MODÈLE TEMPOREL SOUS FORME DE REPRÉSENTATION D'ÉTAT POUR UN HOULOGÉNÉRATEUR

HAL Id: hal-00874499

https://hal.archives-ouvertes.fr/hal-00874499

Submitted on 22 Oct 2013

HAL is a multi-disciplinary open access archive for the deposit and dissemination of sci- entific research documents, whether they are pub- lished or not. The documents may come from teaching and research institutions in France or abroad, or from public or private research centers.

L’archive ouverte pluridisciplinaire HAL, est destinée au dépôt et à la diffusion de documents scientifiques de niveau recherche, publiés ou non, émanant des établissements d’enseignement et de recherche français ou étrangers, des laboratoires publics ou privés.

MODÈLE TEMPOREL SOUS FORME DE REPRÉSENTATION D’ÉTAT POUR UN

HOULOGÉNÉRATEUR

Sébastien Olaya, Jean-Matthieu Bourgeot, Mohamed Benbouzid

To cite this version:

Sébastien Olaya, Jean-Matthieu Bourgeot, Mohamed Benbouzid. MODÈLE TEMPOREL SOUS

FORME DE REPRÉSENTATION D’ÉTAT POUR UN HOULOGÉNÉRATEUR. EMR 2013, Oct

2013, Brest, France. pp.1-5. �hal-00874499�

B725

7 !1"#7$2CA628

1%"&'7$6F$2C(3

1

234567289AB5C9672DEFCCB72D727A238F2322 2!2"7C72#74$C5%&672!'(2)65*9C2+9C472,2 569-9.7CB/012/575A.7CB/01

22CB"7BA2D727A9C72344BD7CA9672232322 2472D725759A26 2!'72!'27A267D782(2+9C47292 5$9:7D07C/5*BD.CB"9/7A01

037885*F832%78$5'732378%38#2"68"3#*1%8$2%58%385'%$'5%58"2'354*8"78.4%782%8&2%24'3'5%5 8

"37 8 8 "2#*3 8 #$25 8 3 8 #2%.#3 8 5*+ 8 35 8 "%) 8 25$7 8 27*3 8 "37 8 8 &2%F 8 2%3 8 +23 8 8 2%5 8

*##54'F878)$2*'8+*38"2)5*588$%*7738*3*"38"88.4% 8438776#8#'3*1%8"*58"8$8$*4323 5'#*65823.5*788#2%.#38*3'*5838%38#2%.#38"852*238$5#38*37*8"2355358%384'3'55* 8 73&523868*#378$5#337 892%782&$2&678"88&'25*8$23*F88$526#8"83%8688#58785'72% 8

"3788"2#*38+5'1%3*8$58%38#'&2"8"*87#*3*1%8878$5#6578&"52"3#*1%787* 878#777 8 82%'7F878#25*77#378"85"**238878++2578"2)**23987238*37*8"'5#*3'7 8438+2*7878$5#657 8 23%7F 8 32%7 8 $2%.237 8 %**75 8 8 +25#%*23 8 " 8 1%##*37 8 $2%5 8 "'5*5 8 8 #2%.#3 8 " 8 8 75%%5 8 3 8 &2% 8

*55'4%*65 838$5*3*$8*323.'3*38"88+25#8*3'452"*++'53*87885*#383%#'5*1%8"785#78" 8 23.2%*238"'5*.3878++2578"85"**238878++2578"2)**23 8438425*&#8"2*3"3*+**23878"238#*783 8

$ 8"3788"2#*38+5'1%3* 8+*38"2*3"3*+*58%38#2"6 8'1%*.38"%832% 8"823.2%*23872%78+25#8" 8 5$5'73*238"2'

