Please work out problems for credit Consider the PD controller for the system wi

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Please work out problems for credit

Consider the PD controller for the system with transfer function T(s) = Gc(s)G(s)/1 + Gc(s)G(s) where the PD controller is Gc(s) = Kp+ KDs and the process is G(s) = 4/s2 + 4. Show that the process transfer function is marginally stable. Show that it is possible to find values of Kp and KD such that the closed loop system is stable. Design the PD controller to have steady state error to the unit step input 0.1 and damping ratio of the closed-loop system is zeta .

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