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Consider the system whose transfer function is given by: 1()(21)(3)Gsss=++. (a)Use the root-locus design methodology to design a lead compensator that will provide a closed-loop damping ζ =0.4and a natural frequency ωn=9 rad/sec.The general transfer function for lead compensation is given by(b)Use MATLAB to plot the root locus of the feed-forward transfer function, D(s)*G(s), and verify if the closed loop system pole is located on a root locus for the calculated value of K

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transfer function from R(s) to E(s) and determine the steady-state error (ess) for a unit-step reference input (c) Select the system parameters (k, kP, kI) such that the closed-loop system has damping coefficient ζ = 0.707 Figure Control system diagram.

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