!27+78C 8 A2%24'3'5%5F 8 &'25* 8 $23*F 8 +25#%*23 8 " 8 1%##*37F 8 5$5'73*23 8 "2'F 8 *"3*+**23 8 +5'1%3*

:38&*78$$5F8;8$57388*#"$3"38#2"87"8238&81%##*378+25#%*238+2588;282"8;.8354 8 23.558&8237*7782+88*3"5*8%287*"*34823488$5*87%#54"8$+25#8#"8%$82+88$83"8 8 2%#3 8<&*78#2"8*78*33""8288%7"8+258-/1823528$%5$2778*38*554%58;.823"**237 83*358$23*8*7 8 77%#"83"887#*3*8$$52&8*78$52$27"8+258&82#$%*2382+8&8&"52"3#*82++**3783"8& 8 )**23 8 +257 8 "% 8 2 8 &. 8 #2*23 8 *3 8 +*3* 8 "$& 8 ;5 8 =*.3 8 8 +51%3 8 57$237 8 +25 8 2& 8 5"**23 8 3" 8 )**238+25F823838%788+51%38"2#*38*"3*+**238425*&#8282*388$5#5*8#2"8*38&8+25#82+ 8 77$85$573*238;&*&8*78#2582##238%7"8*3823528+*"

>;25"7C8-/1F8$23*8&25F81%##*378+25#%*23F877$8#2"F8+51%38"2#*38*"3*+**23 F8A23C*82F

#$B2;5<2;92:5AB"9A7D215:2A$72C77D2A52%5"BD7292AB:79D7%7CD9CA2:5D76215292;9"727C7-245C"7A72

=362BC25D72A529C96-72BA2/7$9"B52BC2B7692;9"702#$72=362D7"B4724$7:9AB4966-2D7%B4A7D2BC2+B7 2 1245CBA2512924-6BCDB4962/5-2BDBC2BC2;9"729CD26BDBC2965C292%9AB966-2/:77D2%69A15:2:9D72%2512 9 2 %69A7 2 9CD 2 9 2 456:C0 2 3C7- 2 76ABC 2 15: 2 A$7 2 769AB"7 2 :5AB5C 2 /7A;77C 2 A$7 2 A;5 2 45C47CAB4 2 /5DB7 2 B 2 78A94A7D215:2A$72BC45:BC2;9"72/-29279/5829CD292%7:9C7CA2:9C7A2-C4$5C527C79A50

445DBC2A52>?29CD2+96C721!!@29CD2:572747CA6-2A52>#9$B%527A29602(('@29CD2>)77*29CD2+57C2 (11@26BC792:5D762/97D25C2A$726::BC215:69AB5C2>6::BC21!A@29729255D2A9ABC2%5BCA215 2 :5D766BC2A$727%5C7251292:9BC72A4A72BC2;9"70285A25C6-2A$9A2/A2BC2A$7245CA78A2512;9"727C7-2 45C"7A729A$52BC2>)77*29CD2+57C2(11@2D71BC7D2A$B2:5D7629292/9B2152BCBAB962D7BC29CD2%7DB4AB5C2 51 2 %5;7 2 49%A70 2 6::BC2 7B9AB5C2 B2 9C2 BCA759DB1177CAB96 27B9AB5C2 ;$B4$2 769A72 A$72 :5AB5C2 51 2 A$72 :9BC72A4A72A52A$72BC45:BC2;9"702575"725C472A$B2:5D762B25/A9BC7D2C5C6BC792A7:292"B45 2 D9:%BC252:55BC26BC7249C2/7279B6-2BCA5D47D2A524574A29CD2B:%5"72A$72B96BA-2512A$72:5D7602C5;7"72 A$7 2 :9BC 2 D9;/94< 2 51 2 A$B 2 15:69AB5C 2 45:7 2 15: 2 A$7 2 A;5 2 45C"56AB5C 2 A7: 2 5C7 2 7%77CABC 2 16BD2 :7:5-271174A2954B9A7D2;BA$2A$729DB9AB5C2154729CD2A$725A$727%77CABC2A$72;9"72784BA9AB5C215472D7 2 A529C2BC45::BC2;9"72>#9$B%527A29602(('@0

1

DB74A245:%A9AB5C2/97D25C292DB47A72AB:729%%58B:9AB5C2512A$7245C"56AB5C2A7:27BB72A529"727C5$2

%9A 2 D9A9 2 A5 2 7"969A7 2 A$7 2 BCA796 2 9A 2 794$ 2 A7% 2 51 2 B:69AB5C0 2 #$B 2 9%%594$ 2 49C 2 /7 2 AB:7 2 45C:BC 2 BC 2 B:69AB5C 2 9CD 2 :9- 2 7BB7 2 BCB1B49CA 2 9:5CA 2 51 2 45:%A7 2 :7:5-0 2 C 2 9%%594$ 2 A5 2 5"745:7 2 A$B2

