From 1d5089f12954388d22868d6b2de92e45cb2c4eab Mon Sep 17 00:00:00 2001 From: Feror Date: Wed, 8 Apr 2026 13:49:35 +0200 Subject: [PATCH] Premier TD d'automatisation --- Automatisation/TD1.md | 65 ++++++++++++++++++ Automatisation/TD1_2025_AutomNiv2.pdf | Bin 0 -> 287773 bytes .../Pasted image 20260408101521.png | Bin 0 -> 53838 bytes 3 files changed, 65 insertions(+) create mode 100644 Automatisation/TD1.md create mode 100644 Automatisation/TD1_2025_AutomNiv2.pdf create mode 100644 Automatisation/attachments/Pasted image 20260408101521.png diff --git a/Automatisation/TD1.md b/Automatisation/TD1.md new file mode 100644 index 0000000..8a76c6a --- /dev/null +++ b/Automatisation/TD1.md @@ -0,0 +1,65 @@ +![[TD1_2025_AutomNiv2.pdf]] + +# A. Notions fondamentales: + +## A.1 Qu'est-ce que la fonction de transfert d'un système ? +La fonction de transfert d'un système qui a une entrée $e(t)$ et une sortie $s(t)$ définie la relation entre $e$ et $s$. + +## A.2 Comment déterminer la fonction de transfert ? +La fonction de transfert se détermine par équation différentielle. + +## A.3 Comment mettre sous forme canonique une fonction de transfert de premier dégrée ? +Pour mettre une fonction de transfert de premier degré $f$ sous forme canonique, il faut lui appliquer une transformée de Laplace ($\mathcal{L}(f)$) + +## A.4 Qu'est-ce que la réponse indicielle d'un système ? + + +# B. Schémas blocs: + +## B.1 On considère les systèmes représentés ci-dessous : +![[Pasted image 20260408101521.png]] +Le premier système a pour fonction de transfert $H_1(p)$ et le deuxième $H_2(p)$. +### a. Calculer $H_1(p)$ et $H_2(p)$. + +$H_1$ +```mermaid +flowchart LR + +A(["E(p)"]) --> B(["+/-"]) --> C("K1(p)") --> D("K2(p)") --> S("S(p)") +D --> E("K3(p)") --> B +``` +```mermaid +flowchart LR + +A(["E(p)"]) --> B(["+/-"]) --> D("K1(p)K2(p)") --> S("S(p)") +D --> E("K3(p)") --> B +``` +```mermaid +flowchart LR + +A(["$$E(p)$$"]) --> B("$$\frac{K_1(p)K_2(p)}{}$$") +``` +$H_2$ +```mermaid +flowchart LR + +A(["E(p)"]) --> B(["+/-"]) --> C("K1(p)") --> B2(["+/-"]) --> D("K2(p)") --> S("S(p)") +C --> E("K4(p)") --> B +D --> E2("K4(p)") --> B2 +``` +```mermaid +flowchart LR + +A(["$$E(p)$$"]) --> C("$$\frac{K_1(p)}{1+K_1(p)K_4}$$") --> D("$$\frac{K_2(p)}{1+K_2(p)K_4}$$") --> S("$$S(p)$$") +``` + +### b. On pose $K_1 = K_2 = K$ . Calculer $K$ tel que $H_1(p) = H_2(p)$ + +$H_1=H_2$ +$\frac{K^2}{1+K^2+K_3}=\frac{K^2}{(1+KK_4)^2}$ +$1+K^2K_3=(1+KK_4)^2$ +$1+K^2K_3=1+2KK_4+K^2K_4^2$ +$KK_3=2K_4+KK_4^2$ +$KK_3=2K_4+KK_4^2$ +$KK_3-KK_4^2=2K_4$ + diff --git a/Automatisation/TD1_2025_AutomNiv2.pdf b/Automatisation/TD1_2025_AutomNiv2.pdf new file mode 100644 index 0000000000000000000000000000000000000000..29723e42b1a5fb4106cbce20e95bef17cd98741b GIT binary patch literal 287773 zcmdSB1yEhf)-{S-ut2at(BQUlcMI+o+?|cPLvRVfU4j#w;BLV+I6;C#aQC+%=iHNg z=iK|>SKnW+>aC(`uf2A!?%6#@kJ&wDC!})1qO=TjY)A;CpFtNA0s|p{5U6jCguu;B zujFcDL@%W0pl1m*p_kJ$F|sFQ1pTZ)FQsQ~LSbx2Nl35gVCQJypk!xcqyPju5VEj5 z{VuI%XCZEF38V;mX4c1VT7t++wSc+>YS-b9ekmB)10C%^R)7o_1zI~ielQUJ?2{-XA;)8-^rB3J43DD(x??6} zcxs4Vl!cIi{pT}QLPo&PJ2pbbKVD@gWO{lA8UYa(2QftlJqIID-C~Mtgltb`#T3~I zpWX+RP?Oa+H!^r^TigmX=1h!)puflFetu;lWP0i*lD??is@!0w)Xrp#Ygk?& z@+&}z`gI4QsV0&6wmZnm66jnEw%r6xTrD>^bI2kipQCJ^EUp9Zir2o~cdwmK--XH6 z-rW(nv-#Tsc@x7gMz9DrT(;-E4vP5poMJx4tgfx@%k(hbuBNVw$8TveQKIFu4~Q`C 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