For the following transfer function, derive expressions for the real and imaginary part for s = jω in terms of the frequency variable ω. Then write a MATLAB script to plot the imaginary part versus the real part (and its reflection about the real axis) for a frequency ω range of 10−2 to 102 radians per second. Verify that your plots match the output of the nyquist function in MATLAB. • G(s) = 1 /(s+0.5)(s+1)(s+2) Suppose G represents an open-loop plant transfer function. Use your plot to determine the Gain Margin for the closed-loop system, i. e., determine how much the loop gain could be increased before the closed-loop becomes unstable