From 793fb895bdf4bf091d4e4cca3fdf9a357d226a93 Mon Sep 17 00:00:00 2001 From: Tournesol02 Date: Wed, 15 Apr 2026 23:30:06 +0200 Subject: [PATCH] =?UTF-8?q?Sch=C3=A8ma=20bloc=20ajout=C3=A9?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- latex/Illustrations/Regression_pos_volt.png | Bin 0 -> 14925 bytes latex/contents.tex | 111 ++++++++++++++++++-- 2 files changed, 103 insertions(+), 8 deletions(-) create mode 100644 latex/Illustrations/Regression_pos_volt.png diff --git a/latex/Illustrations/Regression_pos_volt.png b/latex/Illustrations/Regression_pos_volt.png new file mode 100644 index 0000000000000000000000000000000000000000..061729d0393808efe96f81ecb9aa8da256a61d38 GIT binary patch literal 14925 zcmch82UJtvw`KsbprWXNfPji1MLgt)efHUVpYQu_l&-ewRXSEW003}R z?S+y)06+}^0H{D0&r{BD*hGZ@0CxduO3y)lnZzmIAOq5A=az4Jjg|(pu6=kFADc(*iihm}Vbj*i~l zQ*h9?*ES;u$Z;ILTj<$8>XLjo)9PvH+;N+W((S>>X4qQ<r6`3jn;N zQeXxE!e}p2#s^^fue%_WzC57kc+)wt&u58Co+|uabhJ~hwr@PC1ZsIF!>d5y zt?6ocpX;X%M+6SnB*=MmOfnV^(VjGs4^!;_=m8(uvkZ`YQz~-u7*W6PK=P0Xl-?|Y zX4Yr@K9a~O%i+|=-e4z9pG|{GbE|>-c0g+EN)fiZwW2=YIUU)PYN11KkakvoPPeZ~ zZur6pJX3qSBPkyuVCT@wrn54Ua|Zg8;EUnwHp~StiQDZQ?e+(*I$Dg9H-u>=eZIwp zj{4YECDnyyErlLKKTKf^)pCTfcCuDUIcDRM8zWhTMrL)`56nJ}K??5S$jHnCB-Huj ziErzkc!MI&eAGbeCfiE!@=t-KS@8fo;#yJ&A&_+nHr(ZZSDrx(-km)FUVuJET${b6 zz`Px$^$MI(>e7Td%X}&AZBTD2ge7i8sRT=c*pE{BaKMjtI}PR{;o-?z+u>VT-oDMs z?-=tdgIQ*Pg!?dJSpjN#5JVL_u{u=`9MO>FFo+F04h-Boddk;R^MKDxZ`r@)@ur#9 zx?no+Ob6TqEr5S8(mNIdYoiy&8%^BCoIQTl8!iiZ3tly~VqA=-XC{K)hr{T?c{4H3l|Dy3K~wIx z)Qd5XkYx4?_>=a~u7hoqhuqgMs69{F5Gw<)5F`AhUBhdqdMuG^$!WhUeFVCz`*DZ0 zWq(qfHNc7s{K!P1zrq8x*6}JGeb!6u>AN@9x6S12Kzmk*E#-hMl>iNUo?*2-;CKG(rE&m zMn(_SI~YzdXss-Ll|`X#V}w7tv_aR{t9Lc)dq8sEOFk!nG5ES6)1aRV4X({wE*YO? z0+*cD({Fn>LoKq=m4R$OmTmsnWI=w}iRjGJFozG)qI)K)o`<5?qsw&-ebj8vu1rm} z!c^Q^%zxOP<(0FYmc}2Qx9@lzrp7|f;QBeykE{sJBAvPE3DZzopEQf&rBU;JMGtp7s(-* z+V10RJ?~I^=xMi=+@^QN=a^IS8$@!1ukLcsyY1jBGs$YxxHMscqFnqn^9MBM5B5jv zwFtTLBi3X5iK`wgxGq)04oh2tFlV|nK7uvy(5$cKgu_a+&g96$;O1>iZ!