DC Shunt Motor
Schematic
Electrical ODE
\[\begin{split}\frac{\mathrm{d} i_\mathrm{a}}{\mathrm{d} t} &= \frac{u - L_\mathrm{e}^\prime i_\mathrm{e} \omega_\mathrm{me} - R_\mathrm{a} i_\mathrm{a}}{L_\mathrm{a}} \\
\frac{\mathrm{d} i_\mathrm{e}}{\mathrm{d} t} &= \frac{u - R_\mathrm{e} i_\mathrm{e}}{L_\mathrm{e}}\end{split}\]
Torque Equation
\[T = L_\mathrm{e}^\prime i_\mathrm{e} i_\mathrm{a}\]