timeresponse14 - 0.015 0.01 % 100 50% 0.01 OS-= = ....

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Time Response Q UESTION 14 For each of the unit step responses shown in Figure 14.1, find the system transfer function. 0 0.5 1 1.5 2 2.5 0 0.05 0.1 system 1 response 0 0.5 1 1.5 2 2.5 3 0 0.01 0.02 time (s) system 2 response Figure 14.1 For system 1, a suitable model is of the form K s a + . The system reaches 63% of its final response at approximately 0.5 s. Therefore, the time constant is 0.5 sec and a = 1/0.5 = 2. From the graph, the steady–state output is 0.1; therefore, K / a = 0.1 and K = 0.2. For system 1, a suitable model is of the form 2 2 2 n n K s s ζϖ ϖ + + . The percent overshoot is
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Unformatted text preview: 0.015 0.01 % 100 50% 0.01 OS-= = . Therefore, the damping ratio is Time Response 2 2 2 2 % 50 ln ln 100 100 0.2155 % 50 ln ln 100 100 OS OS -- = = + + (1) The peak time is T p = 0.35 s; therefore 2 2 rad 9.192 s 1 0.35 1 0.2155 n p T = = =--(2) From the graph, the steadystate output is 0.01; therefore 2 0.01 84.49 n K K = = and K = 0.8449. 2...
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timeresponse14 - 0.015 0.01 % 100 50% 0.01 OS-= = ....

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