Ulsoy midterm2 ME360

# Ulsoy midterm2 ME360 - Department of Mechanical Engineering...

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Department of Mechanical Engineering The University of Michigan, Ann Arbor ME 360-01 Prof. A. Galip Ulsoy Modeling, Analysis and Control of Dynamic Systems Second Midterm Examination Winter 2007 Thursday, March 29, 2007 (8:30 am – 10:30 am) Student Name:_____________________ Student ID:___________________ I have neither given nor received any unauthorized aid on this exam, nor have I concealed any violations of the honor code. Signature:____________________ Note: There are 4 problems. Problem 1 is worth 15 points, Problem 2 is 30 points, Problem 3 is 30 points and Problem 4 is 25 points. There are 100 points in total. GOOD LUCK!!!

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2 Problem 1 ( Total 15/100 points ) Part a) (9 points) Match the transfer functions given below with the corresponding time-domain responses (those responses could be step, or impulse responses – you should figure out what they are). Please note that one of the plots cannot be matched to any of the transfer functions offered to you. Transfer Functions: 1 4 1 ) ( 1 + = s s G ; 13 13 ) ( 2 2 + + = s s s G ; 10 7 10 ) ( 2 3 + + = s s s G Transfer function Time-domain response number Explain your answer 1 4 1 ) ( 1 + = s s G 13 13 ) ( 2 2 + + = s s s G G 3 ( s ) = 10 s 2 + 7 s + 10
3 Part b) (6 points) A system with the transfer function G ( s ) = s ( s ± 3) s 2 + 5 s + 6 () s + 1 is (circle one) Stable / Marginally Stable / Unstable Explain your answer: A system described with the state space model x = Ax + B u y = Cx where [] 1 1 , 0 1 , 3 0 4

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Ulsoy midterm2 ME360 - Department of Mechanical Engineering...

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