Abstract-The rotor position is required in many control schemes in electrical drives. Replacing position sensors by machine self-sensing estimators increases reliability and reduces cost. Solutions based on tracking magnetic anisotropies through the monitoring of the incremental inductance variations are efficient at low-speed and standstill operations. This inductance can be estimated by measuring the response to the injection of high-frequency signals. In general however, the selection of the optimal frequency is not addressed thoroughly. In this paper, we propose discrete-time operations based on a rotating voltage injection at frequencies up to one third of the sampling frequency used by the digital controller. The impact on the rotation-drive, the computational requirement, the robustness and the effect of the resistance on the position estimation are analyzed regarding the signal frequency.Index Terms-AC motor drives, Sensorless control, Highfrequency signal-injection, Permanent-magnet (PM) machine NOMENCLATURE αβ axes of the stationary frame; qd axes of the synchronous frame; xy axes of the anisotropy frame; ϕ x angle of the anisotropy frame with respect to αβ; x denotes a space vector, that can be the current i, the voltage v, the flux ψ or the back-emf e PM ; a denotes an anisotropic parameter, that can be the resistance r or the incremental self-inductance l t ; a + , a -positive and negative parameters, corresponding to a; x(t) continuous-time value; ν s , T s sampling frequency and sampling period: ν s = 1/T s ; x(t [k] ) samples of the value at sampling instants t [k] ; x [k] mean of x(t) between two sampling instants;
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