Hw3-S05_Solution - HW 3 SOLUTION ME 304 Modeling Transfer...

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HW 3 - SOLUTION ME 304 Modeling, Transfer Functions &Block Diagrams CONTROL SYSTEMS (01) March 30, 2005 Prof. Dr. Y. Samim Ünlüsoy, Res. Asst. Kemal Çal ı ş kan 1 PROBLEM 1: a) Elemental equations: R 1 => R1 1 1 V= iR R 2 => R2 2 2 L => 2 L di V=L dt C => C 3 dV i=C dt or C3 1 Vi d t C = Continuity equation: 31 2 ii - i = Compatibility equations: Left Loop => iR 1 C V=V V + Right Loop => R2 C L VV V 0 += Substitute elemental equations and continuity equation in Loop equations, 11 12 i 1 ( i- i )dt V C 2 22 di 1 ( i)d t L 0 Cd t −+ = We can take the derivatives of these equations to obtain governing differential equations for the system, 2i 1 di i -i dV R dt C dt 2 21 2 2 2 2 di i -i d i RL 0 dt C dt = V i (t) V o (t) i 1 i 3 i 2 L C R 2 R 1 + _
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HW 3 - SOLUTION ME 304 Modeling, Transfer Functions &Block Diagrams CONTROL SYSTEMS (01) March 30, 2005 Prof. Dr. Y. Samim Ünlüsoy, Res. Asst. Kemal Çal ı ş kan 2 1 () I s 3 I s 2 LsI s 2 I s 2 I s b) Take Laplace transforms of the above equations, 12 11 i I(s) - sI (s)R =sV (s) C + (1), 2 22 2 I(s)- sI (s)R Ls I (s) 0 C += (2) re-arrange (1) 112i (R s
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This note was uploaded on 05/16/2011 for the course ME 304 taught by Professor Samim during the Spring '11 term at Middle East Technical University.

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Hw3-S05_Solution - HW 3 SOLUTION ME 304 Modeling Transfer...

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