦ ❝♦♠♣❛r❛❞♦ ❝♦♠ ♦ ❝♦♥tr♦❧❡ ❞❛ ♠áq✉✐♥❛ ❞❡ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛ ✭❇■▼✱ ✷✵✶✷✮✳

❆ ♣r✐♠❡✐r❛ ❡str❛té❣✐❛ q✉❡ s✉r❣✐✉ ♣❛r❛ ❝♦♥tr♦❧❡ ❞❛ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ ❢♦✐ ♦ ❝♦♥tr♦❧❡ ❡s❝❛❧❛r✳ ❈♦♠ ❡st❛ ❡str❛té❣✐❛ ❞❡ ❝♦♥tr♦❧❡ ❛ ✈❡❧♦❝✐❞❛❞❡ é ❝♦♥tr♦❧❛❞❛ ❛ ♣❛rt✐r ❞❛ ❢r❡q✉ê♥❝✐❛ ❡❧étr✐❝❛✱ ♣r♦❝✉r❛♥❞♦ ♠❛♥t❡r ❝♦♥st❛♥t❡ ❛ r❡❧❛çã♦ t❡♥sã♦✴❢r❡q✉ê♥❝✐❛ ✭❱✴❋✮✳ ❊♥tr❡t❛♥t♦✱ ♦s ❛❝✐♦♥❛♠❡♥t♦s ❜❛s❡❛❞♦s ♥❡st❛ té❝♥✐❝❛ ❞❡ ❝♦♥tr♦❧❡ ♥ã♦ ❝♦♥s❡❣✉❡♠ ❛t✐♥✲ ❣✐r ❞❡s❡♠♣❡♥❤♦s ❞✐♥â♠✐❝♦s ✐❣✉❛✐s ♦✉ s✉♣❡r✐♦r❡s ❛♦s ❞♦s ♠♦t♦r❡s ❈❈✳ ▼❡s♠♦ ❛ss✐♠✱ s✉❛ ✉t✐❧✐③❛çã♦ t❡♠ ❣r❛♥❞❡ ❢❛✐①❛ ❞❡ ❛♣❧✐❝❛çã♦ ♦♥❞❡ s❡ ♥❡❝❡ss✐t❛ ❛❝✐♦♥❛♠❡♥t♦s ❛ ✈❡❧♦❝✐❞❛❞❡ ✈❛r✐á✈❡❧ ❝♦♠ ♣❡q✉❡♥❛s ❡①✐❣ê♥❝✐❛s ❞✐♥â♠✐❝❛s ✭❋❊❘❘❆❘■✱ ✷✵✵✻✮✳ ❇♦♠❜❛s ❡ ✈❡♥t✐❧❛❞♦r❡s sã♦ t✐♣✐❝❛♠❡♥t❡ ❡①❡♠♣❧♦s ❞❡ ❛♣❧✐❝❛çõ❡s q✉❡ ❡①✐❣❡♠ ❛❝✐♦♥❛♠❡♥t♦s ❞❡ ❜❛✐①♦ ❞❡s❡♠♣❡♥❤♦✱ ♣♦rq✉❡ ♥❡ss❛s✱ s❡ ❤♦✉✈❡r ❛ ♥❡❝❡ss✐❞❛❞❡ ❞♦ ❝♦♥tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡✱ ♥ã♦ é ❡①✐❣✐❞♦ q✉❡ ❛ r❡s♣♦st❛ s❡❥❛ rá♣✐❞❛ ❡ ❡♥tã♦✱ ♠✉✐t❛s ✈❡③❡s ♦ ❝♦♥tr♦❧❡ ❡s❝❛❧❛r✱ ❛t❡♥❞❡ ♦s r❡q✉✐s✐t♦s ❞❛ ❝❛r❣❛ ✭❇■▼✱ ✷✵✶✷✮✳

❊♠ ✶✾✻✾✱ ❍❛ss❡ ✭❍❆❙❙❊✱ ✶✾✻✾✮ ♣r♦♣ôs✱ ♣❡❧❛ ♣r✐♠❡✐r❛ ✈❡③✱ ♦ ❝♦♥✲ tr♦❧❡ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ ❜❛s❡❛❞♦ ❡♠ ♠♦❞❡❧♦ ✈❡t♦r✐❛❧ ❡ ❛❧✐♠❡♥t❛❞♦ ♣♦r ✐♥✈❡rs♦r P✉❧s❡ ❲✐❞t❤ ▼♦❞✉❧❛t✐♦♥ ✭P❲▼✮✱ q✉❡ r❡♣r❡✲ s❡♥t♦✉ ✉♠ ♠❛r❝♦ ♥♦ ❝♦♥tr♦❧❡ ❞❛s ♠áq✉✐♥❛s ❞❡ ✐♥❞✉çã♦ r♦t♦r ❣❛✐♦❧❛ ❞❡ ❡sq✉✐❧♦✱ ♣♦✐s ♦ ❝♦♥tr♦❧❡ ❡①✐❜✐✉ ✉♠❛ r❡s♣♦st❛ ❞✐♥â♠✐❝❛ ♥♦tá✈❡❧✳ ▼❛s ❢♦✐ ✭❇▲❆❙❑❊✱ ✶✾✼✹✮ q✉❡♠ ❢♦r♠✉❧♦✉ ❛ t❡♦r✐❛ ❣❡r❛❧ ❡✱ ❞❡ss❛ ❢♦r♠❛✱ ❡①♣❛♥❞✐✉ ❛ ❛♣❧✐❝❛çã♦ ❞♦ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ♣❛r❛ q✉❛❧q✉❡r t✐♣♦ ❞❡ ♠áq✉✐♥❛ ❞❡ ❝♦r✲ r❡♥t❡ ❛❧t❡r♥❛❞❛ ❡ ✐♥✈❡rs♦r✱ ❞❡♥♦♠✐♥❛♥❞♦✲♦ ♦r✐❡♥t❛çã♦ ❞❡ ❝❛♠♣♦ ✭❇■▼✱ ✷✵✶✷✮✳ ❖ ❛✈❛♥ç♦ ❞❡st❛s t❡❝♥♦❧♦❣✐❛s ❞❡✉ ♦r✐❣❡♠ ❛♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡ té❝♥✐❝❛s ♥ã♦ ❧✐♥❡❛r❡s ❞❡ ❝♦♥tr♦❧❡✱ ♣♦❞❡♥❞♦✲s❡ ❝✐t❛r ♦s ♠ét♦❞♦s ❜❛s❡❛❞♦s ❡♠ ❣❡♦♠❡tr✐❛ ♥ã♦✲❧✐♥❡❛r✱ q✉❡ ✈✐s❛♠ ❛ ❧✐♥❡❛r✐③❛çã♦ ❞♦s s✐st❡♠❛s ❛tr❛✈és ❞❡ r❡❛❧✐♠❡♥t❛çã♦✱ ❡ ♦ ❝♦♥tr♦❧❡ ❜❛s❡❛❞♦ ♥❛ t❡♦r✐❛ ♣♦r ♠♦❞♦s ❞❡s❧✐③❛♥t❡s ✭❇❖❙❊✱ ✶✾✾✼✮ ❡ ✭▲❊❖◆❆❘❉✱ ✶✾✾✻✮✳

