timeresponse6 - 17 10 100 70 10 OS-= = Therefore the...

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Time Response Q UESTION 6 For each of the unit step responses shown in Figure 6.1, find the system transfer function. 0 0.1 0.2 0.3 0.4 0.5 0 1 2 system 1 response 0 5 10 15 0 10 20 time (s) system 2 response Figure 6.1 For system 1, a suitable model is of the form K s a + . The system reaches 63% of its final response at approximately 0.1 s. Therefore, the time constant is 0.1 sec and a = 1/0.1 = 10. From the graph, the steady–state output is 2; therefore, K / a = 2 and K = 20. 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: 17 10 % 100 70% 10 OS-= = . Therefore, the damping ratio is Time Response 2 2 2 2 % 70 ln ln 100 100 0.1128 % 70 ln ln 100 100 OS OS ζ π -- = = + + (1) The peak time is T p = 1.25 s; therefore 2 2 2.529 1 1.25 1 0.1128 n p rad s T ϖ = = =--(2) From the graph, the steady–state output is 10; therefore 2 10 6.398 n K K = = and K = 63.98. 2...
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timeresponse6 - 17 10 100 70 10 OS-= = Therefore the...

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