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# hw7_sol - EML 4312 Spring 2011 Stste Space Realization...

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EML 4312 Spring 2011 Stste Space Realization, Ackerman’s Formula The due date for this assignment is Friday 4/15. No late HW will be accepted for any reason due to the end of the semester. 1. Given the State-Space Representation (SSR), write down the unique transfer function. a) A = 1 1 1 4 ¸ B = 0 1 ¸ C = £ 0 1 ¤ Sol. H = C ( sI A ) 1 B = £ 0 1 ¤ s 1 1 1 s 4 ¸ 1 0 1 ¸ = s 1 s 2 5 s + 3 b) A = 0 1 0 0 0 1 1 3 4 B = 0 0 1 C = £ 0 0 1 ¤ Sol. H = C ( sI A ) 1 B = £ 1 0 0 ¤ s 1 0 0 s 1 1 3 s + 4 1 0 0 1 = s 2 s 3 + 4 s 2 + 3 s + 1 alternatively (better) since SSR is in RCF,just write it down from inspection. c) A = 1 2 3 4 1 0 0 0 1 B = 1 0 1 C = £ 0 1 1 ¤ Sol. H = C ( sI A ) 1 B = £ 0 1 1 ¤ s 1 2 3 4 s 1 0 0 0 s 1 1 1 0 1 = s 2 + 2 s + 1 s 3 3 s 2 5 s + 7 2. Given the transfer function, determine a SSR.

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hw7_sol - EML 4312 Spring 2011 Stste Space Realization...

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