Repeat HP$5$ but include the inductor $L_a$ in the model. The given spec sheet lists $L_a=2\mathrm{.}5mH.$ Specifically, in slide #$5$ of the video, keep the inductance $L_a$ which means the KVL equation is as given at the top of the slide. The figure below should help you in figuring out the overall transfer function:

Consider the dC motor model that includes THE ArmatUrE IndUCtance

Show in your report that $\{p^2+(\frac{R_a}{L_a}+\frac{D_m}{J_m})p+(\frac{D_m}{J_m}\frac{R_a}{L_a}+\frac{K_t}{J_m}\frac{K_b}{L_a})\}{}_m(t)=\frac{K_t}{J_m{L}_a}{e}_a(t)$

Show your ability in using Laplace Transforms to solve the differential equations $($open$-$loop and closed$-$loop$).$

Compare$/$contrast with the results in HP$5$ where the inductance was neglected.

Examine the response of the system under Integral control for gains $K_c=1$;$20$;$50$; Comment on the very strikingly different responses when compared with the simplified model in HP$5.$