Voltage
$$ \begin{aligned} u_d &= (R_s + p L_d )i_d - {\omega_e L_q} i_q \\ u_q &= (R_s + p L_q )i_q + {\omega_e L_d} i_d + \omega_e {\it\Psi_f} \end{aligned} $$Torque
$$ \begin{aligned} T_e &= \frac{3}{2}\; p_n[(L_d-L_q)i_d i_q + {\it\Psi_f} i_q] \end{aligned} $$Current limit condition 电流极限环
$$ \begin{aligned} i_d^2+i_q^2 \le I_{max}^2 \end{aligned} $$Voltage limit condition 电压极限环
$$ \begin{aligned} u_d^2 + u_q^2 \le U_{max}^2 \end{aligned} $$$$ \begin{aligned} (\omega_e L_q i_q)^2+(\omega_e L_d i_d + \omega_e {\it\Psi_f})^2 &\le U_{max}^2 \end{aligned} $$Field-weakening
Reference
[1] Matlab PMSM Drive Characteristics and Constraint Curves [2] Matlab Field-Weakening Control