Permanent Magnet Synchronous Motor
Schematic
Electrical ODE
\[\begin{split}\frac{\mathrm{d} i_\mathrm{sd}}{\mathrm{d} t}&=\frac{u_\mathrm{sd} + p \omega_\mathrm{me} L_\mathrm{q} i_\mathrm{sq} - R_\mathrm{s} i_\mathrm{sd}}{L_\mathrm{d}} \\
\frac{\mathrm{d} i_\mathrm{sq}}{\mathrm{d} t}&=\frac{u_\mathrm{sq} - p \omega_\mathrm{me} (L_\mathrm{d} i_\mathrm{sd} + \mathit{\Psi}_\mathrm{p}) - R_\mathrm{s} i_\mathrm{sq}}{L_\mathrm{q}} \\
\frac{\mathrm{d} \varepsilon_\mathrm{el}}{\mathrm{d} t}&= p \omega_\mathrm{me}\end{split}\]
Torque Equation
\[T=\frac{3}{2} p (\mathit{\Psi}_\mathrm{p} +(L_\mathrm{d}-L_\mathrm{q})i_\mathrm{sd}) i_\mathrm{sq}\]