A feedback control system with the configuration of Figure has the following parameters: K_p = 0.5 V/rad, K_a = 100 V/V, K_m = 2.7 × 10^-4 N·m/V, J = 1.5 × 10^-5 kg·m² , and F = 2 × 10^-4 kg·m² /s.

(a) With an applied step-input command, describe the dynamic response of the system, assuming the system to be initially at rest.

(b) Find the position lag error in radians, if the load disturbance of 1.5×10^-3 N·m is present on the system when the step command is applied.

(c) In order that the position lag error of part (b) be no greater than 0.025 rad, determine the new amplifier gain.

(d) Evaluate the damping ratio for the gain of part (c) and the corresponding percent maximum overshoot.

(e) With the gain of part (c), in order to have the percent maximum overshoot not to exceed 25%, find the value of the output-rate gain factor.