>C?ik85Z3pM(v21_x5Y(l(@7%NC_Oc$iE%T*a3!a}$)`)|B z+xcf5ou{!+ct(Pz#J`^#1(G%r`{G=lXfT&Q2^?u@3HdX_moxP;GhDDQBcm$z$+#`{ z(^ak9>K2yjso;(q>S8m~;Ax5cGaFlIHoWnD7?Khr^LxQcMPk+zh zPvgE`C$(|O7@`KcRfx?>#^FNmD2c5%8-q?kOSZOMfzLi>JTLgTb3pnujc{L>@S`cS zzIvX=W?;j%W5h+PMz-54Ahc(d*mi_!`0VW*>xC-y+=Z z_^l68F=F!DyKedhuZE&k^*@{b{+wGyP=(ulrwIuD?JPKzd|$^{3^HAn{aUfPCHu$y z$6cn4UhgzX0$BKQ8fUpKWEw9r9*-F97JPWke@vic$Yv-sXU6uj5$HXHhf8af+4BKc zeTXc@$X!gV@OdZb$|{E-sNPgLN!UocGARH*63k&!Xt&S+(-;Qg+PiH25K>zu1Ent; zDjjyF8-amV$XtV~!boA&j`Q3uJwIyS z`kMgLK0WoFdsDmi+mN9({&W44W}!rx5TTtaxgb`~28s7V3pXPjXZ9nKA3@+n8Yzye z!Aei?#XZp`a^&oOJ4S9Cz^V9Mz=zX#*DCOtEmLeHSCG3MoO;=PSNIog0*^{&YR z2|Dcimu#nlUvykqdrIuoHw->Z66(U?Ggnnk;sR%ZoOeGcz-3ljBu3J+=G}8T9PNr4Bk4 zMItcaERqc*wHayURyJ{-`aW0$-|PL#z}WB7xF%|Nc)NmO@zqH~awv>em95k>QpCUM zHjmC^SiMa`=YUQ2XrwSD=0=t>f6;NKE7!Hu5wWP_6I4ywj#r!D<(5?DxvRj< zMP1l3odUHyKsonXrXP)KvcsibSjM3Y%C%1zx-0lZg+m8-M4$uxQ~e&UOY^ADvTlSi zCx0dv8Xm1q{ee4eynfQYE{*w3dgoaVjIdypq8)Oyz&Jkq1)+7Bbnk zBqOK491%hbv!rVT6;kSpxh6*~cV{4WAAW!Y4>$N5HN?Tycv|m!EektUPgvBoyn75$ zW$HQE_hcrHuztb5Ke?>7Z!`zp5k((X3BftKj-=%Jcstu)VxP@UBe>B-$@vHS^JJ@b zsm338`19K4bIO)L;mN0GM_SQ@F}2!l^AI^#nrXRuJ7l%OS(?%t#g(_5@1uYr4CJ=q{;# zdR%$Qw931_PA~@wJFhvMw>{1C!jha)2ohus&O!Nd=K3y`4MK_1HQq#F@^N33>8gF9 zKt}3sOE=c!`LWuKAan7gV=(fHpIWscac~+!*!__j9uVY+N|$|VOcY*_$qSmFue!ur zYAXouDoZchM^6<82R_56=$t1czZp`uXDY5KTr{l}Z}0r!CKs31qOdXTlNivl1+-Zl z2_#W+q%(~q!m5jjDbL+3-B2*Kl(AIY5iNk6xA-kBs*)h6X(s0{kK{p&#v86ZmmlQ{-RQ(L*bo%cyG#+phTRv;TSNH*N2V_3b_>wL-I>6 z!;5Z;7&Ti9U8~G!2odc)O-!M+aXy{6Ld1Rt39`SYX8*rjc`Xx8IP}^LtlYG(Q%E`=9QIT2L?7hFZl0o((J! zn-I@P-Kyy?o2Jf1w5LwExQQYMCT+~+nq7MvjiOkrG$&A9OIvKL8PQ+9@jT}3{aT9a zx)S8}MRK95d`VNZK>XdRXT@i3&-S->s zoeBKyoZh_nYSgiNH^3 zgGfXa9sQFc`1EVJfB}?C+wFMC-7aq)iQ*QP!;z;u#wjQssM6<4aq!oOW~VZfHy-}v z5YnHh(B;+;nWarT@$`@S_36R}{phlRP*VQZt1B}pl-7Oj<#c^Adl)wGVLYa5q>{Sr z{QGyE(Tl+pHBGt5 zH51Vk>BD0E9~%4#ELY|4b=;!OwXZNT80jeTNUe#9W0&N|wWb9WduxF|^1N`t)28M=)&r_&oUpFK>)C(vtEsv}Jc1W@Q+AOY8?lg(zef61~ zlCt+G$nr;%@6dX^rCz;9-CM+Mc?O&6aZIffE{K3MjzE-^J>q`w;FcE)K&azQirh6# z&@mX2G`P8ND|t{Wc)-~cLc@JFta;f*5F?gX*4&Qx`BQ1>JYe~Sre-hhRHFG}?nh6; z<_AmCWU`eAET<>A$0m`h!Z;XtPWKlB3UKRjS6eoFBoorfod_r0v>bXUZAR#z z*R$C7pb7(1_W057%V@6^s}~#e|C&xuZ&pD*yOub@Qe*~g@*1B{6sv@Xn3n|i52x9L!gjU5N5xQg3gW`cO5KhBP_b6af%w%8R}#p-d$3B zTKwj{Gaa~GngiQ6F1p+PdgG=Xz&K*?