From 4243ec81862f340dfb535ec625af3fad8dd0d6d4 Mon Sep 17 00:00:00 2001 From: Nolan Date: Thu, 7 May 2026 13:27:36 +0200 Subject: [PATCH] Chgt Latex --- latex/contents.tex | 41 ++++++++++++++++++++++++----------------- latex/main.pdf | Bin 499357 -> 562706 bytes latex/main.tex | 1 + 3 files changed, 25 insertions(+), 17 deletions(-) diff --git a/latex/contents.tex b/latex/contents.tex index 94e19fd..659242c 100644 --- a/latex/contents.tex +++ b/latex/contents.tex @@ -364,10 +364,11 @@ En utilisant la fonction \texttt{lqr()} de MATLAB avec $Q = I_8$ et $R = 1$, on \subsection{Question 13} +\includegraphics[width=\textwidth]{Illustrations/Question13} \subsection{Question 14} - +\includegraphics[width=\textwidth]{Illustrations/Question14} \section{Rejection de perturbation} @@ -385,18 +386,19 @@ Or on a : \end{equation*} Donc, puisque $\dot{x}_{d}(t) = A x_d(t) + B u(t) + B_p q_0(t)$, on trouve : \begin{equation*} - B_p = \begin{pmatrix} - 0_{4 \times 1} \\ - -\int_{0}^{L}\phi(\zeta)d\zeta - \end{pmatrix} - - = \begin{pmatrix} - 0_{4 \times 1} \\ - 1/2 \\ - 1/2 \\ - 1/12 \\ - -1/12 - \end{pmatrix} +B_p = +\begin{pmatrix} + 0_{4 \times 1} \\ + -\int_{0}^{L}\phi(\zeta)d\zeta +\end{pmatrix} += +\begin{pmatrix} + 0_{4 \times 1} \\ + \frac{1}{2} \\ + \frac{1}{2} \\ + \frac{1}{12} \\ + -\frac{1}{12} +\end{pmatrix} \end{equation*} \subsection{Question 16} @@ -418,11 +420,16 @@ On trouve alors : \subsection{Question 18} En utilisant la fonction \texttt{place()} de MATLAB, on trouve la matrice de gain $K$ suivante : \begin{equation*} - K_{aug} = \begin{pmatrix} - K_1 & K_i - \end{pmatrix} \text{ avec } K_1 \in \mathbb{R}^{1 \times 8} \text{ et } K_i \in \mathbb{R} +K_{aug} = +\begin{pmatrix} + K_1 & K_i +\end{pmatrix} +\quad \text{avec} \quad +K_1 \in \mathbb{R}^{1 \times 8}, \; +K_i \in \mathbb{R} +\end{equation*} - +\begin{equation*} K_{aug} = \begin{pmatrix} -0.89 & -16.59 & 0.28 & 1.68 & 19.39 & -0.84 & 2.36 & -1.94 & 12.00 \end{pmatrix} diff --git a/latex/main.pdf b/latex/main.pdf index 24a2a5920ca2fabfe79ec42b5a46f9d4e93e6420..2919c88fb550a7b59b0b21a4a513bc3ac1bbb43b 100644 GIT binary patch delta 204125 zcmXVXV{k4!v~_LUwr$(CZQD<6+qP|-+U==r+wG~p_ul)>>>oROvXjY7CRux}B(IMk zxt1i69GE@h!4{GxNeLE!!BuD_3>9x+6)tB#zU8)94ry|fN-b+b^#1AJ92%m}l4lW1 z{`K7Vy~HZ47+IJD+_g?!3#KdvJsR|!XvT0_pV0ok4-R|@fnNj~?7a{B9GWKL`49D)pH`~Os#^~13L$*?|N=jj6|D221XzX|0)n6Fj4?hBM}9~EDh}@_!Qd2 z0Xk?fVAI;|aQ1+m@}uh$LSG$DUiz&*n~XfpM7D~SBoA+3VbMXXAMkRbVJ;aGzv5@9 z#Aw|uB3z|v#is!H+wv7CM6^V`vv0`}a+OV68LOJui+rAacp%j)A~4cj5VS^6lqiVA z?2dq5`y#QX1)e>oM6t?2t0{JZkQ7-)flh`QjgNqPa7z*pXTsE@{-$fF=U%uua$t- zWAt7A{%OM(LL$u>=23-7gt#hqE+Vu*)JxRNfu^l$jjHql!KPm<<;GfISn%~gpVb&% zMGZ@xqM*&8xq!7VuH_p?%9O3;nM^6>NP{Wq-`1R$G0qv&)~VryCkUUTxn>1;Qav>* z$f`0VJO=@=jAw$xf5ZiLo)o5gj+bgL6Kx&_>rBP;eK9E(&lvMkZOA_GP;U#I5hW0z zE4$oaMl-V!>!}?-QdjBU+s%~;(MDxRsos1NX1(>6t<%@lv>NEu2~xNmZ6RF$qL*8g zoFSw51doV$^jcv^v(tq#;9V;&0^-RE!T*8NUxUQH z>v!XP5eQ-WCi*l_iKh~+Zcod+gwk+DYfSJkKxBM@tSTCKZI;=qo@Ko-PVS$FKB&x# zC!)}HwfIfdfKH1}yhJ*Z!(R3Hvjg(vB$V+G0A!ZU{7#@qLJI_12qX+e)z+=`9HL;? 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