%5/67:2B2A$727251292%99:7AB42:5D762A$9A29%%58B:9A72A$7245C"56AB5C2A7:2BC2A$726::BC27B9AB5C02 +5: 2 A$7 2 6BA79A7 2 7"B7; 2 7"796 2 BD7CAB1B49AB5C 2 4$7:7 2 $9"7 2 /77C 2 BC"7AB9A7D 2 7BA$7 2 BC 2 17B7C4- 2 D5:9BC252BC2AB:72D5:9BC02A$52BC2>#9$B%527A29602(('@29CD2>)77*29CD2+57C2(('@2%5"BD729 2 7"B7;2512DB1177CA2:7A$5D2BC2/5A$2D5:9BC2/A2:5A29AA7CAB5C2$9"72/77C27%5A7D25C29DB9AB5C215472:5D762 7AB:9AB5C02#9$B%52$5;2A$9A2BA2B2/7AA72A527217B7C4-2D5:9BC2BD7CAB1B49AB5C2/74972;7249C27BC15472 A$72BD7CAB1B49AB5C2965BA$:2/-29DDBC2%B52<C5;67D702FC2A$72C78A274AB5C2;B662B"729C25"7"B7;2512A$72

;$5672%5472A5294$B7"72A$B2AB:79D5:9BC2:5D766BC0 18618*57123655F7$*+A2CF3

2CD72A$729:%AB5C25126BC792;9"72%5A7CAB962A$75-27B9AB5C2512:5AB5C2152A$72B82D7772512177D5:2 972B"7C2BC29C279A$/5CD27177C47219:72455DBC9ABC2-A7:2;BA$2BA25BBC2326549A7D29A2A$72BCA774AB5C 2 51 2 A$7 2 CDBA/7D 2 177 2 1947 2 67"76 2 ;BA$ 2 4-6BCD7 2 987 2 9CD 2 A$7 2 998B 2 B 2 %5BAB"7 2 %;9D0 2 +5: 2 A$72 87;A5CE2745CD269;29CD2BC2:9AB82C5A9AB5C2;72$9"72

1

;$77

1 2B2A$72BBD9/5D-27C796B7D2BC7AB92:9AB820

1 2 B 2 A$7 2 7C796B*7D 2 %5BAB5C 2 "74A5 2 51 2 A$7 2 /5D-91B87D 2 19:7 2 ;BA$ 2 7%74A 2 A5 2 A$72 7BB6B/B: 2 19:7 2 ;BA$ 2 A$7 2 A$77 2 A9C69AB5C 2 B070 2 897 2 - 2 9;9- 2 * 2 9$79"7 2 9CD 2 A$7 2 A$77 2 5A9AB5C2 78%77D 2 BC 2 A7: 2 51 2 367E 2 9C67 2 B070 2 E9566 2 F9%BA4$ 2 9CD 2 G 2 9-9;0 2 2 9CD 2 2 D7C5A7 2 7%74AB"76- 2 A$72 7C796B*7D2"7654BA-29CD29447679AB5C2"74A502

1 2B2A$727C796B7D215472"74A520

#$727C796B7D215472"74A5249C2/7278%77D2BC2A7:25127"796245:%5C7CA24$29

=$77

1 2B2A$72;9"72784BA9AB5C215472954B9A7D2;BA$2A$7249AA7BC2%5/67:2;$B4$249C2/7278%77D2BC2A$7 2 AB:79D5:9BC292

;BA$ 2 2 A$7 2 ;9"7 2 767"9AB5C 2 9A 2 A$7 2 5BBC 2 9CD 2 2 B 2 A$7 2 B:%67 2 7%5C7 2 :9AB8 2 51 2 A$7 2 ;9"72 784BA9AB5C215472>?29CD2+96C721!!@02