-#f5Kt;2~B7{QJlk#4)Q1vemm9Cef6wQ~3Z za1Z&rZZf(+rYO~WdH1Ta0{WTq2X*;m#j+?Z4D$Ls9Dc~d!{l`dAoRg0&8JD><;q*UW|rA?7ghpjzlo1cQiYd=Y$k(K6;#Q}#-t2umf^@2h<=-14s z8#ivyq0RxA=NmL~F7WW5!V&8BE1$oXH_X7D{`7C7r1DA?xK|Gp`hqJmC-&A0TwSPJ ze9}@=fBgn5h)yQ-4U10(JDM2-Ll4={Oa9~K#UaS)=!~6Y6=7Na_~lf?;KvH0_sPX> zo*Utp0cC$z_ycP}KY6f1mWRsTC}u${pw>S%v!8cLL{>459Pco^az5Qxqgg!(4$WvS z%V#k705_@F520$~Z(rZMAC}Lzf`2lREVtB*?A#Ag1@47(evbw$@YG?VGH%YeD+eKn zwx_7BXb(Etzu;K=SO+9@H9GR)io5!{?@d>8E){|4jSWw<*1Q!M=~08z_0}4J%k7(B zD60^_+d*Gc7ZAc#!mlUcBkH$wjm+W3Uu z22-d~hSSATew7&^sJ{^3Ezh1Abak!EO6C#+7qU^EGFBN=?wf{ ze5Pg0tN4oxevYT-hLtX5S+&%8o|pXk<)GnTS9Ad))m1x~RxhQG4_4>a`#fC4@jXS% z<~NT&Q6NTn2Hj`;AaRJvh*PnnIaf!1^k<`gp5vpi<%-@Q_w0Rl(*6JK8gB?-0O&f~ zG|5^_j?qwCS07H>b-BattDocJ78Jnwgwr=|Wc^9_n~`p5n2fv9TJC?KoZSQ1^!X1j zhrGMv!yQUmY5)2`JXK`VG#@3w^e#JJ&AmMYm z3*-EdBC{s*(k37TK@1efPhNN@mgj5Pf{rNd7h;^IPI+JxXgtIFJ9;Xck`#Wv6{3=F zbt-0)(wI0%Y@OugtEx3k@mI=;%P!-`DRrkDnTm*;vu;;$RLgb>YL+a$fSi{!q#fn-;uz~^~GEd;ilP`^V6@kmwa?%%VWCLRK zW-kz$rz3l8=iOA_B+a~P8jBDDq_7rD8F1>tSX`b;Ze4{KeJlD`su`!(lOrxFY~6ZU zy|}8q)7JhclM;h66;ov8OspokSBH3PZZUvOvS!3tC0sJeM%K|Zx_%WDa}F(+70DGW zl?)WW6*>p#kEi&}FL9R6YMZY|m+;{}P1Njb5lUN%lqp`w_?4m3okZN5aD5TKMBZ;J z6)e8UD?^#hu%LO3*#NkXK#QD>UbZ5Rn8mt4CLe4BH+^T|<)yfseBQqMzAYftD&CJfGl>(vWT+68tONQ#gwn{pbdbz-7U`ve_^J}-%~?5 zut_aWvao#w_qPaYgfpSpoaO5a_j zcG2G2rYYQ;U==x{`PWq!9ix4Vq}^`^RF342n9UC%sFS!!Y<2KeWp^hg0I&OHBciUU zts%mNzf%bwk|e?eK4(roWh^tgV9q!PkMI}WwEU) z=g`m30caP}VbEWTdm(|5Dp;$U?RTe4puY`d22$TLtc@khN*m6UPZoKPa2k%p9I}qq zA{@Q_AR6YU?CgNgqL$RSHbgAxDEY)6k7HRmX*wntF!4dHqhv^z&FRXTN}{%Y&HMCZ zWeKJTn7Qh#18-6RcmqUiffj?@fQaNA#T3=fy5ln8hr!SRp5T%h5dweS3^8D}Dc;+= z@5SE=Gwk&bw>&~hrOxWRONpdD$C5eHiPuqTdwPhsmU2Q303iQlp?