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♦❧ ✭❈❉❈ ✷✵✶✹✮

❖❘❈ ❢♦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✳ ✷ ✴ ✶✺

❈♦♥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 ✢♦✇ ˙ m exh ✭❡st✐♠❛t❡❞✮✳ ❊①❤❛✉st t❡♠♣❡r❛t✉r❡✿ T exh ✭♠❡❛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 h i ✭❢♦r ❡❛❝❤ ③♦♥❡✮ ✇❛❧❧ t❡♠♣❡r❛t✉r❡s✿ T w , 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✳ m ( h in , i − h out , i ) + ˙ ❊♥❡r❣② ❜❛❧❛♥❝❡✿ ✵ = ˙ Q f , i L i ✱ ✇❤❡r❡ ˙ Q f , i = S f α i ( T w , i − T f , i ) ❉②♥❛♠✐❝s ♦❢ t❤❡ r❡❞✉❝❡❞ ♠♦❞❡❧✿ ✇❛❧❧ ❡♥❡r❣② ❜❛❧❛♥❝❡ dt T w , i = ˙ Q exh , i − ˙ m w c w d Q f , i ✱ � � ✇❤❡r❡ ˙ ✶ − exp ( − α exh S exh Q exh , i = ˙ m exh c exh m exh c exh ) ( T exh − T w , i ) ˙ ✽ ✴ ✶✺