1) A closed loop servo is represented by differential equation, where c is displacement of output shaft, r is the displacement of the input shaft and e= r-c. Find out undamped natural frequency, damping ratio and percentage maximum overshoot for unit step input.
2) For unity feedback control system the open loop transfer function G(S) = 10(S+2)/ S^{2}(S+1). Determine
(a) Position, velocity and acceleration error constants.
(b) The steady state error when input is R(S) where R(S) =3/S –2/S^{2}+1/3S^{3}
3) Open loop transfer function of servo system with unity feedback system is G(S) = 10/S(0.1S+1). Estimate static error constants of system. Get the steady state error of system when subjected to the input given by polynomial r(t) = a_{0}+a_{1}t +a_{2}/2t^{2}.
4) Plot Bode diagram for following transfer function and get the gain and phase cross over frequencies: G(S) = 10/ S(1+0.4S)(1+0.1S)
5) Open loop transfer function of unity feedback system is G(S) = 1/S(1+S)(1+2S). Draw the Polar plot and find out the Gain margin and Phase margin.
6) Draw the Bode plot and therefore determine Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. G(S) = 0.75(1+0.2S)/ S(1+0.5S) (1+0.1S).
7) Draw the Bode plot and therefore determine Gain cross over frequency, Phase cross over frequency, Gain margin and Phase margin. G(S)=10(S+3)/S(S+2)(S^{2}+4S+100).