❖ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ♣♦r ♦r✐❡♥t❛çã♦ ❞♦ ✢✉①♦ ♠❛❣♥ét✐❝♦ ❞❡ r♦✲ t♦r tr❛♥s❢♦r♠❛ ❛ ❡str✉t✉r❛ ❞❡ ❝♦♥tr♦❧❡ ❞♦ ♠♦t♦r ❞❡ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛ s❡♠❡❧❤❛♥t❡ ❛♦ ❞♦ ♠♦t♦r ❞❡ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛✱ ❝♦♠ ❡①❝✐t❛çã♦ s❡♣❛r❛❞❛ ❡✱ ❞❡ss❡ ♠♦❞♦✱ ♦s ❛❝✐♦♥❛♠❡♥t♦s ❡❧étr✐❝♦s ❞❡ ❝♦rr❡♥t❡ ❛❧t❡r♥❛❞❛ ♣❛ss❛♠ ❛ t❡r ✉♠ ❞❡s❡♠♣❡♥❤♦ ❝♦♠♣❛rá✈❡❧ ❛♦ ❞❛s ♠áq✉✐♥❛s ❞❡ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛ ❝♦♠ ❡①❝✐t❛çã♦ s❡♣❛r❛❞❛ ✭❇■▼✱ ✷✵✶✷✮✳

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✷✾

❆♣❡s❛r ❞♦ s✉r❣✐♠❡♥t♦ ❞❛s té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ♥❛ ❞é❝❛✲ ❞❛ ❞❡ ✼✵✱ ❛ ♥❡❝❡ss✐❞❛❞❡ ❞❡ ❤❛r❞✇❛r❡ ❡ s♦❢t✇❛r❡ ❞❡ ❝♦♥tr♦❧❡ ❝♦♠♣❧❡①♦s ✜③❡r❛♠ ❝♦♠ q✉❡ ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❞❡st❛s té❝♥✐❝❛s ❢♦ss❡♠ ❛❞✐❛❞❛s ♣♦r ❝❡r❝❛ ❞❡ ✶✵ ❛♥♦s✳ ❖s ❛✈❛♥ç♦s ♥❛ ár❡❛ ❞❡ ❡❧❡trô♥✐❝❛ ❞❡ ♣♦tê♥❝✐❛ ❡ ♥❛ t❡❝♥♦❧♦❣✐❛ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦ ❞✐❣✐t❛❧ ❞❡ s✐♥❛✐s✱ ❛❧❝❛♥ç❛❞♦s ♥❛s ❞✉❛s ú❧✲ t✐♠❛s ❞é❝❛❞❛s✱ ✈✐❡r❛♠ ❛ s✉♣r✐r ❡ss❛s ♥❡❝❡ss✐❞❛❞❡s✱ t♦r♥❛♥❞♦ ♣♦ssí✈❡❧ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❡ ❡①♣❛♥sã♦ ❞❛s té❝♥✐❝❛s ❞❡ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ✭❙❚❖P❆✱ ✶✾✾✼✮✳

❆ ❞✐s♣♦♥✐❜✐❧✐❞❛❞❡ ❞❡ ❝❤❛✈❡s ❞❡ ♣♦tê♥❝✐❛ ❞❡ ❡st❛❞♦ só❧✐❞♦ ❛❧t❡r♦✉ ❡ss❡ q✉❛❞r♦ ✐♠❡♥s❛♠❡♥t❡✳ ❆❣♦r❛✱ é ♣♦ssí✈❡❧ ❞❡s❡♥✈♦❧✈❡r ❛ ❡❧❡trô♥✐❝❛ ❞❡ ♣♦tê♥❝✐❛ ❝❛♣❛③ ❞❡ ❢♦r♥❡❝❡r ♦ ❛❝✐♦♥❛♠❡♥t♦ ❞❡ t❡♥sã♦✱ ❝♦rr❡♥t❡ ❡ ❢r❡q✉ê♥✲ ❝✐❛ ✈❛r✐á✈❡✐s ♥❡❝❡ssár✐♦ ♣❛r❛ s❡ ♦❜t❡r ✉♠ ❞❡s❡♠♣❡♥❤♦ ❞❡ ✈❡❧♦❝✐❞❛❞❡ ✈❛r✐á✈❡❧ ❡♠ ♠áq✉✐♥❛s ❈❆✳ ❆t✉❛❧♠❡♥t❡✱ ❛s ♠áq✉✐♥❛s ❈❆ s✉❜st✐t✉ír❛♠ ❛s ♠áq✉✐♥❛s ❈❈ ❡♠ ♠✉✐t❛s ❞❛s ❛♣❧✐❝❛çõ❡s ♠❛✐s tr❛❞✐❝✐♦♥❛✐s✱ ❡ ✉♠❛ ❛♠✲ ♣❧❛ ❣❛♠❛ ❞❡ ♥♦✈❛s ❛♣❧✐❝❛çõ❡s s❡ ❞❡s❡♥✈♦❧✈❡✉ ✭❋■❚❩●❊❘❆▲❉❀ ❑■◆●❙▲❊❨❀ ❯▼❆◆❙✱ ✷✵✵✻✮✳

❆t✉❛❧♠❡♥t❡ ❛ ♠áq✉✐♥❛ ❞❡ ✐♥❞✉çã♦ é ✉t✐❧✐③❛❞❛ ❡♠ ✉♠❛ ❛♠♣❧❛ ✈❛r✐❡❞❛❞❡ ❞❡ ❛♣❧✐❝❛çõ❡s✱ ❝♦♠♦ ✉♠ ♠❡✐♦ ❞❡ ❝♦♥✈❡rsã♦ ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ♣❛r❛ tr❛❜❛❧❤♦ ♠❡❝â♥✐❝♦✱ s❡♥❞♦ s❡♠ ❞ú✈✐❞❛✱ ♦ ❡❧❡♠❡♥t♦ ♠❛✐s ✉t✐❧✐③❛❞♦ ❝♦♠ ❡st❡ ♣r♦♣ós✐t♦ ❞♦ s❡t♦r ❞❡ ❡♥❡r❣✐❛ ❡❧étr✐❝❛ ✭❑❘❆❯❙❊❀ ❲❆❙❨◆❈❩❯❑❀ ❙❯❉❍❖❋❋✱ ✶✾✾✺✮✳ ❆s ♠áq✉✐♥❛s ❞❡ ✐♥❞✉çã♦ sã♦ ♠✉✐t♦ ✉t✐❧✐③❛❞❛s ♣♦r s❡r❡♠ ♠❛✐s ❜❛r❛t❛s✱ ♠❛✐s r♦❜✉st❛s ❡ ♠❡♥♦r❡s q✉❛♥❞♦ ❝♦♠♣❛r❛❞❛s às ♠áq✉✐♥❛s ❞❡ ❝♦rr❡♥t❡ ❝♦♥tí♥✉❛ ❡ sí♥❝r♦♥❛s ❞❡ ♠❡s♠❛ ♣♦tê♥❝✐❛ ✭❇■▼✱ ✷✵✶✷✮✳

