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Unformatted text preview: Name MAE 340: Test II March 25, 2003 Q: ”3 Q:
Transiationnl ' Rotational
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{a} (’53 Number 13 are 25 points each. For each system shown, derive a statespace model in the standard form: quq +Bu , y=Cq +Du You must define the vectors q , u , and y , and the matrices A, B, C, D. lnput is the voltage source e5 Outputs are the voltage drop from node 1
to ground, and the current through the
capacitor. Input is the pump pressure source P5 Outputs are the flow rate out the pipe end,
and the flow rate through R1 Input is the fluid flow rate Q5 Outputs are the voltage through the
electrical inductor, and the fluid flow rate throughthe F—M transducer (15 pts) Find the conditions on the design variable k to insure that the settling time is
less than 1 second, if the system’s characteristic equation is given by s3+kg2 +10s+4=0 (10 pts): Find the transfer function for a system modeled by 2'6 + 35c + x = 21 +13 , if the
output is given by 45c ,7 Input is the voltage source es Outputs are the voltage drop from node i
to ground, and the current through the
capacitor. input is the pump pressure source PS Outputs are the flow rate out the pipe end,
and the flow rate through R] input is the fluid flow rate Q5 Outputs are the voltage through the
electrical inductor, and the fluid flow rate through the F—M transducer (15 pts) Find the conditions on the design variable k to insure that the settling time is
less than 1 second, if the system’s characteristic equation is given by s3 +k'5l103+4=0 (10 pts): Find the transfer function for a system modeled by )‘c‘ + 35c + x 2 2t +13 , if the
output is given by 45c ‘ ,i L f O ”QR. C‘, O ( ‘ R: r w L I A VT— 0 0 SM .
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to ground, and the current through the
capacitor. Input is the pump pressure source PS Outputs are the flow rate out the pipe end,
and the flow rate through R1 input is the fluid flow rate QS Outputs are the voltage through the
electrical inductor, and the fluid flow rate
through the F—M transducer (15 pts) Find the conditions on the design variable k to insure that the settling time is
less than 1 second, if the system’s characteristic equation is given by s3+kf+103+4=0 (10 pts): Find the transfer function for a system modeled by 56 + 35c + x = 21‘ +13 , if the
output is given by 45c c '5 ‘ i ”Z
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 Spring '09

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