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Question C
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Question C
Question C
The transfer functions of the control system shown in Figure Q1a are as follows: G(9) = 632, 6000 s) K (s + ) 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-locus 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 SO. [8 marks] (c) Derive an expression for the open-loop frequency response of the system with respect to K for w → and w 700 and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks]
The transfer functions of the control system shown in Figure Q1a are as follows: G(9) = 632, 6000 s) K (s + ) 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-locus 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 SO. [8 marks] (c) Derive an expression for the open-loop frequency response of the system with respect to K for w → and w 700 and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks]