*4.1. System Description*

Simulations were performed in the below-based speed region and the field-weakening region based on the IRFOC with a speed sensor. The rotor field angle is usually calculated by (21) and (22) in IRFOC.

$$
\theta\_r = \int \omega\_r dt + \int \omega\_{sl} dt \tag{21}
$$

$$
\omega\_{sl} = \frac{1}{t\_r} \times \frac{\dot{i}\_{qs}^\*}{\dot{i}\_{ds}^\*} \tag{22}
$$

where *θ<sup>r</sup>* is the rotor field angle, *ω<sup>r</sup>* is the actual electric angular velocity of the rotor, which can usually be obtained with a photoelectric encoder or rotating transformer, *ωsl* is the slip angular velocity, *tr* is the rotor time constant and *tr* = *Lr*/*Rr*. *Rr* is the resistance of the rotor, *i* ∗ *qs* is the torque current command, and *i* ∗ *ds* is the magnetic current command. To reflect the inaccuracy of the rotor field orientation, the slip angular velocity is calculated with different rotor resistances, namely,0.5*Rr*, 0.8*Rr*, and 1.5*Rr*. The specifications of the simulated and experimental induction machines are shown in Table 1.


**Table 1.** Specification of the simulated and experimental induction machines.
