timeresponse7 - 2 2 0.2029 0.0531 0.2030 + = . Since the...

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Time Response Q UESTION 7 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 3 2 3 10 s Y s s s s s + = + + + b. ( 29 ( 29 ( 29 2 2.1 2 5 s Y s s s s s + = + + + From partial fraction expansion ( 29 ( 29 2 2 3 31 7 7.364 3 3 1 1 1 1 2 4 20 16 2 80 2 3 10 3 31 2 4 s s s s s s s s s + + + = - - + + + + + + The amplitude of the damped sinusoidal term is 2 2 7 7.364 0.1270 80 + = . 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 1 19 0.2029 0.0531 2.1 1 1 2 4 0.21 0.007143 2 2 5 1 19 2 4 s s s s s s s s s + + + = - - + + + + + + The amplitude of the damped sinusoidal term is
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Unformatted text preview: 2 2 0.2029 0.0531 0.2030 + = . Since the amplitude of the damped sinusoidal term is an order of magnitude greater than the damped exponential term, polezero cancellation can be assumed. Time Response The systems natural frequency and damping ratio, respectively, are 5 rad/s and 1 2 5 . The systems percent overshoot, settling time, and peak time, respectively, are 2 2 5 1 0.05 1 % 100 100 48.64% OS e e - -- - = = = (1) 4 4 8 s 0.5 s n T = = = (2) 2 1.441 s 5 1 0.05 1 p n T = = =--(3) 2...
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This note was uploaded on 02/01/2012 for the course MECH ENG 279 taught by Professor Landers during the Spring '11 term at Missouri S&T.

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timeresponse7 - 2 2 0.2029 0.0531 0.2030 + = . Since the...

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