Q3) [40 points] Consider a unity feedback system with the following transfer function: From the Bode plot of G(s), you observe that the phase is -140◦ at ω = 2.24 rad/s, and the corresponding magnitude is −24.7 dB. Compute the gain K that will yield Mp=0.25. Using the gain K from part (a), compute the parameter α of a lag compensator so that the steady-state error to a unit step reference input is ess = 0.02. Also determine τI such that the desired phase margin does not change too much. Does the choice of τI affect the steady-state error?
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