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✸✵

❞❡ ❇ü♥t❡ ❡ ❍✳ ●r♦tst♦❧❧❡♥ ✭✶✾✾✸✮ ✱ ❈♦✐r❛✉❧t✱ ❚r✐❣❡❛ss♦✉✱ ❑✬❡r✐❣♥❛r❞ ❡ ●❛✉❜❡rt ✭✶✾✾✻✮ ✱ ❑✇♦♥✱ ▲❡❡✱ ▼♦♦♥✱ ❑✇♦♥ ❡ ❈❤♦✐ ✭✷✵✵✾✮ ✱ ❈♦rt❛❥❛♥❡r❛✱ ▼❛r❝♦s✱ ❆❧✈❛r❡③ ❡ ❱✐❝❛♥❞✐ ✭✷✵✶✵✮ ✳ ◆❡st❡ tr❛❜❛❧❤♦✱ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♠ét♦❞♦s ❜❛s❡❛❞♦s ♥♦ ❡st✐♠❛❞♦r ✈✐❛ ♠í♥✐♠♦s q✉❛❞r❛❞♦s ❡ s✉❛s ✈❛r✐❛çõ❡s ♥♦ ✐♥t✉✐t♦ ❞❡ ❡st✐♠❛r ♦s ♣❛râ♠❡tr♦s ❞♦ ♠♦t♦r✱ ♣❛r❛ q✉❡ s❡❥❛ ♣♦ssí✈❡❧ ❡♠ ✉♠ s❡❣✉♥❞♦ ♠♦♠❡♥t♦✱ ❛♣r✐♠♦r❛r ❛ ❞✐♥â♠✐❝❛ ❞❡ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝♦✳

❖ ♣r❡s❡♥t❡ tr❛❜❛❧❤♦ ❡stá ♦r❣❛♥✐③❛❞♦ ❡♠ ✼ ❝❛♣ít✉❧♦s✱ ❞❡ ❢♦r♠❛ ❛ ❛❜♦r❞❛r ❝❛❞❛ ❡t❛♣❛ ❞✐st✐♥t❛ ❡♥✈♦❧✈✐❞❛ ♥♦ ♣r♦❝❡ss♦ ❞❡s❞❡ ❛ ♠♦❞❡✲ ❧❛❣❡♠ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦✱ ❛ s✐♠✉❧❛çã♦ ❞❛ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❡ ❡str❛té❣✐❛ ❞❡ ❝♦♥tr♦❧❡ ❛té ❛ ✐♠♣❧❡♠❡♥t❛çã♦ ❡ r❡s✉❧t❛❞♦s ♣rát✐❝♦s✳

◆♦ ❝❛♣ít✉❧♦ ✷✱ ❛ ♣❛rt✐r ❞❛s ❡q✉❛çõ❡s ❞♦s ❝✐r❝✉✐t♦s ❞♦ ♠♦❞❡❧♦ ❞❛ ♠áq✉✐♥❛ ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝❛✱ ❛♣r❡s❡♥t❛✲s❡ ❛s ❡①♣r❡ssõ❡s ♠❛t❡♠át✐❝❛s q✉❡ ❞❡s❝r❡✈❡♠ ♦ ❝♦♠♣♦rt❛♠❡♥t♦ ❞♦ ♠♦t♦r✳ P♦r ♠❡✐♦ ❞❡ tr❛♥s❢♦r♠❛çõ❡s ❞❡ ❝♦♦r❞❡♥❛❞❛s✱ sã♦ t❛♠❜é♠ ❞❡s❝r✐t♦s ♦s ♠♦❞❡❧♦s ❜✐❢ás✐❝♦s ♥♦ r❡❢❡r❡♥✲ ❝✐❛❧ ❡st❛❝✐♦♥ár✐♦✱ sí♥❝r♦♥♦ ❛♦ ❝❛♠♣♦ ❣✐r❛♥t❡ ❡ r♦tór✐❝♦✳ ❊ss❡s ♠♦❞❡❧♦s ❜✐❢ás✐❝♦s sã♦ út❡✐s ♥❛ ❢♦r♠✉❧❛çã♦ ❞♦ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧✱ ❡str❛té❣✐❛ q✉❡ ❢♦✐ ❛❞♦t❛❞❛ ♥♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❡st❡ tr❛❜❛❧❤♦✳

◆♦ ❝❛♣ít✉❧♦ ✸ s❡rã♦ r❡❛❧✐③❛❞❛s ❛♥á❧✐s❡s ❞♦ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧✱ s✉❛s ❞❡✜♥✐çõ❡s✱ ❡①♣r❡ssõ❡s ❡ ❢♦r♠❛s ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦✳ ◆❡st❡ ❝♦♥t❡①t♦ s❡rã♦ ❝♦♠♣❛r❛❞❛s ❞✉❛s ❝❛t❡❣♦r✐❛s ❞✐st✐♥t❛s ❞❡ ✐♠♣❧❡♠❡♥t❛çã♦ ❞♦ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧✿ ❛ ❞✐r❡t❛ ❡ ❛ ✐♥❞✐r❡t❛✳

◆♦ ❝❛♣ít✉❧♦ ✹ é ❞❡s❝r✐t♦ ♦ ❝♦♥tr♦❧❡ ❛❞❛♣t❛t✐✈♦ ✉t✐❧✐③❛❞♦ ♥♦ ♠♦✲ t♦r ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝♦✳ ❆ ❡st✐♠❛çã♦ ❞♦s ♣❛râ♠❡tr♦s ❡❧étr✐❝♦s ❞♦ ♠♦t♦r é r❡❛❧✐③❛❞♦ ♣♦r ♠❡✐♦ ❞❡ ✉♠❛ ♠ét♦❞♦ ❞❡♥♦♠✐♥❛❞♦ ▼í♥✐♠♦s ◗✉❛❞r❛❞♦s ❘❡❝✉rs✐✈♦s ✭▼◗❘✮✱ ♦♥❞❡ s❡rá ❞❛❞❛ ê♥❢❛s❡ ♥❛ té❝♥✐❝❛ r❡❝✉rs✐✈❛ q✉❡ s❡rá ✉t✐❧✐③❛❞❛ ♦♥❧✐♥❡ ♣❛r❛ ❛t✉❛❧✐③❛çã♦ ❡♠ t❡♠♣♦ r❡❛❧ ❞♦s ❣❛♥❤♦s ❞♦ ❝♦♥tr♦✲ ❧❛❞♦r ❛❞❛♣t❛t✐✈♦✳