*;8^~(Kr^mb+P zKFUu*Z(-Q;cbWjVB+x|P=;DxC^8UsGx4W8$+fYNe@L}l{N;FaU<`#(h zO_(-J!RPP}I%%XN#Mg}OobsOoL|0ts=p6~HP7ZXb-z#VW*L&2^GEz0@hFpde7zu&l zDH%gKOxKr?B7oc%JKXLhM>AE@`soYX=@E(rXB7?wz1j^+=a2|00CS02P>i8-_X&r& zl^qfjYlNvOzCSx`Hx*3rj);!!{e~WymtwB7l%f8MW;y0Si6rvi!-cfKrHVgh4mOEL*cP7^|wJ zb;n}4{fEWi21`{+h0cpPWByg7a=46Th(yGOydk^42lq0u-Wnx-Rx(4U7uy^=kZ>pY>S8|l;)?qzdF8d}q9%^kZ@2+Z~a8C+vIqraAG?Eb&3<2)yqZa4G~ zKb14API2B-ECNJ}0&`x3Dmf*n!v_?_;XYl7M!0idbr<&(ciR}vYMg`XEF&-I-m!Kf z)vQXTK300is`?A6i$%@rO=Zd|T0UBO%?^l&3{^}K)O<2@p~iWf%D+EIF1S3ICxRdP z2(55#_O*@U2pIx5m$rZneE0ZSs$I)vik{0I%c0M$*xZqXwU*a))g9hV%W-WSqD;Pzn4{t@JAH9^UB~GbM zO=No4@A;l?PFPu67kb_0(&;&tAS^eJg`9j^BmfUjXuBv;dKk^>ptpg<;y)2~zvq{E zvYq=0pLx$odaV)CO5N7T^pH6E0TQ}60kuvwz|}_^omjLm;yK~Q8le<3=ddTP1D7THqqc&R(tM4BXM#am#6Z%w zpN#l}4yl$QYTg&&i(STg{ zZO;`c=+8N%V_=gwX_b(~xGpiz#84-ng!s>MUqH)3`)-Q^Qd*~=gpviz(TuCLC(zzuE< zd7G{FyTn;dADX~JuiwP_Bsxy06fU?iIF?jGYwoVso=M;oIyqdl!kfb~^EHwTi@ zet;bwT67OAIvsag?S&kEWO?jSDY>$}@nV@icu;f0Y#f7jOCEpoJGE>|RI8pG+gqv; z&z2}Pa|LcOzI&&BsE{pQ&EhoO!Kg0HfAL!Br$^+f(N>!YY>6v>WUc7Nx;vZIZ(Bkt zJ=A#z)~9o!I##mvN67B#cNMf>{aJFGbmzR8RhmaT5j(a#IzdSF+<$oK^D*r)hiM=Ee?VyG)@ zCP*xfxO<;F)DspZkn(cc#Q$f5?5gd~`)TOw)r`IcMUKSUZQ2puxcReJ|kX(8T2KPWabL0=Q^6YzOw?Y1{nJFd!Oxbu0+*p+= zv}`piZWOjC+2-ykRxr=}qbqhL<`1{;-~UFJb9eHRZ^GNUA&~Xb0jycs)z)eS6B;AnNJ~03fbA}yS;YT);l91U$BL0qcoqR4Wsk=%t+9|_SDu}oH&00QJo#DFJ}(D$oO#9iTSA|z z?y*?Vf`;H>LrT8aW6Koej2p|)T-R2*>=@LO{sH+gQwTS)Xv$`$9XYd6o}8HC=;mVr zZrxU?T?xn%5qAculTM?7vdsot-hXObNGgq9X=g~Gh6mOTeUtkRL46G55~t+zIRR3E z)d_VS#fE(!M+m>Rp!^O^W{xj~a|1qI545R0FMX_m~&L%NmgQ~Yq7D&4p z_PmSx*+G!jkbY)LHCG<4u8|-OiQIoEkn1IxR5Pn;FWaTMi|d%Fk+4l(DlZp4g6d$4 z`mW19E=OBvYNQB00NsO`P2OT#HBi+zm+`OX^pNpn}QX`gURH~8&3)K|%49-l*<+#0T}&l2wr#c|8|;8$+z)@Gm@| zr_%d6vNFLX9Y612brhRQ0&^Gwwj_O9g)GlPg|#h9FTI;6Q3n;ihWlX5oT_RFiKlqU zfQaF3m(QAgYn-r^6?ux+1f*n+nCLL6;1c@QbDS*3}WbWlCYgBiiR4sU@fx zn5Kj7%fz%Tewr_(xIMpd|I0|$J(j{!fpc9;yrp&V^q?NWom#T4JH;xLfY3d<;r2T( zl#{beSX{?om?o=Mn~HyiXq)7G7Q?f5V7R~3vvnPYiZMrsA+rzqZ{0RD{nkW)cWljg zNkH@myKGger0?*X!Rqom%7y|`v^kh{M##0&;Fjma5v?~L+L!