Assume that the motor whose transfer function is shown in Figure P5.47(a) is used as the forward path of a closed-loop, unity feedback system.

a. Calculate the percent overshoot and settling time that could be expected.

b. You want to improve the response found in Part a. Since the motor and the motor constants cannot be changed, an amplifier and a tachometer (voltage generator) are inserted into the loop, as shown in Figure P5.47. Find the values of K₁ and K₂ to yield a 20% overshoot and a settling time of 0.25 second.

Motor R(s) Els) 25 C(s) s(s + 1) (a) Motor Amp R(s) E(s) 25 C(s) K s(s + 1) Tachometer (b) FIGURE P5.47 a. Position control; b. position control with tachometer