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22. For the unity feedback system given in Figure P9.1 with G(S) = 5(+ 5)(s +...


22. For the unity feedback system given in Figure P9.1 with G(S) = 5(+ 5)(s + 11) do the following: [Section: 9.4] a. Find th
22. For the unity feedback system given in Figure P9.1 with G(S) = 5(+ 5)(s + 11) do the following: [Section: 9.4] a. Find the gain, K, for the uncompensated system to operate with 30% overshoot. b. Find the peak time and K, for the uncompensated system, c. Design a lag-lead compensator to decrease the peak time by a factor of 2, decrease the percent overshoot by a factor of 2, and improve the steady-state error by a factor of 30. Specify all poles, zeros, and gains. R(s) + E(s) C(S) G(s) FIGURE P9.1
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Given that, for the unity feedback system with G(S) - s (5+5)(5+1) a) Now, we have to find system the gain, K.for operate witSquaring 2 on both sides then we qet: 1.44 - => 1.44(1-52), 55,2 => 144-1.446=(9.14)52 >> 1.44 - 1.44s?9.85952 1.44-1.445²-9-b) NOW, formula for peak time Тр: ан : 3.818 3.143.818 Tp = 0. 8aas Kvasi ( from formula tos velocity euros constant) 218 55: condo- TRX design point is located at - Scont joan de-sa -461 +jay, 634 The un compensated System Poles as well as the compFunction at Point -9.61 +57.624 Poduce the k value al 44zo ; Kve 216.6 5(11) Kyo 26:6 218.6 e 55 = 3.9-75 Kv was 30 (3,975)

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