For the feedback control system shown in Figure, the process transfer function is , and the simplification factor of the power amplifier is . The design specifications required for the system are a time constant of 1 sec and a damping ratio of 0.707.

(a) Find the desired locations of the closed loop poles.

(b) Write down the required characteristic equation for the system. Hence determine the PD controller transfer function  when K=1.

(c) Sketch the root-locus for the system.