◆♦ ❝❛♣ít✉❧♦ ✺✱ s❡rã♦ ✉t✐❧✐③❛❞♦s ♦s ❝♦♥❝❡✐t♦s ❛♣r❡s❡♥t❛❞♦s ♥❛s s❡çõ❡s ❛♥t❡r✐♦r❡s ♣❛r❛ ♦ ❞❡s❡♥✈♦❧✈✐♠❡♥t♦ ❞❛s s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s✳ ❙❡rã♦ ❛♣r❡s❡♥t❛❞❛s ❛s ❡st✐♠❛çõ❡s ♦❜t✐❞❛s ♣❡❧♦ ▼◗❘ ❡ ❛ r❡s♣♦st❛ ❞♦ ❝♦♥tr♦❧❡ ✈❡t♦r✐❛❧ ✐♠♣❧❡♠❡♥t❛❞♦✳

◆♦ ❝❛♣ít✉❧♦ ✻ s❡rá r❡❛❧✐③❛❞❛ ✉♠❛ ❛❜♦r❞❛❣❡♠ ❞♦ ❤❛r❞✇❛r❡ ✉t✐✲ ❧✐③❛❞♦ ♣❛r❛ ❛ ❛♣❧✐❝❛çã♦ ♣rát✐❝❛✱ s❛❧✐❡♥t❛♥❞♦ s✉❛s ❝❛r❛❝t❡ríst✐❝❛s ❡ ❝❛✲ ♣❛❝✐❞❛❞❡ ❞❡ ♣r♦❝❡ss❛♠❡♥t♦✳ ❚❛♠❜é♠ s❡rã♦ ❛♣r❡s❡♥t❛❞♦s ♦s r❡s✉❧t❛❞♦s ♣rát✐❝♦s ♦❜t✐❞♦s✱ ❞❡ ♠♦❞♦ ❛ ❝♦♠♣❛r❛r ❝♦♠ ❛s s✐♠✉❧❛çõ❡s ♥✉♠ér✐❝❛s ❡ ✈❛❧✐❞❛r ♦ s✐st❡♠❛ ♣r♦❥❡t❛❞♦✳

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✸✶

✷ ▼❖❉❊▲❆●❊▼ ❉❖ ▼❖❚❖❘ ❉❊ ■◆❉❯➬➹❖ ❚❘■❋➪❙■❈❖

◆❡st❛ s❡çã♦ é ❛♣r❡s❡♥t❛❞❛ ❛ ♠♦❞❡❧❛❣❡♠ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝♦✳ ■♥✐❝✐❛❧♠❡♥t❡ ❛s ❡q✉❛çõ❡s q✉❡ r❡♣r❡s❡♥t❛♠ ❛ ♣❧❛♥t❛ ❡♠ ❡s✲ t✉❞♦ sã♦ ❞❡s❡♥✈♦❧✈✐❞❛s ❡♠ ✉♠ s✐st❡♠❛ ❞❡ ❝♦♦r❞❡♥❛❞❛s tr✐❢ás✐❝♦✱ q✉❡ sã♦ ❜❛s❡❛❞❛s ♥❛s ❡q✉❛çõ❡s ❝✐r❝✉✐t❛✐s ❞❛ ♠áq✉✐♥❛ ❞❡ ✐♥❞✉çã♦✳ P♦st❡r✐✲ ♦r♠❡♥t❡✱ ❞❡ ♠♦❞♦ ❛ s✐♠♣❧✐✜❝❛r ♦ ♠♦❞❡❧♦✱ s❡rá ❛♣r❡s❡♥t❛❞♦ ✉♠ ❡st✉❞♦ q✉❡ r❡♣r❡s❡♥t❛ ❛ ♠áq✉✐♥❛ ❡♠ ✉♠ s✐st❡♠❛ ❜✐❢ás✐❝♦ ❡q✉✐✈❛❧❡♥t❡ ❞♦ ♣♦♥t♦ ❞❡ ✈✐st❛ ♠❛❣♥ét✐❝♦ ❡ ❞❛ ♣♦tê♥❝✐❛ ❛❜s♦r✈✐❞❛✳

❖ ❡q✉❛❝✐♦♥❛♠❡♥t♦ ❞♦ ♠♦t♦r ❞❡ ✐♥❞✉çã♦ ♣♦❞❡ s❡r ❡s❝r✐t♦ t♦♠❛♥✲ ❞♦✲s❡ ♣♦r ❜❛s❡ três r❡❢❡r❡♥❝✐❛s ❞✐❢❡r❡♥t❡s✱ q✉❡ sã♦ ❞❡♥♦♠✐♥❛❞❛s ✭❲❊■◆✲ ●❆❘❚◆❊❘✱ ✷✵✵✼✮✿

• ❙✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ❡st❛❝✐♦♥ár✐♦ ✕ q✉❛♥❞♦ ❛s ❣r❛♥❞❡③❛s sã♦ r❡❢❡✲

r❡♥❝✐❛❞❛s ❛♦ ❡✐①♦ ✜①♦ ❞♦ ❡st❛t♦r❀

• ❙✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ ♠ó✈❡❧ ✕ q✉❛♥❞♦ ❛s ❣r❛♥❞❡③❛s sã♦ t♦❞❛s r❡❢❡✲

r❡♥❝✐❛❞❛s ❛♦ ❡✐①♦ ♠ó✈❡❧ ❞♦ r♦t♦r❀

• ❙✐st❡♠❛ ❞❡ r❡❢❡rê♥❝✐❛ sí♥❝r♦♥♦ ✕ q✉❛♥❞♦ ❛s ❣r❛♥❞❡③❛s sã♦ r❡❢❡r❡♥❝✐❛✲

❞❛s ❛♦ ❝❛♠♣♦ ❣✐r❛♥t❡ ❞♦ ❡st❛t♦r✳

P❛r❛ ❝❤❡❣❛r ❛ ✉♠ ♠♦❞❡❧♦ ♠❛t❡♠át✐❝♦ ❛♥❛❧ít✐❝♦ r❡♣r❡s❡♥t❛♥t❡ ❞❡ ✉♠ ▼♦t♦r ❞❡ ■♥❞✉çã♦ ❚r✐❢ás✐❝♦ ✭▼■❚✮✱ é ♥❡❝❡ssár✐♦ ❛ss✉♠✐r ❛❧❣✉✲ ♠❛s ❤✐♣ót❡s❡s ❞❡ s✐♠♣❧✐✜❝❛çã♦ ✭❇❆❘❇■✱ ✶✾✽✺✮✱ ✭❈❆❱❆▲❈❆ ❡t ❛❧✳✱ ✷✵✶✸✮✳ ◆❡st❡ tr❛❜❛❧❤♦✱ s❡❣✉✐♥❞♦ ❛s ♣r♦♣♦st❛s ❛♣r❡s❡♥t❛❞❛s ❡♠ ✭❇❆❘❇■✱ ✶✾✽✺✮✱ ❛ ♦❜t❡♥çã♦ ❞♦ ♠♦❞❡❧♦ ❞❛ ♠áq✉✐♥❛ é r❡❛❧✐③❛❞❛ ❝♦♠ ❛s s❡❣✉✐♥t❡s ❝♦♥s✐✲ ❞❡r❛çõ❡s✿

