A Unified Safeguarded Scalar Framework for Convex Performance-Index-Based Current-Reference Generation in IPMSM Drives Under Current and Voltage Constraints

Interior permanent-magnet synchronous motor (IPMSM) current-reference laws are commonly derived for one objective or operating region at a time. This study develops a safeguarded scalar framework that separates exact torque-equality elimination, current/voltage feasibility, torque-command derating, and performance-index selection. On the positive-motoring branch, the torque equality reduces the two-current problem to one variable, while convex current and voltage residuals define a connected feasible interval. Taylor-based quadratic boundary estimates are refined by fixed-count Newton steps and accepted only after residual, slope, and interval checks; failed candidates are routed to a deterministic convex-sublevel fallback. For a strictly convex reduced objective, safeguarded Newton proposals are followed by mandatory derivative-bisection contractions, which provide an explicit final-bracket error bound. Maximum-torque-per-ampere, fixed-torque voltage minimization, loss-oriented indices, a normalized current–voltage stress index, and two structurally convex design extensions are treated in the same pipeline. A 3844-point steady-state numerical sweep over two published IPMSM parameter sets and both zero-resistance and full-resistance voltage models contained 3071 feasible cases. The low-cost setting produced a maximum d-axis current error of 1.331×10−3 A, whereas the conservative setting reduced it to 2.892×10−4 A. The evidence is numerical and steady-state; processor timing and hardware validation remain future work.