This paper proposes a practical way to generate current commands for six‑phase permanent‑magnet synchronous machines (PMSMs) after one phase goes open. The authors make and store Fourier coefficients for each healthy phase in lookup tables (LUTs). Online, the controller reads those tables together with rotor position and speed to create the phase currents that deliver the requested torque while respecting the drive limits.

The core idea is to allow unbalanced and nonsinusoidal phase currents after a fault, instead of forcing balanced or purely sinusoidal currents. The offline step computes the best Fourier coefficients for the healthy phases. That computation is arranged as a lexicographic optimization: first it minimizes torque ripple (the fast fluctuation of torque that causes vibration and noise), then, holding that minimum ripple, it minimizes stator copper loss (heat from currents in the motor windings). The optimization enforces timing and hardware limits such as the required torque, that the sum of phase currents matches the neutral condition, peak current and peak voltage limits, and a cap on allowable torque ripple.

A practical advantage is that cogging torque — a pattern of torque wiggles caused by the magnets and iron — can be included in the offline optimization so it is compensated in the generated current references. In simulation the method extended the motor’s feasible speed range after a phase‑open fault by about 30% at low torque and about 23% along an example load curve. A finite‑element analysis reported a 77% reduction in peak‑to‑peak torque ripple when cogging‑torque compensation was included.

The method has an offline/online split. The heavy optimization work runs offline over a grid of operating points (torque and electrical frequency) and fills the LUTs. Online, the LUTs are interpolated to produce time‑varying current references using the rotor position. The authors also redesigned the offline step compared with past work so the LUT generation is faster: they solve a linear program to find the minimum torque ripple and then a quadratic problem to minimize copper loss subject to that ripple level, rather than repeatedly solving a full problem while raising the allowed ripple in many small steps.