•❖s ❡♥r♦❧❛♠❡♥t♦s ❡st❛tór✐❝♦s sã♦ ✐❞ê♥t✐❝♦s ❡ ✐❣✉❛❧♠❡♥t❡ ❞❡❢❛s❛❞♦s ❡♥✲

tr❡ s✐❀

•❖s ❡♥r♦❧❛♠❡♥t♦s r♦tór✐❝♦s sã♦ ✐❞ê♥t✐❝♦s ❡ ✐❣✉❛❧♠❡♥t❡ ❞❡❢❛s❛❞♦s ❡♥tr❡

s✐❀

• ❖ ❡♥tr❡❢❡rr♦ é ❝♦♥st❛♥t❡❀

• ❖ ♠❛t❡r✐❛❧ ❢❡rr♦♠❛❣♥ét✐❝♦ ♥ã♦ s♦❢r❡ s❛t✉r❛çã♦❀

• ❆ ❞❡♥s✐❞❛❞❡ ❞❡ ✢✉①♦ ♠❛❣♥ét✐❝♦ ♥♦ ❡♥tr❡❢❡rr♦ só ❛♣r❡s❡♥t❛ ❝♦♠♣♦✲

♥❡♥t❡ r❛❞✐❛❧ ❡ s✉❛ ❞✐str✐❜✉✐çã♦ ❡s♣❛❝✐❛❧ é ❝♦♥s✐❞❡r❛❞❛ s❡♥♦✐❞❛❧❀

• ◆ã♦ s❡rã♦ ❝♦♥s✐❞❡r❛❞❛s ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s✳

✷✳✶ ▼❖❉❊▲❖ ❚❘■❋➪❙■❈❖

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✸✷

s❡rã♦ ♦♠✐t✐❞❛s ❛q✉✐ ❛ ♥♦t❛çã♦ q✉❡ r❡♣r❡s❡♥t❛ s✐♥❛✐s ❝♦♥tí♥✉♦s ♥♦ t❡♠♣♦ ✲(t)✳

❋✐❣✉r❛ ✶ ✕ ❘❡♣r❡s❡♥t❛çã♦ ❡sq✉❡♠át✐❝❛ ❞❛ ♠áq✉✐♥❛ tr✐❢ás✐❝❛

Las i as

L bs

ibs

Lcs

ics

Lar iar

Lbr

ibr

Lcr

icr

ωr

θr

❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❇❆❘❇■✱ ✶✾✽✺✮ ♦♥❞❡✿

•Las✱Lbs❡Lcs r❡♣r❡s❡♥t❛♠ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞♦ ❡st❛t♦r❀

•Lar✱Lbr ❡Lcr r❡♣r❡s❡♥t❛♠ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞♦ r♦t♦r❀

•ωré ❛ ✈❡❧♦❝✐❞❛❞❡ ❛♥❣✉❧❛r ♠❡❝â♥✐❝❛ ❞♦ r♦t♦r✳ ❆ ♣♦s✐çã♦ ❛♥❣✉❧❛r ❞♦ r♦t♦r ✭θr✮ é ❞❛❞❛ ♣♦r✿

θr= Z

npωrdt+θr0 ✭✷✳✶✮

s❡♥❞♦ q✉❡np é ♦ ♥ú♠❡r♦ ❞❡ ♣❛r❡s ❞❡ ♣♦❧♦s ❞♦ ♠♦t♦r ❡ θr0 é ❛ ♣♦s✐çã♦

✐♥✐❝✐❛❧ ❞♦ r♦t♦r✳

(35)

✸✸

Las= Lbs= Lcs= Labcs

Lar = Lbr= Lcr= Labcr

Mas= Mbs= Mcs= Ms

Mar = Mbr= Mcr= Mr

Ras= Rbs= Rcs= Rs

Rar = Rbr= Rcr= Rr

✭✷✳✷✮

♦♥❞❡✿

• Labcs✿ ✐♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❡ ❡st❛t♦r✱ ♣♦r ❢❛s❡❀

• Labcr✿ ✐♥❞✉tâ♥❝✐❛ ♣ró♣r✐❛ ❞❡ r♦t♦r✱ ♣♦r ❢❛s❡❀

• Ms✿ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❞✉❛s ❢❛s❡s ❞❡ ❡st❛t♦r❀

• Mr✿ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ❞✉❛s ❢❛s❡s ❞❡ r♦t♦r❀

• Rs✿ r❡s✐stê♥❝✐❛ ❞❡ ❡st❛t♦r✱ ♣♦r ❢❛s❡❀

• Rr✿ r❡s✐stê♥❝✐❛ ❞❡ r♦t♦r✱ ♣♦r ❢❛s❡✳

❆s ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ❡♥tr❡ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞❡ ❡st❛t♦r ❡ r♦t♦r sã♦ ❢✉♥çõ❡s s❡♥♦✐❞❛✐s ❞❛ ♣♦s✐çã♦ ❛♥❣✉❧❛r✱θr✱ ❝♦♠♦ s❡❣✉❡✿

Mas−ar=Msra1 Mas−br=Msra2 Mas−cr=Msra3 Mbs−ar =Msra3 Mbs−br=Msra1 Mbs−cr=Msra2 Mcsar =Msra2 Mcsbr=Msra3 Mcscr=Msra1

✭✷✳✸✮

♦♥❞❡✿

• Msr✿ ✐♥❞✉tâ♥❝✐❛ ♠út✉❛ ❡♥tr❡ ✉♠❛ ❢❛s❡ ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r❀

• a1=cosθr❀ • a2=cos θr+23π

• a3=cos θr−23π✳

P♦r ♠❡✐♦ ❞❛ ❛♣❧✐❝❛çã♦ ❞❛s ❧❡✐s ❞❡ ❑✐r❝❤❤♦✛ ❛♦s ❝✐r❝✉✐t♦s ❡❧étr✐✲ ❝♦s ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r✱ ❡♥❝♦♥tr❛♠✲s❡ ❛s s❡❣✉✐♥t❡s ❡q✉❛çõ❡s✱ ♥❛ ❢♦r♠❛ ♠❛tr✐❝✐❛❧ ❝♦♠♣❛❝t❛✿

VVVabcs=RRRabcsIIIabcs+ ˙φφφ˙˙abcs ✭✷✳✹✮

V

(36)

