Quiz_5_sol

# Quiz_5_sol - ECE 483 Quiz 5 Solution Problem 1(10 pts...

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ECE 483 Quiz # 5 Solution Problem 1. (10 pts) Suppose the sample period is T = 0 . 5 s. A feedback sampled-data system is given whose closed-loop transfer function is known to be: Y ( z ) U ( z ) = z - 0 . 9 z ( z + 0 . 2)( z 2 - 0 . 4 z + 0 . 08) . (a) (4 pts) Find its dominant pole (or poles) p . Solution: The poles are 0, - 0 . 2, and 0 . 2 ± j 0 . 2. The dominant poles are 0 . 2 ± j 0 . 2. (b) (3 pts) Find the corresponding pole q on the s -plane corresponding to p on the z -plane. Solution: By taking one of the dominant poles p = 0 . 2 + j 0 . 2 = 0 . 2 2 e j π 4 , we have q = 1 T ln(0 . 2 2) + j 1 T π 4 = - 2 . 5257 + j 1 . 57 . Other choices of q include q = - 2 . 5257 - j 1 . 57, or more generally, q = - 2 . 5257 ± j (1 . 57+4 ) for arbitrary intergers n . (c) (3 pts) Based on q , what are your estimates of the settling time t s (2% criterion) and the maximum overshoot M p of the step response of the sampled-data system? Solution:

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Quiz_5_sol - ECE 483 Quiz 5 Solution Problem 1(10 pts...

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