1 2 B 2 A$7 2 9DB9AB5C 2 1547 2 954B9A7D 2 ;BA$ 2 A$7 2 9DB9AB5C 2 %5/67:0 2 FC 2 6BC79 2 %5A7CAB96 2 A$75- 2 BA 2 B2 45C"7CAB5C962A52D745:%572A$B215472BCA52A;52%9A2;$B4$297217B7C4-2D7%7CD7CA023C72B2%5%5AB5C962A52 A$729447679AB5C2512/5D-29CD29C5A$72B2%5%5AB5C962A52BA2"7654BA-29CD29727%74AB"76-27177C47D2929DD7D 2 :929CD29DB9AB5C2D9:%BC2:9AB8

B*4%58 80+*3**2387?&82+8&8-/1

;$772 2B2A$72BC1BCBA7917B7C4-29DD7D2:92:9AB82D71BC7D292

7

#$72745CD2A7:2B27177C47D292A$7216BD2:7:5-271174A29CD249%A727C7-2A9C17A215:2A$72:5AB5C251 2 A$72A4A72A52A$729DB9A7D2;9"702-27%694BC29CD245:/BCBC2A7:2BC212/-229CD2A2;725/A9BC2A$7 2 6::BC27B9AB5CH

'

;$77 2 ;7 2 9DD 2 9 2 A7: 2 2 :5D766BC 2 C5C6BC79 2 71174A 2 4$ 2 9 2 "B45 2 D9:%BC 2 5 2 :55BC 2 6BC72 96A$5$02FC2A$7215665;BC2;72;B662C5A2BC"7AB9A72A$B29%74A0229679D-2:7CAB5CC7D2BC2BCA5D4AB5C25C7251 2 A$72:9BC2D9;/94<2512A$B215:69AB5C2B2A$7245C"56AB5C2A7:2;$B4$2972C5A245C"7CB7CA2152AB:79D5:9BC2 9C96-B02FC2A$72C78A274AB5C2;72B"7292$5A2BCA5D4AB5C25C2$5;2A529%%58B:9A72A$77245C"56AB5C2BCA79602 *C11FB799A2,18637B886!B9*6712365

FC2/5A$24972B0702152A$72;9"72784BA9AB5C29CD216BD2:7:5-2A7:2A$72:9BC2BD792B2A529%%58B:9A72A$7 2 45C"56AB5C2A7:2/-2926BC799AB:79BC"9B9CA2%99:7AB42:5D762BC2A9A79%94727%77CA9AB5C02+52A$724972 51216BD2:7:5-2A7:2;72972655<BC215292:5D7624$292

!

;$772:9AB472 2 29CD2 297245CA9CA29CD29%%58B:9A72A$7245C"56AB5C2<7C76252B:%6727%5C72 :9AB82;$B4$2B2A$72BC"772+5B72A9C15:2512A$7217B7C4-27%5C721C4AB5C2>)77*29CD2+57C2(11@ 2 D71BC7D2/-2

1(

#$B21C4AB5C2D7%7CD25C2A$729DB9AB5C2D9:%BC2A$729DD7D2:929CD2A$72BC1BCBA7917B7C4-29DD7D2:9 2 :9AB802#$7269AA72972C5A296;9-29"9B69/672D7%7CD25C2A$72A$75-27D2A5256"72A$72/5CD9-2"9672%5/67: 2 9CD2A$7C2BA2$9"72A52/727AB:9A7D2A57A$72;BA$2A$7216BD2:7:5-2A7:02FC2>)77*29CD2+57C2(('@29A$5 2 7A2A$727D2512A$729AB5C962A9C17A2:9AB82;$B4$215:2!2B2B"7C2/-2

11 9CD2152;$B4$2;72$9"72152794$27CA-

1

#$771572A$72BD7CAB1B49AB5C2%5/67:215425C2A$72D7A7:BC9AB5C2512A$72A9C17A21C4AB5C2 29CD249C2/72 15:69A7D2BC2A7:2512679A9B972%5/67:2BC2A$7217B7C4-2D5:9BC292

1

;BA$

1

;$772 2:79C2A$9A2;7272921BCBA727A251217B7C4B72 2972;7B$ABC2457114B7CA29CD2 2B2A$72%99:7A72

"74A52D71BC7D292

1

)77*27A2+57C2((!2%5D47292#2#556582;$B4$2B21776-29447B/672>)77*29CD2+57C2((!@ 2 152A$72BD7CAB1B49AB5C2512A$7216BD2:7:5-2A7:2BC2A$B29%%594$02+52A$724972512;9"72784BA9AB5C21547292 B:B692%547D72B29%%6B7D02C5;7"72+96C72BC2>+96C721!!@2$5;2A$9A2A$72B:%6727%5C72B2C5A 2 C747796-2499629CD2A$7C2;72972655<BC21529C29%%58B:9A7D2:5D7624$292

