Block diagram model of a position control system is shown in figure.
(a) In absence of derivative feedback (K_t=0) , determine damping ratio of the system for amplifier gain K_A=5. Also find the steady state error to unit ramp input.

(b) Find suitable values of the parameters K_A and K_t so that damping ratio of the system is increased to 0.7 without affecting the steady state error as obtained in part (a).

Bode plot of a stable system is shown in fig. The transfer function of the system is

A unity feedback system has open-loop transfer function $$G(s) = {1 \over {s\left( {2s + 1} \right)\left( {s + 1} \right)}}$$

Sketch Nyquist plot for the system and there from obtain the gain margin and the phase margin.

A process with open-loop model $$G(s) = {{K{e^{ - s{\tau _d}}}} \over {\tau s + 1}},$$ is controlled by a PID controller. For this process