Refer to Figure 10.3.9, which shows a speed control system
Chapter , Problem 10.64(choose chapter or problem)
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.
\(\begin{aligned}K_b & =0.199 \mathrm{~V}-\mathrm{sec} / \mathrm{rad} & R_a & =0.43 \Omega \\K_T & =0.14 \mathrm{lb}-\mathrm{ft} / \mathrm{A} & c_e & =3.6 \times 10^{-4} \mathrm{lb}-\mathrm{ft}-\mathrm{sec} / \mathrm{rad} \\I_e & =2.08 \times 10^{-3} \text { slug-ft }{ }^2 & L_a & =2.1 \times 10^{-3} \mathrm{H} \\N & =1 & &\end{aligned}\)
a. Compute the time constants of the plant transfer function \(\Omega_L(s) / V_m(s)\).
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 \(0.5 \leq \zeta \leq 1\).
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