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# hw11 - d dt h X 8 i = A 4 h X 8 i B 4 Y sp P = C 4 h X 8 i...

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Interconnected Systems Problem 1 : Consider the following interconnected system: System 2 System 1 + - Y Y e U Y sp Suppose System 1 is modeled as: d dt " X 1 X 2 # = A 1 " X 1 X 2 # + B 1 e U = C 1 " X 1 X 2 # + D 1 e (1) and System 2 is modeled as: d dt " X 3 X 4 # = A 2 " X 3 X 4 # + B 2 U Y = C 2 " X 3 X 4 # + D 2 U (2) Compute the overall system with input Y sp and output Y for the following values of the matrices: A 1 = " 1 2 3 8 # B 1 = " 1 2 # C 1 = h 1 1 i D 1 = [1] A 2 = " - 1 2 4 - 5 # B 2 = " 1 0 # C 2 = h - 1 2 i D 2 = [0] (3) 1

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Problem 2 : Consider the following interconnected system: Ysp Y P Q E U Y Q + - System 1 System 2 System 3 System 4 Suppose System 1 is modeled as: d dt " X 1 X 2 # = A 1 " X 1 X 2 # + B 1 E U = C 1 " X 1 X 2 # + D 1 E (4) System 2 is modeled as: d dt X 3 X 4 X 5 = A 2 X 3 X 4 X 5 + B 2 U Y = C 2 X 3 X 4 X 5 + D 2 U (5) System 3 is modeled as: d dt " X 6 X 7 # = A 3 " X 6 X 7 # + B 3 Y Q = C 3 " X 6 X 7 # + D 3 Y (6) System 4 is modeled as:
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Unformatted text preview: d dt h X 8 i = A 4 h X 8 i + B 4 Y sp P = C 4 h X 8 i + D 4 Y sp (7) Compute the overall system with input Y sp and output Y for the following values of the matrices: 2 A 1 = " 1 2 3-4 # B 1 = " 1 # C 1 = h 1 0 i D 1 = [1] A 2 = -1 2 4-5 1 3 8 B 2 = 1 1 C 2 = h 1 1 0 i D 2 = [0] A 3 = "-1 3-2 # B 3 = " 1 1 # C 3 = h 1 0 i D 3 = [0] A 4 = [5] B 4 = [1] C 4 = [3] D 4 = [0] (8) 3...
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