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Estimations of magnetic flux linkages, either between the stationary windings of the stator for the direct torque control (DTC), or between the stationary windings and the rotor for the sensorless field-oriented control (FOC), are based on integration of corresponding voltages. Integration of voltages with offsets that come from improperly calibrated measurements as well as from transient states generally produces unwanted drifts in the resulting magnetic flux linkages, which when used within any type of control of sensorless electrical drives results in instability. This paper addresses that problem and proposes a simple self-contained solution based on orthogonal properties of waveforms of input voltages and resulting magnetic flux linkages in the frame of reference fixed to the geometry of the stator. The proposed solution requires only two periodic orthogonal input waveforms with a distinct common fundamental harmonic, which as such is independent of the type and parameters of the used machine. The idea of the proposed solution is presented analytically, its stability is proven by means of the quadratic Lyapunov theory, and its functionality is demonstrated by standalone simulations and experiments within the sensorless FOC of a permanent magnet synchronous machine (PMSM).

A Driftless Estimation of Orthogonal Magnetic Flux Linkages in Sensorless Electrical Drives