(Solution) - Refer to Figure 10 3 9 which shows a speed control system -(2025 Original AI-Free Solution)

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Refer to Figure 10.3.9, which shows a speed control system using an armature-controlled dc motor. The motor has the following parameter values.
Kb = 0.199 V-sec/rad
Ra = 0.43?
KT = 0.14 lb-ft/A
ce = 3.6 x 10-4 lb-ft-sec/rad
Ie = 2.08 x 10-3 slug-ft2
La = 2.1 x 10-3 H
N = 1
a. Compute the time constants of the plant transfer function ?L(s)/Vm(s).
b. Modify Figure 10.3.9 to use PI control instead of P control. Compute the PI control gains required to give a response having a dominant time constant of no less than 0.05 sec and a dominant damping ratio in the range 0.5 ? ? ?1.