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SampleMidterm

# SampleMidterm - AME451 Midterm Examination Fall 2007...

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AME451: Midterm Examination Fall 2007 November 7 ,2007 The examination is closed notes and closed books. Calculators are allowed. Duration of the examination is 1 hour and 15 minutes. 1. (50 points) Given the system in the f gure. + - R(s) Y(s) s 2 1 + K(s) 2 + - (a) Assume a controller K ( s ) given by K ( s )= K s + a where K> 0 ,a> 0 . The following requirements for the closed-loop performance are spec- i f ed i. A. Percent overshoot to step input M p 16 . 3% B. Steady state error to unit step input e ss 0 . 1 C. Settling time t s < 0 . 5sec Find the relations in terms of K and a that need to be satis f ed in order to achieve the above speci f cations. ii. What is a steady state error for ramp input? 1

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(b) Assume the following controller K ( s )= K s N ( s + a ) , where K> 0 ,a> 0 ,N 0 ,N an integer i. What is a minimum steady state error to ramp input for N =1 ? Express your answer in terms of the parameter a. ii. What is a minimum steady state error to parabolic input
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SampleMidterm - AME451 Midterm Examination Fall 2007...

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