✸✹

s❡♥❞♦ q✉❡✿

VVVabcs= vas vbs vcs T

; VVVabcr= var vbr vcr

T ✭✷✳✻✮

IIIabcs= ias ibs ics T

; IIIabcr= iar ibr icr

T ✭✷✳✼✮

R R Rabcs=

Rs 0 0

0 Rs 0

0 0 Rs

 ; RRRabcr= 

Rr 0 0

0 Rr 0

0 0 Rr

 ✭✷✳✽✮

˙

φ˙ φφ˙abcs=

d

dtφφφabcs= d dt

φas φbs φcs

T ✭✷✳✾✮

˙

φφφ˙˙abcr=

d

dtφφφabcr= d dt

φar φbr φcr

T ✭✷✳✶✵✮

•φφφabcs ❡φφφabcr sã♦✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s ✈❡t♦r❡s ❞❡ ✢✉①♦ ❡♥❧❛ç❛❞♦ ❝♦♠ ♦s ❡♥r♦❧❛♠❡♥t♦s ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r❀

•VVVabcs ❡VVVabcr r❡♣r❡s❡♥t❛♠✱ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s ✈❡t♦r❡s ❞❡ t❡♥sã♦ ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r❀

•IIIabcs❡IIIabcrsã♦ ♦s ✈❡t♦r❡s ❞❡ ❝♦rr❡♥t❡ ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r❀

•RRRabcsé ❛ ♠❛tr✐③ ❞❡ r❡s✐stê♥❝✐❛s ❞❡ ❡st❛t♦r❀

•RRRabcré ❛ ♠❛tr✐③ ❞❡ r❡s✐stê♥❝✐❛s r♦tór✐❝❛s✳

❖s ✈❡t♦r❡s ❞❡ ✢✉①♦ ❡♥❧❛ç❛❞♦✱φφφabcs❡φφφabcr✱ ♣♦❞❡♠ s❡r ❡s❝r✐t♦s ❝♦♠♦✿

φφφabcs=LLLabcsIIIabcs+MMMsrIIIabcr ✭✷✳✶✶✮

φφφabcr=LLLabcrIIIabcr+MMMrsIIIabcs ✭✷✳✶✷✮ ♦♥❞❡ ❛s ♠❛tr✐③❡s ❞❡ ✐♥❞✉tâ♥❝✐❛s ❞❡ ❡st❛t♦r ❡ r♦t♦r sã♦✿

LLLabcs= 

Labcs Ms Ms

Ms Labcs Ms

Ms Ms Labcs 

(37)

✸✺

LLLabcr= 

Labcr Mr Mr

Mr Labcr Mr

Mr Mr Labcr 

 ✭✷✳✶✹✮

❡ ❛ ♠❛tr✐③ ❞❡ ✐♥❞✉tâ♥❝✐❛s ♠út✉❛s ❡st❛t♦r✲r♦t♦r é✿

M M

Msr=Msr 

 

cosθr cos θr+23π

cos θr−23π

cos θr−23π cosθr cos θr+23π

cos θr+23π

cos θr−23π

cosθr 

 ✭✷✳✶✺✮

M M

Msr ❡MMMrs tê♠ ❛ s❡❣✉✐♥t❡ r❡❧❛çã♦ ❡♥tr❡ s✐✿

MMMrs=MMMTsr ✭✷✳✶✻✮ ❆s ❞❡r✐✈❛❞❛s t❡♠♣♦r❛✐s ❞♦s ✢✉①♦s ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r✱ ♦❜t✐❞❛s ❞❡ ✭✷✳✶✶✮ ❡ ✭✷✳✶✷✮✱ sã♦✿

˙

φ˙

φφ˙abcs=LLLabcsIII˙˙˙abcs+MMMsrIII˙˙˙abcr+ ˙θr

∂MMMsr

∂θr

IIIabcr ✭✷✳✶✼✮

˙

φ˙ φ˙

φabcr=LLLabcrIII˙˙˙abcr+MMMrsIII˙˙˙abcs+ ˙θr

∂MMMrs

∂θr

IIIabcs ✭✷✳✶✽✮ ❉❡st❡ ♠♦❞♦✱ r❡❛❧✐③❛♥❞♦ ❛ s✉❜st✐t✉✐çã♦ ❞❡ ✭✷✳✶✼✮ ❡♠ ✭✷✳✹✮ ❡ ❞❡ ✭✷✳✶✽✮ ❡♠ ✭✷✳✺✮✱ ❛s ❡q✉❛çõ❡s ❞❛s t❡♥sõ❡s ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r r❡s✉❧t❛♠✱

V

VVabcs=RRRabcsIIIabcs+LLLabcsIII˙˙˙abcs+MMMsrIII˙˙˙abcr+ ˙θr

∂MMMsr

∂θr

IIIabcr ✭✷✳✶✾✮

V V

Vabcr=RRRabcrIIIabcr+LLLabcrIII˙˙˙abcr+MMMrsIII˙˙˙abcs+ ˙θr

∂MMMrs

∂θr

IIIabcs ✭✷✳✷✵✮ ❆ r❡❧❛çã♦ ♠♦t♦r✲❝❛r❣❛ ♣♦❞❡ s❡r ♠♦❞❡❧❛❞❛ ❞❛ s❡❣✉✐♥t❡ ❢♦r♠❛✿

(38)

✸✻

♦♥❞❡✿

•τm✲ r❡♣r❡s❡♥t❛ ♦ t♦rq✉❡ ❡❧❡tr♦♠❛❣♥ét✐❝♦❀

•Bωr✲ ♦ t♦rq✉❡ ❛ss♦❝✐❛❞♦ às ♣❡r❞❛s ♠❡❝â♥✐❝❛s ❞♦ ♠♦t♦r❀

•B ✲ é ♦ ❝♦❡✜❝✐❡♥t❡ ❞❡ ❛tr✐t♦ ✈✐s❝♦s♦ ♥♦ ❡✐①♦ ❞♦ ♠♦t♦r❀

•Jω˙r ✲ é ♦ t♦rq✉❡ ❛❝❡❧❡r❛♥t❡ ❞♦ s✐st❡♠❛ ♠♦t♦r✲❝❛r❣❛ ✭J é ♦ ♠♦♠❡♥t♦ ❞❡ ✐♥ér❝✐❛ ❞♦ s✐st❡♠❛✮❀

•τc ✲ é ♦ t♦rq✉❡ r❡s✐st❡♥t❡ ❞❡ ❝❛r❣❛✳

❆ ❡q✉❛çã♦ ❞❛ ♣♦tê♥❝✐❛ ❛❜s♦r✈✐❞❛ ♣❡❧♦ ♠♦t♦r ❞❛ r❡❞❡ ❡❧étr✐❝❛ é✿

Pt=IIITabcsVVVabcs+IIITabcrVVVabcr ✭✷✳✷✷✮ ❉❡st❛ ❢♦r♠❛ ❛ s✉❜st✐t✉✐çã♦ ❞❡ ✭✷✳✶✾✮ ❡ ✭✷✳✷✵✮ ❡♠ ✭✷✳✷✷✮✿

