Sketch the root locus of the armature-controlled dc motor

Chapter , Problem 11.3

(choose chapter or problem)

Sketch the root locus of the armature-controlled dc motor model in terms of the damping constant c, and evaluate the effect on the motor time constant. The characteristic equation is

                                                  \(L_a I s^2+\left(R_a I+c L_a\right) s+c R_a+K_b K_T=0\)

Use the following parameter values:

\(\begin{array}{clrl}K_b=K_T & =0.1 \mathrm{~N} \cdot \mathrm{m} / \mathrm{A} & I & =12 \times 10^{-5} \mathrm{~kg} \cdot \mathrm{m}^2 \\R_a & =2 \Omega & L_a & =3 \times 10^{-3} \mathrm{H}\end{array}\)