Answer Happy

A unity feedback system has the following open-loop transfer function: G(s) = K 5000(s+12) s(s+8)(8 +20) Bode plot for the above system when K=1 is given in Figure 4. a) Sketch the asymptotic approximations for the magnitude response and specify clearly in your sketch the corner frequencies and slopes. b) From the given plots, confirm that the numerical values for the low frequency magnitude and low/high frequency slopes and phase angles as predicted from Figure 4 are correct. c) Report the phase margin. Based on the phase margin, comment on the system stability. d) Describe how you would increase the phase margin using a “Lead compensator" and show the effect of a suitable compensator on the magnitude and phase plot, clearly illustrating the improvements. For parts (a) to (d), translate all relevant values onto the Bode plot given in Figure 4 (You may use a printout or draw a clean sketch on your answer booklet before translating the labels) Bode Diagram 100 50 Magnitude (dB) -88 Phase (deg) -135 -180 104 10° 101 102 10 Frequency (rad/s) Figure 4 (For Question 5)