The transfer functions of the control system shown in Figure Q1a are as follows: Gc(s) K (s + 3)2 Gp(s) (s + 5) (s + 1)(

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The Transfer Functions Of The Control System Shown In Figure Q1a Are As Follows Gc S K S 3 2 Gp S S 5 S 1 1 (170.67 KiB) Viewed 54 times

The transfer functions of the control system shown in Figure Q1a are as follows: Gc(s) K (s + 3)2 Gp(s) (s + 5) (s + 1)(s + 4) and H(S) = 1. R(S) r(t) E(S) e(t) Gc(s) Gp(s) C(s) c(t) H(S) Figure Q1a (b) Sketch the root-ocus diagram, including any asymptotes. Indicate the point of instability and the positions of small positive values of K. Comment on the nature of system damping for 0 <K 30. [8 marks] (c) Derive an expression for the open-loop frequency response of the system with respect to K for W - 0 and wo and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks) (d) With the aid of the Routh-Hurwitz stability criterion, investigate the range of the gain K that would guarantee the stability of the system and hence, find the frequency of oscillation at the marginal stability point.