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This paper presents an online maximum torque per ampere (MTPA) control that considers both magnetic saturation and cross-magnetization effects of interior permanent-magnet synchronous machines (IPMSMs). For IPMSM drives, especially in torque-controlled applications, torque accuracy and high-efficiency operations are important issues. They can be dealt as a constrained optimization problem to satisfy both torque reference tracking and loss-minimizing operation. In this paper, nonlinear simultaneous equations are derived from Lagrange multiplier method, which could be solved by numerical algorithms. Among them, Levenberg–Marquardt algorithm (LMA) is employed to guarantee a robust calculation of optimal current references. It is optimized to alleviate calculation burden while maintaining the stability of the proposed algorithm. In addition, a torque reference limiter is implemented to satisfy a current limit in real time. The feasibility of the proposed method is verified under various operating conditions by simulation and experimental results. Through the proposed algorithms, accurate MTPA control is achieved under not only unsaturated but also highly saturated operating conditions. [ABSTRACT FROM AUTHOR]