{?BY{tUx;)5$JfEC4 zSdKla-I(S{=Thq)%v-qC*ODJM+Ikj?$BrQz)l_Xvm3nx(TKr>2FO2FT`PY{EqgqB! z$c|W|2aDP>nEH8*r8eJygNbkCoxKwB+&3ON;NiFrs2rBQerVb>RZjRrOpuYPaLtMv zT`Nkrkn79og%nY7p-JQ&Gua8u@NVAJ&U`teMchHCGwjCXYJ1OM`hLJFR0ocqxh#hz zG3vN{{ssrvSJjnI?5;|^oN*qCv9 zM@O+&s^T82ET(=glr*~OKS2=b9+NSdc_f9PhX@%(3AkeW(#sff9`N-wcpsqM92dT$ z@VL_CF(uC%g&##8rnqUcBsp&7Cv%L!vL@>sChJ@#>gIqbxvC-yvX~mDS7{!bt4m4I zMk|8$sM<#48DYl=2;SDJU&U9v4dIOV%B5Lk^;$=0hL<+b$ML%?P3Gz#U<~W|-##2VP&k0H(_*jE{5D#M6e|6%vt4c2Sv4a>wHUD~Q&I?YchYdYG!_o&o zcd&xa(XlL2cDfI)Z06*OYx!_q>i|e(Klsd=GzD9`0R}BkbdvUBxoxUzhbs6eJCJE1 z_^x&Iok~Hk&d8f2d6_SSKeWZK&*H^gk7NTXUa=70M3gRh>)7KnaJ>1s8UpuwTa~m9 zTvL+!9EuW<$0yANb33Nn1X0v0jI~R%TLt2gxcq9rx})#egOlaaG3rUH$ERE8rcQ11 zaX$5j?lXdfV^8U+FYCHfY!)x2TV4tYW#&PB|kVDDvBr{*_UQ+Z}4TwctYjEGqTi@aGnf?PF9{zjxzM-hX z6&Cs&K9PQ^0?C-s-oS|g>@A_*s{oIL0nZ=qXyR(Ox-?I{sQEqbb!;zC%6_i?^6pXG z==Rr-;BrGN3Zm?hSwl}LjIW|25b|$Wl~{#S4-PpB&@e0^bkZj^4|Vs#3c&ja9k&Q7RyNqHZ}wfwmoT<=;q@!6N^){XZ+4@PdN{; zON6*mocc;t612i!=}DpHjQ)lD(iqm63uW91*L(w@yJq{qe7kO47G4)00)<4zElwa5 z3%X4=JIa~B5uX_ThR~6-?ooWnwc?SOXX%*-9}uOp!{jLBN@7+y$vKi28Q2JDZ zm4N-9u<`CaA2r6lEqH-fb`a*SItb!-#dlw~Nd-(`3MI3pw1Rr?FVpeYAXcj;{`mU$ zqPhtf#H%9nNkQ{kE}auG9wj0_kaQA{+y}# zjT41a0LXv&9<}=)CMI{~g&C6XTAeL!=7jJWwPlXIRHF*?$2T9%k`8GOC;a9EkKs{Qu^oA7t)#lsK*4-lliWJp{ z-zV~%jE&{Ra+1KEX4ytlNnF?u@mInW-VTBMoY~lWMWnQQKSiZNO>xAozWQ zERPORXG(|AH7)4rBL3%7JB7`9$r30g=JIIuU|iVxA22RRx%sV*?BYkGEJxL+-anqF z?Je3=*XRO%nN(heP*5#e$al%Ao$JtT)6ivdQS%3Q>c?D#M)R;cjsIRopc&2NGN5nT zd-hcN$*OgmI_|?)XQG9aS=5`wAUa6UdBA}grMXL&F8$M7)zomRm|Sh2(@Df8ky`E- zruS6L3s6Xa1Cw9mD(RNzbA-7Mo~28p;8?9wX_sRFN_-7AuKAO%iiv!52+ z;s?XiUCC9^Dw-^C+i%lHw184~KL+_P*S$!$T{Jj7r*ZRv=mO3_wACwRz-RHb)&DM6 zDZPHNW|EPe1z(#b8)op9LQcRXnvE}xIS+qxxW-6PU;x_U$3`f))4y=}eU}2Z`03m`!NxFn|_;mwqa0Ure;UBml z6edD78$=OQgeBdfkNhX;T>&uvsMTzO@QDBi4F701Jt$acdEy9}M5tVPhe0>j*v%cW zPPcsWL7zmUlBy3ef}S*h&}xdH>p6v*J^NaccH*>xFiA_e1K*n&eh_8F1|AS2;04n_KJ-@A3F!oI(w6f?Kfzv(@Rj*SI7JIAO;E;41u z_~-=7X9dW>B%9(ic))~*t@%1Wb)&KD`C~m4(ZpZ1#*Hc_nOy!nZAq>`C&z8pmI)b6 zZM(0oY3su_@j9bpK579qYAni1V8iA8*z?