Figure below shows a unity-feedback control system.

a. Use MATLAB to create a root-locus plot for a closed-loop system that uses pure PD control Gc(s) = K(s + 1). Use rlocus and/or rloc find to estimate the control gain K so that closed-loop damping ratio is 7= 0.8. b. Now consider the more realistic lead controller instead of pure PD control: G c(s)=K(s+1) /(s+12) Use MATLAB to create the root locus. Use rlocus and/or rlocfind to compute the gainK that provides the maximum amount of closed-loop damping. c. Use Simulink to obtain the closed-loop responses using the PD controller from part (a)and the lead controller from part (b). The reference input is r(t) = 0.2U(t) in both cases.Plot both closed-loop responses on the same figure.

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