Pt=IIITabcsRRRabcsIIIabcs+IIITabcsLLLabcsIII˙˙˙abcs+IIITabcsMMMsrIII˙˙˙abcr

+IIIT abcs

∂MMMsr

∂θr

IIIabcrθ˙r+IIITabcrRRRabcrIIIabcr+IIITabcrLLLabcrIII˙˙˙abcr

+IIITabcrMMMrsIII˙˙˙abcs+IIITabcr

∂MMMrs

∂θr

IIIabcsθ˙r

✭✷✳✷✸✮

❉❛ ♣♦tê♥❝✐❛ t♦t❛❧ q✉❡ ♦ ♠♦t♦r ❛❜s♦r✈❡✱ ✉♠❛ ♣❛rt❡ é ❞✐ss✐✲ ♣❛❞❛ ❡♠ ❝❛❧♦r✱ ♦✉tr❛ ✜❝❛ ❛r♠❛③❡♥❛❞❛ ♥♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ❡ ♦ r❡st❛♥t❡ tr❛♥s❢♦r♠❛✲s❡ ❡♠ t♦rq✉❡ ❡❧❡tr♦♠❛❣♥ét✐❝♦✳ ❆s ♣❛r❝❡❧❛s ❝♦rr❡s♣♦♥❞❡♥t❡s às ♣❡r❞❛s ❏♦✉❧❡ ❞❡ ❡st❛t♦r ❡ ❞❡ r♦t♦r sã♦ ❢❛❝✐❧♠❡♥t❡ ✐❞❡♥t✐✜❝❛❞❛s ♣❡❧♦s t❡r♠♦sIIIT

abcsRRRabcsIIIabcs❡IIITabcrRRRabcrIIIabcr✳ ◆❛s ❤✐♣ót❡s❡s s✐♠♣❧✐✜❝❛❞♦r❛s ❞❛ ♠♦❞❡❧❛❣❡♠ ♥ã♦ ❢♦r❛♠ ❝♦♥s✐❞❡r❛❞❛s ❛s ♣❡r❞❛s ♠❛❣♥ét✐❝❛s✳

❆ ❡♥❡r❣✐❛ ❛r♠❛③❡♥❛❞❛ ♥♦ ❝❛♠♣♦ ♠❛❣♥ét✐❝♦ ♣♦❞❡ s❡r ❡s❝r✐t❛ ❝♦♠♦✿

W = 1 2III

T

abcsLLLabcsIIIabcs+

1 2III

T

abcrLLLabcrIIIabcr

+1

2III

T

abcsMMMsrIIIabcr+

1 2III

T

abcrMMMrsIIIabcs

✭✷✳✷✹✮

(39)

✸✼

˙

W =IIIT

abcsLLLabcsIII˙˙˙abcs+IIITabcrLLLabcrIII˙˙˙abcr+

1 2III

T

abcsMMMsrIII˙˙˙abcr

+1

2III

T

abcrMMMrsIII˙˙˙abcs+

1 2III

T abcs

∂MMMsr

∂θr

˙

I˙ I˙

Iabcrθ˙r+

1 2III

T

abcrMMMrsIII˙˙˙abcs

+1

2III

T

abcsMMMsrIII˙˙˙abcr+

1 2III

T abcr

∂MMMrs

∂θr

IIIabcsθ˙r

✭✷✳✷✺✮

❡ ✭✷✳✷✸✮ ♣♦❞❡ s❡r r❡❡s❝r✐t❛ ❞❛ s❡❣✉✐♥t❡ ♠❛♥❡✐r❛✿

Pt=IIITabcsRRRabcsIIIabcs+IIITabcrRRRabcrIIIabcr+ ˙W

+1

2III

T abcs

∂MMMsr

∂θr

IIIabcrθ˙r+

1 2III

T abcr

∂MMMrs

∂θr

IIIabcsθ˙r

✭✷✳✷✻✮

❝♦♠♦ ❛ s❡❣✉✐♥t❡ ✐❣✉❛❧❞❛❞❡ é ✈❡r❞❛❞❡✐r❛✱

IIITabcs

∂MMMsr

∂θr

IIIabcrθ˙r=IIITabcr

∂MMMrs

∂θr

IIIabcsθ˙r ✭✷✳✷✼✮ ❛ ❡q✉❛çã♦ ❞❛ ♣♦tê♥❝✐❛ ❛❜s♦r✈✐❞❛ ♣❡❧♦ ♠♦t♦r t♦♠❛ ❛ ❢♦r♠❛✿

Pt=IIITabcsRRRabcsIIIabcs+IIITabcrRRRabcrIIIabcr

+ ˙W +IIITabcs

∂MMMsr

∂θr

IIIabcrθ˙r

✭✷✳✷✽✮

♦♥❞❡ ♣♦❞❡ s❡r ♦❜s❡r✈❛❞♦ q✉❡ ♦ t❡r♠♦

IIIT abcs

∂MMMsr

∂θr

IIIabcrθ˙r ✭✷✳✷✾✮

❝♦rr❡s♣♦♥❞❡ à ♣♦tê♥❝✐❛ ♠❡❝â♥✐❝❛✱Pm✱ ❛ss♦❝✐❛❞❛ ❛♦ t♦rq✉❡ ❡❧❡tr♦♠❛❣♥é✲

t✐❝♦✳ ❈♦♠♦ ♦ t♦rq✉❡ ❡❧❡tr♦♠❛❣♥ét✐❝♦ é ❛ss♦❝✐❛❞♦ ❝♦♠ ❛ ♣♦tê♥❝✐❛ ♠❡❝â✲ ♥✐❝❛ ♣♦r✿

τm=

Pm

ωr ✭✷✳✸✵✮

(40)

✸✽

τm=

IIIT

abcs∂M∂θrMMsrIIIabcrθ˙r

ωr

✭✷✳✸✶✮ ❋✐♥❛❧♠❡♥t❡✱ ❝♦♠ ❛ ✉t✐❧✐③❛çã♦ ❞❛ r❡❧❛çã♦

ωr=

˙

θr

np

✭✷✳✸✷✮ ♣♦❞❡✲s❡ ♦❜t❡r ✉♠❛ ❡q✉❛çã♦ ♣❛r❛ ♦ ❝♦♥❥✉❣❛❞♦ ❡❧❡tr♦♠❛❣♥ét✐❝♦ ❡♠ ❢✉♥çã♦ ❞❛s ❝♦rr❡♥t❡s ❞❡ ❡st❛t♦r✱ ❞❛s ❝♦rr❡♥t❡s ❞❡ r♦t♦r ❡ ❞❡ ✐♥❞✉tâ♥❝✐❛s✱ ❝♦♥✲ ❢♦r♠❡ ❛ s❡❣✉✐r✿