+Kuv5mgKY&{tnSb4FHuT3K>&5>nx1&>; zxJ9~HDe!Cc>j>q;0!J`nG~Dob>@f&goTtx3ODI-y6(T|9z<=?V4*%@?YJ_8Y5Dr#*o=WrOb)5#ydl0AHWREg z)l_3tZCZ<&JB*Ne?I9p#Kmaxwl{@|96GEU&r=J)K7!<8B4wUFsABp`bnMUow&%=i{ zp9Q04J!L26O>0XmAzJHc2*_de{8f2|zbciFehYhJHuV=?bTY3lPRjED^J68TmlI_Ee=<;9G)r|{pC{MlelYnf+bq@9UdCBU|+_qhu&9f;prU`J_}T= zwT&IcxD*QIHr%63_8pm$iDN8U>`fpW#5clV{pyU8V8TVhE5|qlQ74IQ~I(m5)_kA`}&^*fh#as4z*`pdJu@K zbJ=6Hx)nU!@XzNxb~#H45viI@>64+FlmHO@S89RPx&a&^vXjs))Mc^955dWp>wkoU z1dvrm=H)!x50Z-W9c|)QX8n(7-AnHO^-F{$Nhxda=ELC>UgWbM^zeN<&SJMRt?YtO zKJNS)^$DH2s~`2dUexQ)XY2oQBGux{r%`3*HW0~K#d4Ws!jrZ{8L4ffDh2f<{a+=p zw*?@P2g<4mI;Wv#9~BgxVdp{eVP7QOa2)KiL7;D6zR<}X#>hTZVEFbB2DbaPx=gc1 zFPQ~1>*9F1uvKIYNTIyQ753J1DQcI6Z=#9p)G}C-N&SHK>!b2t3yNd{#wIu$?R8MB z$gR-{4?(_4KbQ|7PDvTa?l%`c-*DTV!=nL7kJyW1(DVW)7=yIXRdM1pgdz=H4 zmY`K$n>%t|DB%7VqWVPI{q0*}nUsR`minG)7M9N=oQHco(M+G5-j!ZglEhj@C_?;T z5*X(iFMz|fi*9T;49J0&b#rAQe0+A(!{4B(dk|3Qs)WbS6Fb`T8;bsB)0n4Ng&`C10{*i-NKj;#Btsq_*e?6Hf(17jnXZb z^V89p7B!A#x~BV1JqcW-ZXg?6fu3eHHro?DL$<)BykbYnT5G>&~i~)e-#K04R=latex] \node [input, name=input] {}; @@ -106,7 +108,8 @@ node[midway, below=10pt] {$H(s)$}; %\draw [->] \end{tikzpicture} -\bigskip + +\end{center} \begin{equation} @@ -174,15 +177,105 @@ Le choix de P restait sur plusieurs tests du système bouclé avec un P de diffe \begin{equation} P=1 \end{equation} -Cela nous a donné un temps de reponse respectif aux attentes que nous avions. - +Cela nous a donné un temps de reponse respectif aux attentes que nous avions.\\ +\vspace{5cm} \section{Loi de commande du bille sur rail} \subsection{Système bouclé avec la bille} -Ajouter un gros système bouclé. Il faut savoir où mettre le correcteur avance de phase. + +Le schèma complet du système \textit{Bille sur rail} si dessous. \\ L'entrée du commande est une position dont on veut ballader la bille entre \textit{-50cm} et \textit{+50cm}. Il faut donc translater la position en tension. Le correcteur choisit est un correcteur: \textit{Avance de