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hw2_sol

# hw2_sol - MAE 171a Homework Problem Set 2 Revised July 1st...

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Unformatted text preview: MAE 171a Homework Problem Set 2 - Revised July 1st, 2:30PM Prof. Schwartz Due: Wednesday, July 7th 1. Sketch the output time response of a step input to the following transfer functions. Use partial fractions to decompose the response. (a) G ( s ) = 20 ( s +5)( s +10) (b) G ( s ) = 20( s +4 . 5) ( s +5)( s +10) (c) G ( s ) =- s +1 s 2 +4 s +1 2. The response of a system, y ( t ) to an input, u ( t ) , is given by ¨ y ( t ) + 5 ˙ y + 6 y ( t ) = u ( t ) . (a) Convert the system into a state space equivalent Define the state vector x = bracketleftbigg y ˙ y bracketrightbigg . Now ˙ x = bracketleftbigg 1- 6- 5 bracketrightbigg bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright A x + bracketleftbigg 1 bracketrightbigg bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright B u y = bracketleftbig 1 0 bracketrightbig bracehtipupleft bracehtipdownrightbracehtipdownleft bracehtipupright C x + 0 bracehtipupleftbracehtipdownrightbracehtipdownleftbracehtipupright D...
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