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MMAN3200 Assignment2 Question1 To obtain the state equation, the output of the system are h1, h2, h3, hence 𝑥 1 = ℎ 1 𝑥 2 = ℎ 2 𝑥 3 = ℎ 3 Input: ?(?) = ? 1 (?) Use the formula of fluid system: ? 𝑖𝑛 − ? 0?? = ?ℎ Tank1: ? 1 (?) − 𝑄 12 = ? 1 1 Tank2: 𝑄 12 − 𝑄 23 = ? 2 2 Tank3: 𝑄 23 − 𝑄 3 = ? 3 3 ??ⅇ𝑎 = 𝜋? 2 ? = ?(ℎ) = ? 0 + 𝑎ℎ Where r0 = 2m, a = 1. ? 1 (?) − 0.5√ℎ 1 − ℎ 2 = 𝜋(2 + ℎ 1 ) 2 1 0.5√ℎ 1 − ℎ 2 − 0.5√ℎ 2 − ℎ 3 = 𝜋(2 + ℎ 2 ) 2 2 0.5√ℎ 2 − ℎ 3 − 0.5√ℎ 3 = 𝜋(2 + ℎ 3 ) 2 3 𝑑𝑥(?) 𝑑? = 1 2 3 Rearranging: 𝑑𝑥(?) 𝑑? = 1 2 3 = 𝑞 1 (?)−0.5√ℎ1−ℎ2 𝜋(4+4ℎ1+ℎ1 2 ) 0.5√ℎ1−ℎ2 −0.5√ℎ2−ℎ3 𝜋(4+4ℎ2+ℎ2 2 ) 0.5√ℎ2−ℎ3 −0.5√ℎ3 𝜋(4+4ℎ3+ℎ3 2 )
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Question2 When system reach equilibrium, 1 = ℎ 2 = ℎ 3 = 0 Step1: ?
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