To cancel harmonics and get fundamental back EMFs for precise rotor position and speed estimations under short-circuit fault, this article introduces a new sensorless fault-tolerant control method for 5-phase PMSM using a sigmoid sliding mode observer (SSMO) with a second-order generalized integrator (SOGI) to replace the LPF. For tuning SOGI, two different frequency estimators are proposed. First, a closed-loop synchronous reference frame phase-locked loop (SRF-PLL) is fed back to SOGI for frequency adaptation based on two orthogonally estimated filtered-back EMFs. Second, an independent open-loop frequency estimator (OLFE), based on two-estimated adversely distorted back EMFs, is proposed to ensure simple implementation. The speed and rotor position estimations are eventually accomplished from the quadrature PLL. Both SOGI-SRF-PLL and SOGI-OLFE-based SMO achieve satisfactory estimation performance under SC fault conditions, eliminate chattering issues, have good tracking errors, and have strong robustness against load disturbance. The results of simulation and practical experiments proved the effectiveness of these methods in all conditions.INDEX TERMS Multi-phase PMSM, single-phase short-circuit fault, sensorless fault tolerant control, sliding mode observer SMO, second-order generalized integrator SOGI.