timeresponse15

# timeresponse15 - Time Response QUESTION 15 For the response...

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Time Response Q UESTION 15 For the response functions below, determine if pole–zero cancellation can be approximated. If it can, find the percent overshoot, settling time, and peak time. a. ( 29 ( 29 ( 29 2 2.5 2 4 20 s Y s s s s s + = + + + b. ( 29 ( 29 ( 29 2 2.01 2 5 20 s Y s s s s s + = + + + From partial fraction expansion ( 29 ( 29 ( 29 ( 29 2 2 3 2 2 16 2.5 1 1 1 1 1 16 64 2 64 2 4 20 2 16 s s s s s s s s s + + + = - - + + + + + + The amplitude of the damped sinusoidal term is 2 2 3 2 0.0563 64 + = . Since the amplitude of the damped sinusoidal term is not an order of magnitude greater than the damped exponential term, pole–zero cancellation cannot be assumed. From partial fraction expansion ( 29 ( 29 2 2 5 55 0.04989 0.03383 2.01 1 1 2 4 0.0503 0.0003571 2 2 5 20 5 55 2 4 s s s s s s s s s + + + = - - + + + + + + The amplitude of the damped sinusoidal term is 2 2 0.04989

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timeresponse15 - Time Response QUESTION 15 For the response...

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