A differential-algebraic approach to speed estimation in an induction motor

This note considers a differential-algebraic approach to estimating the speed of an induction motor from the measured terminal voltages and currents. In particular, it is shown that the induction motor speed ω satisfies both a second- and a third-order polynomial equation whose coefficients depend on the stator voltages, stator currents, and their derivatives. It is shown that as long as the stator electrical frequency is nonzero, the speed is uniquely determined by these polynomials. The speed so determined is then used to stabilize a dynamic (Luenberger type) observer to obtain a smoother speed estimate. With full knowledge of the machine parameters and filtering of the sensor noise, simulations indicate that this estimator has the potential to provide low speed (including zero speed) control of an induction motor under full rated load.