An inverter for controlling an electric machine, the inverter comprising: a switching circuit comprising a low-side switch and a high-side switch, the low-side switch and the high-side switching each having a control terminal and two switched terminals; a driver circuit for providing control signals to the control terminals of the switching circuit; a pulse width modulation module for providing pulse-width modulated signals to the electric machine based on a commanded direct-axis voltage (V d *) and a commanded quadrature-axis voltage (V q *); an electronic data processor; a data storage device in communication with the electronic data processor; a control module stored in the data storage device, the control module comprising software instructions for execution by the electronic data processor, the control module characterized by: an inductance estimator to estimate direct inductance and quadrature inductance associated with the electric machine based on a first set of equations that assume constant rotor resistance and constant magnetic flux, wherein the first set of equations for estimation of the direct inductance, Ld, and quadrature inductance, Lq, comprise the following: v d = R s i d − L q i q ω e L q = R s i d − v d i q ω e v q = R s i q + L d i d ω e + λ f ω e L d = v q − λ f ω e − R s i q ω e i d where: L d is direct-axis inductance; L q is quadrature-axis inductance; v d or V d is direct-axis voltage; vq or V q means quadrature-axis voltage; R s is stator resistance; i d or I d is direct-axis current; i q or I q is quadrature-axis current; λ f iss the back emf constant; and ω e is the electrical speed of the rotor; a torque estimator to estimate an observed torque (T em) associated with a rotor of the electric machine based on the commanded direct-axis voltage and the commanded quadrature-axis voltage, where the observed torque is proportional to the observed power consumption of the electric machine; and a back-electromotive force module configured to determine a back-electromotive force adjustment (λ f) derived from the estimated, observed torque (T em) and a commanded torque (T final *). a switching circuit comprising a low-side switch and a high-side switch, the low-side switch and the high-side switching each having a control terminal and two switched terminals; a driver circuit for providing control signals to the control terminals of the switching circuit; a pulse width modulation module for providing pulse-width modulated signals to the electric machine based on a commanded direct-axis voltage (V d *) and a commanded quadrature-axis voltage (V q *); an electronic data processor; a data storage device in communication with the electronic data processor; a control module stored in the data storage device, the control module comprising software instructions for execution by the electronic data processor, the control module characterized by: an inductance estimator to estimate direct inductance and quadrature inductance associated with the electric machine based on a first set of equations that assume constant rotor resistance and constant magnetic flux, wherein the first set of equations for estimation of the direct inductance, Ld, and quadrature inductance, Lq, comprise the following: v d = R s i d − L q i q ω e L q = R s i d − v d i q ω e v q = R s i q + L d i d ω e + λ f ω e L d = v q − λ f ω e − R s i q ω e i d where: L d is direct-axis inductance; L q is quadrature-axis inductance; v d or V d is direct-axis voltage; vq or V q means quadrature-axis voltage; R s is stator resistance; i d or I d is direct-axis current; i q or I q is quadrature-axis current; λ f iss the back emf constant; and ω e is the electrical speed of the rotor; a torque estimator to estimate an observed torque (T em) associated with a rotor of the electric machine based on the commanded direct-axis voltage and the commanded quadrature-axis voltage, where the observed torque is proportional to the observed power consumption of the electric machine; and a back-electromotive force module configured to determine a back-electromotive force adjustment (λ f) derived from the estimated, observed torque (T em) and a commanded torque (T final *). L d is direct-axis inductance; L q is quadrature-axis inductance; v d or V d is direct-axis voltage; vq or V q means quadrature-axis voltage; R s is stator resistance; i d or I d is direct-axis current; i q or I q is quadrature-axis current; λ f iss the back emf constant; and ω e is the electrical speed of the rotor; a torque estimator to estimate an observed torque (T em) associated with a rotor of the electric machine based on the commanded direct-axis voltage and the commanded quadrature-axis voltage, where the observed torque is proportional to the observed power consumption of the electric machine; and a back-electromotive force module configured to determine a back-electromotive force adjustment (λ f) derived from the estimated, observed torque (T em) and a commanded torque (T final *).