τm=npIIITabcs

∂MMMsr

∂θr

IIIabcr ✭✷✳✸✸✮

❙✉❜st✐t✉✐♥❞♦ ✭✷✳✸✸✮ ❡♠ ✭✷✳✷✶✮✱ ❛ ❡q✉❛çã♦ ♠❡❝â♥✐❝❛ r❡s✉❧t❛ ❡♠✿

npIIITabcs

∂MMMsr

∂θr

IIIabcr=Bωr+Jω˙r+τc ✭✷✳✸✹✮ ❆ss✐♠✱ ♦ ❝♦♥❥✉♥t♦ ❞❛s ❊q✉❛çõ❡s ✭✷✳✶✾✮✱ ✭✷✳✷✵✮ ❡ ✭✷✳✸✹✮✱ ❛❣r✉✲ ♣❛❞❛s ❛ s❡❣✉✐r✱ r❡♣r❡s❡♥t❛ ♦ ♠♦❞❡❧♦ ❝♦♠♣❧❡t♦ ❞❛ ♠áq✉✐♥❛ ❞❡ ✐♥❞✉çã♦ tr✐❢ás✐❝❛✿

     

    

V V Vabcs=

V V Vabcr=

τm=

RRRabcsIIIabcs+LLLabcsIII˙˙˙abcs+MMMsrIII˙˙˙abcr+ ˙θr∂MMMθrsrIIIabcr

RRRabcrIIIabcr+LLLabcrIII˙˙˙abcr+MMMrsIII˙˙˙abcs+ ˙θr∂MMMrsθr IIIabcs

npIIITabcs ∂MMMsr

∂θr IIIabcr=Bωr+Jω˙r+τc

✭✷✳✸✺✮

(41)

✸✾

✷✳✷✳✶ ❚r❛♥s❢♦r♠❛çã♦ ●❡r❛❧ ❞♦ ❙✐st❡♠❛ ❞❡ ❈♦♦r❞❡♥❛❞❛s ❚r✐❢á✲ s✐❝♦✲❇✐❢ás✐❝♦

❆ ❋✐❣✉r❛ ✷ ♠♦str❛ ❛ r❡❧❛çã♦ ❡♥tr❡ ✉♠ s✐st❡♠❛ ❞❡ ❡♥r♦❧❛♠❡♥t♦s tr✐❢ás✐❝♦(abc)❡ ❞❡ ✉♠ s✐st❡♠❛ ❞❡ ❡♥r♦❧❛♠❡♥t♦s ❜✐❢ás✐❝♦(dq)✳

❋✐❣✉r❛ ✷ ✕ ❘❡♣r❡s❡♥t❛çã♦ ❞❡ ✉♠ s✐st❡♠❛ tr✐❢ás✐❝♦ ✭❛❜❝✮ ❡ ❞❡ ✉♠ s✐st❡♠❛ ❜✐❢ás✐❝♦ ✭❞q✮

a ϕ b

c

d ω

q

❋♦♥t❡✿ ❛❞❛♣t❛❞♦ ❞❡ ✭❋❊❘❘❆❘■✱ ✷✵✵✻✮

❖ â♥❣✉❧♦ ❡❧étr✐❝♦ ϕ ❞❛ ♣♦s✐çã♦ ❞♦ ❡✐①♦ ❞✐r❡t♦ d ❞♦ s✐st❡♠❛

❜✐❢ás✐❝♦ ❡♠ r❡❧❛çã♦ ❛♦ ❡✐①♦ a❞♦ s✐st❡♠❛ tr✐❢ás✐❝♦✱ é

ϕ=

Z

npωdt+ϕ0 ✭✷✳✸✻✮

❆ r❡❧❛çã♦ ❡♥tr❡ ❛ ❢♦rç❛ ♠❛❣♥❡t♦♠♦tr✐③ ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ ❡ ♥♦ s✐st❡♠❛ ❜✐❢ás✐❝♦ é ❞❛❞❛ ♣♦r✿

"

Fd

Fq #

=

"

cosϕ cos ϕ−2π

3

−sinϕ −sin ϕ−2π

3

cos ϕ+2π

3

−sin ϕ+2π

3

#

 

Fa

Fb

Fc 

 

✭✷✳✸✼✮

(42)

✹✵

q✉❛❧q✉❡r é ❞❛❞❛ ♣♦rF =ni✱ s❡♥❞♦n♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❡i ❛ ❝♦rr❡♥t❡

❡❧étr✐❝❛✱ ♥♦ s✐st❡♠❛ tr✐❢ás✐❝♦ s❡ ♦❜s❡r✈❛ q✉❡✱

   Fa Fb Fc   =n3

   ia ib ic    ✭✷✳✸✽✮

♦♥❞❡n3é ♦ ♥ú♠❡r♦ ❞❡ ❡s♣✐r❛s ❞❛s ❜♦❜✐♥❛s ❞♦ s✐st❡♠❛ tr✐❢ás✐❝♦✱ia✱ib❡

ic sã♦ ❛s ❝♦rr❡♥t❡s tr✐❢ás✐❝❛s✳

❉❡st❡ ♠♦❞♦ ❛ tr❛♥s❢♦r♠❛çã♦ ❞❡ ❝♦rr❡♥t❡s ❡♥tr❡ ♦s s✐st❡♠❛s tr✐❢ás✐❝♦✲❜✐❢ás✐❝♦ é✿

"

id

iq #

=n3

n2

"

cosϕ cos ϕ−2π

3

−sinϕ −sin ϕ−2π

3

cos ϕ+2π

3

−sin ϕ+2π

3 #    ia ib ic    ✭✷✳✸✾✮

♦♥❞❡n2✱n3✱id✱iq✱ia✱ib❡icsã♦ r❡s♣❡❝t✐✈❛♠❡♥t❡✱ ♦s ♥ú♠❡r♦s ❞❡ ❡s♣✐r❛s ❡ ❝♦rr❡♥t❡s ❞♦ s✐st❡♠❛ ❜✐❢ás✐❝♦ ❡ tr✐❢ás✐❝♦✳

P❛r❛ t♦r♥❛r ❛ tr❛♥s❢♦r♠❛çã♦ ✐♥✈❡rsí✈❡❧✱ ❞❡✜♥❡✲s❡ ✉♠❛ ❝♦rr❡♥t❡ ❤♦♠♦♣♦❧❛r ✭i0✮✱ s❡❣✉♥❞♦ ❛ ❡①♣r❡ssã♦✿

i0=an3 n2

(ia+ib+ic) ✭✷✳✹✵✮ ❆ ❊q✉❛çã♦ ✭✷✳✹✵✮ ❛♦ s❡r s✉❜st✐t✉í❞❛ ❡♠ ✭✷✳✸✾✮✱ t♦r♥❛✲s❡✿

   id iq i0   = n3 n2      

cosϕ cos ϕ−2π

3

−sinϕ −sin ϕ−2π

3

a a

cos ϕ+23π

−sin ϕ+2π

Figure

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