A unity feedback position control system has a plant,
\(G(s) = \frac{10}{s(s + 1)}\)
It is desired to have the damping ratio, zeta = 0.5 and natural frequency, omega_n = 3 rad/sec. Design a phase-lead compensator by:
(a). placing the compensator or zero on the real axis right under the desired closed-loop pole.
(b). placing the compensator or zero such that it will cancel the open-loop pole at -1. For both compensators you design, show the corresponding closed-loop transfer functions and compare the transient responses (P.O. and Ts). Also, compare the steady-state errors when a unit ramp input is applied to the system.