phase}. + +\begin{center} + + +% +\begin{tikzpicture}[auto, node distance=2cm,>=latex] + + \node [input, name=input] {}; + + %Bloc pos/tension + \node [block, right of=input] (Kb) {$K_b$}; + + %Somme de erreur + \node [sum, right of=Kb, node distance=2.5cm] (sum2) {}; + + % First controller (Tc) AFTER input + \node [block, right of=sum2] (Tc) {$T_c$}; + + % Sum AFTER Tc + \node [sum, right of=Tc, node distance=3cm] (sum) {}; + + % Second controller (P) AFTER sum + \node [block, right of=sum] (Pctrl) {$Controleur : P$}; + + % System + \node [block, right of=Pctrl, node distance=3cm] (system) {$G_{Rail}(s)$}; + + % Output + \node [output, right of=system] (output) {}; + + % Connections + \draw [->] (input) -- node {$x_c$} (Kb); + \draw [->] (Kb) -- node {$V_x$} (sum2); + \draw [->] (sum2) -- node {$\epsilon$} (Tc); + \draw [->] (Tc) -- node {$r$} (sum); + \draw [->] (sum) -- node {$e$} (Pctrl); + \draw [->] (Pctrl) -- node[name=u] {$u$} (system); + \draw [->] (system) -- node[name=y] {$V_\theta$} (output); + + % Feedback path + \coordinate [below of=u] (measurements) {}; + \draw [-] (y) |- (measurements); + \draw [->] (measurements) -| node [near end] {$V_\theta$} (sum); + + % Feedback path 2 + \coordinate [below=2.7cm of sum2] (measurements2) {}; + \draw [-] (y) |- (measurements2); + \draw [->] (measurements2) -| node [near end] {$V_\theta$} (sum2); + + % Brace + \coordinate [below=1.7cm of sum] (u1) {}; + \coordinate [below=1.88cm of y] (u2) {}; + \draw[ + decorate, + decoration={brace, mirror, amplitude=8pt} + ] + (u1.south west) -- (u2.south east) + node[midway, below=10pt] {$H_C(s)$}; + + % Brace 2 + + \coordinate [below=2.8cm of sum2] (u3) {}; + \coordinate [below=3cm of y] (u4) {}; + \draw[ + decorate, + decoration={brace, mirror, amplitude=8pt} + ] + (u3.south west) -- (u4.south east) + node[midway, below=10pt] {$H(s)$}; + + +\end{tikzpicture} +\end{center} + + +\subsection{Translation Position/Tension} +Le système ne prend qu'une tension comme entre. Nous