Performance Specifications and Compensation Design

For a control system shown in figure below, find the value of K & K_t so that the damping ratio (ζ) of system is 0.6 & settling time (t_s) is 0.1 sec for the unit step response.

For the given mechanical system, obtain the transfer function with angular displacement θ(t) as output and torque T(t) as input. Hence find J and D to give 20% overshoot and settling time of 2 second for step input of torque T(t).

A unity feedback system having feed forward transfer function G(s) = 16/[s(s+1)], determine the value of undamped natural frequency, damping ratio. If tachometer feedback is introduced, the feedback transfer function becomes (1+ks). What should be the value of 'k' to obtain damping ratio 0.6. Also calculate the percentage peak overshoot for unit step response before and after introduction of feedback.