A process has dynamics G(s)=1/(4s^s+s+1). Apply a unity negative feedvack controller of the form G.c(s)=1/(s+b).
(a) Report the transfer function T(s) of the closed-loop system.
(b) Report T(s) to 2nd order and report the reduced transfer function T.L(s).
(c) Design b so that T.L(s) exhibits a step response with zero steady-state error.
(d) Submit a plot with both the step response of T(s) and T.L(s) on the same axis. Use your value of b.
(e) Given your choice of b, what is the steady state error for a ramp input?