1A

;$772A$72:9BC2DB11B46AB7245:7215:2A$724996B*BC2AB:72$B1A2 2BD7CAB1B49AB5C02FC2+B722;72B"7292/6542 DB99:27%77CA9AB5C2512A$726::BC29%%58B:9A7D2A9A79%9472:5D7627D2152B:69AB5C0

#$7C2BA215665;2A$9A217B7C4-27%5C721C4AB5C2 29CD2 2A$771572 29CD2 2 97 2 A$7 2 A9ABC 2 %5BCA 2 A5 2 7C79A7 2 A$7 2 D9A9 2 7D 2 BC 2 A$7 2 BD7CAB1B49AB5C 2 %5/67: 2 9CD 2 A$7B 2 D7A7:BC9AB5C 2 B 2 DB47D2BC2A$72C78A274AB5C0

- 3A23F1*79A1686AB73686A1F82F

C-D5D-C9:B42%99:7A72 B0702 9DD7D2 :9 29DB9AB5C2D9:%BC2 9CD2;9"72 784BA9AB5C2 1547 2972 966- 2 D7A7:BC9A7D2BC2C:7B496251A;9724$292=F#2;$B4$2B2/97D25C2A$72/5CD9-2BCA79627B9AB5C2 :7A$5D252:572747CA6-2BC2926+D2%59:02C5;7"72BC2/5A$24972A$B249C2A9<729:5CA2512AB:72152 C:7B496245:%A9AB5C02D72A52A$72B:%6B4BA-2512A$72:5D76275:7A-29C296A7C9AB"72A52A$7729%%594$72B 2 A$7272512927:B99C96-AB4962:7A$5D2;$B4$2B2%5%9/6-2A$7219A7A29CD2:5A276B9/672;9-2A527A2A$7:0257 2 78%69C9AB5C29/5A2:9A$7:9AB4962A$75-2;B662/7215CD2BC2>56BC2((@2>BCA5C29CD24F"72((1@2>+96C72 ((@02479DBC2A$72%74B1B42A4A72D7%B4A7D2BC2+B7212D7A9B62;B662/7215CD2BC2>369-927A29602(1@2152 A$72$79"BC2:5D702FC2A$7215665;BC2;72B"729C25"7"B7;2512A$72:7A$5D02

65CBD7BC2924-6BCDB4962455DBC9A72-A7: 2 2 ;BA$2BA25BBC 2 2 6549A7D29A2A$72BCA774AB5C2512A$72 CDBA/7D217721947267"762;BA$24-6BCD7298729CD2A$72 998B2B2%5BAB"72%;9D02:BC26BC792;9"72 A$75-29CD2%%5BC2A$9A2A$7216BD2B2BC"B4BD2BC45:%7B/6729CD2BA2:5AB5C2B2B5A9AB5C96216BD2165;249C 2 /72D74B/7D2BC29245:%67827%77CA9AB5C2/-2A$72"7654BA-2%5A7CAB96

17

;$77 2 2 D7C5A72A$727962%9A2512A$7245:%678278%7B5C 2 2 B2A$729C69217B7C4- 2 2 B2A$72AB:72 D7%7CD7C4-02#$72%9AB962%9A2512A$72"7654BA-2%5A7CAB9262 2$92A529AB1-2A$7215665;BC2/5CD9-2"9672

%5/67:

1 I5"7CBC27B9AB5C2BC2A$72;$567216BD

1' 1 +77219472/5CD9-245CDBAB5C

1!

