A unity feedback system has the plant transfer function G_p(s)=$${1 \over {\left( {s + 1} \right)\left( {2s + 1} \right)}}$$
(a) Determine the frequency at which the plant has a phase lah of 90^o.
(b) An intergral controller with transfer function G_c(s)=$${k \over s}$$ , isplaced in the forwardpath the value of k such that the compensated system has an open loop gain margin of 2.5.
(c) Determine the steady state errors of the compensated system to unit-step and unit-ramp inputs.

For the feedback control system shown in the figure, the process transfer function is G_p(s) = $${1 \over {s(s + 1)}},$$ and the amplification factor of the Power amplifier is K$$ \ge $$0. The design specifications required for the system, time constant is 1 sec and a damping ratio of 0.707.
(a) Find the desired location of the closed loop poles.
(b) Write down the requiredcharacteristic equation for the system. Hense determine the PD controller transfer function G_p(s) when K = 1.
(c) Sketch the root-locus for the system.