Consider the PI speed control system shown in Figure 10.6.2, where I = 5 and c = 4. The desired time constant is τ = 0.5. (a) Compute the required values of the gains for the following three sets of root locations.
1. s = -2, -20 (root separation factor is 10)
2. s = -2, -10 (root separation factor is 5)
3. s = -2, -4 (root separation factor is 2)
(b) Use a computer method to plot the response of the speed ω(t) for a unit-step command for each of the cases in part (a). Discuss the effects of the root separation factor on the rise time, the overshoot, and the maximum required torque.