The transfer functions of the control system shown in Figure Q1a are as follows: Gc(s) 6#32 , 6(0) = K + , s (s + 5) (s

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The Transfer Functions Of The Control System Shown In Figure Q1a Are As Follows Gc S 6 32 6 0 K S S 5 S 1 (105.97 KiB) Viewed 15 times

The transfer functions of the control system shown in Figure Q1a are as follows: Gc(s) 6#32 , 6(0) = K + , s (s + 5) (s + 1)(s + 4) s s ) 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 SOO. [8 marks] (c) Derive an expression for the open-loop frequency response of the system with respect to K for w → 0 and w+ c and hence, show a simple Nyquist sketch of the open-loop response of the system. [6 marks]