devons donc translater la position de la bille en tension envoyé. Pour arriver à faire cela, nous avons calculé la fonction transferte à partir des equations mecaniques: +\begin{equation} +\Sigma F_x = m \ddot{x} = mg \sin(\theta(t)) +\sin(\theta)\approx\theta, \theta\approx 0 +\Rightarrow m\ddot{x}mg\theta \rightarrow \mathcal{L}\{.\}\rightarrow s^2 X(s)=g\Theta(s) +\end{equation} + +\begin{equation} +\frac{X(s)}{\Theta[s]}=\frac{g}{s^2} \Rightarrow \frac{V_x(s)}{V_\theta(s)}=K_b \frac{g}{s^2} +\end{equation} + +Pour calculer le \textit{K_b} nous avons fait une regression linaire avec la bille sur plusierus endroits sur le rail, et fait la lecture de la tension de sortie de système. +\includegraphics{} \subsection{Analyse des frequences importantes au système} @@ -199,7 +292,7 @@ Le correcteur d'avance de phase a une fonction de transfert sur la forme canoniq %\includesvg{./Illustrations/bodeCorrecteur} $$a = \frac {1 + \sin(\Phi)}{1 - \sin(\phi)} = \frac {1 + \sin(55°)}{1 - \sin(55°)} \approx 10$$ -$$ T = \frac{1}{\omega_m*\sqrt{a}} = \frac{1}{1.4*\sqrt 10} \approx 0,22$$ +$$\omega_m = \frac{1}{T*\sqrt{a}} = \frac{1}{1.4*\sqrt 10} \approx 0,22$$ \newpage \section{Vérification} @@ -217,9 +310,9 @@ En utilisant la fonction de allmargin nous trouvons le marge de phase pour le sy La boucle est bouclée et la balle est en equilibre. \psection{images} \begin{center} -\includegraphics{./Illustrations/fig2.png} -\includegraphics{./Illustrations/Schema_Forces.png} -\includegraphics{./Illustrations/StepRespnseRail.png} +%\includegraphics{./Illustrations/fig2.png} +%\includegraphics{./Illustrations/Schema_Forces.png} +%\includegraphics{./Illustrations/StepRespnseRail.png} %\includesvg{./Illustrations/bodeCorrecteur} %\includesvg{./Illustrations/bodeRail1} %\includesvg{./Illustrations/bodeRail} @@ -229,3 +322,5 @@ La boucle est bouclée et la balle est en equilibre. %\includesvg{./Illustrations/multisine2} %\includesvg{./Illustrations/StepRespnseRail} \end{center} + +