5. For the closed loop system shown in fig, determine the value of gain 'K' for damping ratio 0.5. Also determine peak overshoot, rise time, and time response for unit step input. R(S) C(S) 0.2s+1 / 0.84s^2 Ks
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2 s + 1)/(0.84 s^2) with gain K in series. Closed-loop char. eqn: 1 + K G(s) = 0 ⇒ 0.84 s^2 + 0.2 K s + K = 0. - Put in standard second-order form s^2 + 2 ζ ω_n s + ω_n^2 = 0: 2 ζ ω_n = 0.2 K / 0.84, ω_n^2 = K / 0.84. - For ζ = 0.5: 2(0.5) ω_n = ω_n = 0.2 K / Show more…
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