1 79/7D2/5CD9-245CDBAB5C

( 1 5D-219472/5CD9-245CDBAB5C

1

B*4%5 8 8 2 8 "*45# 8 5$573*23 8 2+ 8 & 8 1%##*37 8 +25#%*23 8 ?*34 8 *32 8 2%3 8 323%7* 8 +25 8 ;. 8

)**238+257

92;766292A$72/5D-219472/5CD9-245CDBAB5C2129A2794$2/5D-2"7AB4962;9660 - *2F*5CB2F

=$7C2AD-BC2A$727%5C725129C2511$572A4A72BC2B7692;9"72152789:%672A5292;9"727C7- 2 45C"7A72A52%7DB4A2BA2%5;7249%A72AB:79D5:9BC2:5D766BC29%%792A52/72C7479-02#$B2%9%72B"729C2 5"7"B7; 2 51 2 A$7 2 ;$567 2 %547 2 A5 2 :5D76 2 A$7 2 497 2 51 2 9 2 A;5 2 /5D- 2 ;9"7 2 7C7- 2 45C"7A7 2 BC46DBC 2 A$72 D7A7:BC9AB5C2512A$72$-D5D-C9:B42%99:7A72BC2927:B929C96-AB49629%%594$0

- *+F2.56316F87

#$B2;5<2;92%%5A7D2BC2%9A2/-2A$72+5CD22CBB72FCA7:BCBAJB762+9C47292)5K74A2L32B6/5B7AM 2 BC2%9A2/-24B5C27A9C729CD2BC2%9A2/-265C7B62IC962D2+BCBAJ70

-7A6D6A6F*6B

6::BC2=021!A02#$72B:%6727%5C721C4AB5C29CD2$B%2:5AB5C02#74$CB49627%5A02

+96C72N021!!023C2C5C949962B:%6727%5C721C4AB5C2769A7D2A52%5%99ABC2;9A72;9"702%%6B7D2 3479C247794$21727!9'!02

+96C7 2 N0 2 ((0 2 3479C 2 =9"7 2 9CD 2 34B669ABC 2 -A7: 2 9 2 BC79 2 FCA794AB5C 2 FC46DBC 2 =9"793C7-2 38A94AB5C0269:/BD722CB"7BA-2)702

BCA5C26029CD24F"72)02((102C9CD/55<25129A$7:9AB4962#74$CBB72152=9"7O A4A72FCA794AB5C021 2 7DBAB5C26$9%:9C29CD2C966O64602

56BC 2 0 2 ((0 2 C-D5D-C9:BB72 D7 2 A4A7 2 511$572 9 2 IBD72 %9ABB72 2 67 2 5"97 2 7C 2 :702

#74$CB%02

369-92 02575A2N09029CD27C/5*BD202(102C-D5D-C9:B42657114B7CA29CD2=9"7259D21529 2

=362 D7"B472 BC2 C79"BC2 5D70 2 FC2 )5477DBC2 51 2A$72(12 # OF3332 3638 2%%0 219A 277C2 85;9-02

)77*2#029CD2+57C2#02F02(('02#B:72"02+7B7C4-9D5:9BC2FD7CAB1B49AB5C2512)99:7AB4249DB9AB5C2+547 2 5D76 2 15 2 9BC7 2 A4A7 2 9A 2 P75 2 %77D0 2 5D76BC 2 FD7CAB1B49AB5C 2 9CD 2 65CA56H 2 2 85;7B9C 2 47794$2667ABC2!2191!02

)77* 2 #0 2 9CD 2 +57C 2 #0 2 F0 2 ((!0 2 2 9A69/ 2 #556/58 2 15 2 )99:7AB4 2 FD7CAB1B49AB5C 2 51 2 49DB9AB5C9+547 2 5D762512 $B%29CD2311$572 A4A7025D76BC2FD7CAB1B49AB5C29CD265CA56H2285;7B9C247794$2 667ABC2(219102

)77*2#029CD2+57C2#02F02(1102)94AB49629%74A251217B7C4-9D5:9BC2BD7CAB1B49AB5C2512D-C9:B42:5D762512 :9BC72A4A7215:2$-D5D-C9:B42D9A9023479C23CBC77BC2'2A902

#9$B%52402)77*2#029CD259C2#02(('02C-/BD217B7C4-9AB:72D5:9BC2:5D762152D-C9:B427%5C72 9C96-B2512:9BC72A4A7023479C23CBC77BC22A'97(0

?2P029CD2+96C72N021!!02 A9A79%9472:5D766BC251292"7AB49624-6BCD72BC2$79"702%%6B7D23479C247794$2 172A970