hw10 - 2 A = 2 0 0 5 2 0 8 4 2 Problem 3 Consider the...

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Home Assignment Problem 1 : Consider the following linearized model in deviation form: dX dt = AX + BU (1) where X = " X 1 X 2 # (2) B = " 1 2 # (3) and U is a scalar. Suppose the input undergoes the following step change: U = ( 0 t < 0 3 t 0 (4) Compute how the X vector changes with time for the following A matrices: 1. A = " 1 2 3 8 # 2. A = " 1 - 3 2 2 # 3. A = " k 1 0 k 1 k 2 # Problem 2 : Consider the following linearized model in deviation form: dX dt = AX + BU (5) where X = X 1 X 2 X 3 (6) B = 1 2 0 (7) 1
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and U is a scalar. Suppose the input undergoes the following pulse change: U = 0 t < 0 3 0 t < 1 0 t 1 (8) Compute how the X vector changes with time for the following A matrices: 1. A = 1 2 3 4 - 5 7 - 6 - 3 - 2
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Unformatted text preview: 2. A = 2 0 0 5 2 0 8 4 2 Problem 3 : Consider the following linearized model in deviation form: dX dt = AX + BU (9) where X = X 1 X 2 X 3 (10) B = 1 0 0 1 0 1 (11) U = &amp;quot; U 1 U 2 # (12) Suppose the input undergoes the following change: U 1 = ( t &amp;lt; 3 t (13) U 2 = ( t &amp;lt; 3 .t t (14) Compute how the X vector changes with time for the following A matrix: 1. A = 1 2 3 4-5 7-6-3-2 2...
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This note was uploaded on 01/07/2011 for the course CHE 452 taught by Professor Dr.srinivaspalanki during the Spring '10 term at S. Alabama.

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hw10 - 2 A = 2 0 0 5 2 0 8 4 2 Problem 3 Consider the...

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