A) For the control system described: R(s) ? ? ? E(s) ? [Gc(s)] ? [Gp(s)] ? C(s) ? [H(s)] ? | Gc(s) = 1, Gp(s) = ?N^2 / (s(s + 2??N)), H(s) = 1 B) If ?N = 10 r/s, and ? = .5, determine the value in radians per second of the open-loop gain crossover frequency.
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First, we need to find the transfer function of the system. We can do this by multiplying all the transfer functions together: G(s) = Gc(s) Gp(s) C(s) H(s) Show more…
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Adi S.
The gain-phase plot of the open-loop transfer function KG(jω) of a unity feedback control system with K = 1 is shown in Fig. 8. Find the following performance characteristics of the system: (a) Gain crossover frequency (b) Phase crossover frequency (c) Gain margin (d) Phase margin (e) Resonant peak Mr (f) Resonant frequency (g) Bandwidth of the closed-loop system (h) The value of K so that the gain margin is 20 dB (i) The value of K so that the system is marginally stable. Find the frequency of the sustained oscillation. (j) Gain margin when K = 5 dB (k) Phase margin when K = 5 dB
2) The open-loop transfer function of a unity negative feedback control system is given by K G(s) H(s) = (s + 5)^3 The value of K for the phase margin of the system to be 45° is: 250√5 250√2 125√5 125√2
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