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SampleFinal - AME451 Final Examination Fall 2006 December 6...

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AME451: Final Examination Fall 2006 December 6, 2006 1. ( 30 points ) Given the system in the fi gure. (a) Let K 2 = 0 . Find the conditions for the gains K 1 and K 3 such that the following speci fi cations are satis fi ed i. Percent overshoot to step input 9 . 48% M p 52 . 66% ii. Settling time 1 t s 4 iii. Indicate the region in the complex plane in which the closed-loop poles of the system need to be in order to satisfy the require- ments. iv. Find the range of K and K t for which the above requirements are satis fi ed v. What is a steady-state error of the closed-loop system for unit step input? vi. What is a steady-state error of the closed-loop system for unit ramp input? 1
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(b) Let K 1 > 0 , K 2 > 0 , K 3 > 0 , N > 0 (an integer). What are the conditions for the closed-loop system to be stable? Useful formulas: M p = e ζπ/ 1 ζ 2 t s = 4 ζω n t p = π ω d = π ω n p 1 ζ 2 K p = lim s 0 G ( s ) H ( s ); e ( ) = 1 1 + K p K v = lim s 0 sG ( s ) H ( s ); e ( ) = 1 K v 2
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2. (35 points) Given a root-locus plot of a unity feedback dynamic system (a) What are the open-loop poles and zeros of the system?
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