The growing demand for fault-tolerant systems requires the use of algorithms that will maintain continuity of operation in the event of faults, e.g., in measuring sensors. Sensorless control methods, originally developed for electric motor drives without speed measurements, can be applied within fault-tolerant control (FTC) strategies when speed sensors fail. Recent research also increasingly addresses failures of current sensors (CS). This study proposes a permanent magnet synchronous motor (PMSM) drive control method based on a current-sensorless vector control structure, eliminating the need to measure phase currents and enabling compensation for damaged CS. Three open-loop estimator types derived from a PMSM mathematical model are introduced, all operating without feedback from state variables. The first estimator uses fixed design parameters optimized via particle swarm optimisation (PSO). The second relies on the relationship between stator flux and dq-axis currents. The third extends this relationship by incorporating rotor position to account for spatial harmonics. The relevant flux functions are stored in look-up tables (LUTs). This study discusses challenges in selecting estimator parameters and issues related to voltage and speed measurement. The proposed solutions were tested on a 2.5 kW PMSM experimental setup across a wide range of operating conditions.