5. Closed-loop specifications from open loop plots. Figure on the side shows the Nichols chart of a transfer function GK(s). Magnified view of a portion of the graph is also shown below, with some points labelled on it. Answer the questions below. R(s) Open Loop Gain (dB) + + 5 N E(s) -180 K G(s) -3 dB 3dB Y(s Nichols Chart 1dB OpenLoop Can(d) System untitled1 Gain (dB): 2.55 Phase (deg): -117 Frequency (rad's ec System untiled. Gain (dB): -5.77 System untitled Gain (dB): 6.4 Phase (deg): -109 Frequency (rad's ec): 0.68 315 Phase (deg); 136 Frequency (rads ec): 204 270 0.5 dB -100-13 Open-Leop Phase ( -1 dB System untided 1 Gain (dB): -0.0 dB Phase (deg):-122 Frequency (radisc): 1.27 Chart -6dB 12* -135 Open-Loop Phase (deg) a. What is the gain margin as read from the Nichols chart? b. What is the phase margin as read from the Nichols chart? c. What is the resonant peak amplitude and the resonant frequency of the closed loop system as read from the Nichol's chart? d. What is a, the cutoff frequency of the closed loop system as read from the Nichol's chart? e. Calculate the damping ratio, < of the closed-loop poles from the phase margin. f. Using the < and w, calculate the % overshoot and settling time of the step response of the closed loop system, by using the 1/2nd order formulae. g. What is GK(s) in the limit as s goes to zero? Hence what is the steady state error for a step input? h. Extra credit: What is SGK in the limit ass goes to zero? Hence what is the steady state error for a ramp input? You are provided the info that at the top-right of the chart, the gain is 43.2dB, the phase is -90 deg. and the frequency is 0.01 rad/s.

Fig: 1