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This study proposes an on-line minimum loss (ML) control strategy that considers the iron and copper losses of an interior permanent magnet synchronous motor in torque-controlled applications. The proposed ML control strategy utilizes a constrained optimization problem to satisfy torque reference tracking and loss minimization. An equivalent iron loss resistance circuit is adopted for the loss minimization. To solve the optimization problem, the Lagrange multiplier method is applied through a numerical analysis algorithm. The resulting solution provides the optimal current reference for every sampling instant. The Lagrange multiplier method needs parameters such as magnetic flux linkages, dynamic inductances, and iron loss resistance. Fundamental magnetic flux linkages are estimated using a flux observer, and the dynamic inductances are estimated with high-frequency voltage signal injection. The proposed iron loss resistance estimator estimates the equivalent iron resistance without any preliminary experiments. DC input power is measured using a current sensor for the accurate on-line estimation of iron loss resistance. To analyze the effectiveness of ML control compared with conventional maximum torque per ampere control, finite element analysis is used. The feasibility of the proposed ML control strategy is verified through simulation and experiments. [ABSTRACT FROM AUTHOR]