The equivalent of the block diagram in Figure is given as

An electrical system and its signal-flow graph representations are shown in Figure (a) and (b) respectively. The values of G₂ and H, respectively are

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.

The Nyquist plot for the open-loop transfer function G(s) of a unity negative feedback system is shown in figure. if G(s) has no pole in the right half of s-plane, the number of roots of the system characteristic equation in the right half of s-plane is