A decoupling-based multivariable H∞ controller for PMSM speed and current regulation

High precision speed regulation of the permanent magnet synchronous motor (PMSM) is a critical challenge in modern industrial applications, including electric vehicles and traction systems. This task is significantly affected by external disturbances, such as variable load torque, as well as physical phenomena often neglected in analytical models, such as magnetic circuit saturation or thermal variations in electrical parameters. In this context, conventional control methods often fail to ensure both dynamic performance and robustness. This paper proposes a multivariable H∞ control strategy based on field-oriented control (FOC) and d/q decoupling to design a robust and high-performance controller. The diagonal multiple-input multiple-output (MIMO) model, linking the direct-axis voltage𝑣𝑑to the current 𝑖𝑑and the quadrature-axis voltage 𝑣𝑞to the rotational speed 𝜔𝑟, is derived directly from the decoupling principles of FOC, without relying on linearization around an operating point or modeling of parametric uncertainties. The H∞ controller is synthesized using the standard configuration, with carefully selected weighting functions to ensure dynamic performance, closed-loop stability, and effective disturbance rejection. Numerical simulations demonstrate that the proposed controller achieves accurate speed reference tracking, fine current regulation, and fast load disturbance rejection, confirming its effectiveness and robustness. This approach provides an advanced alternative to conventional control methods by fully exploiting the multivariable structure of the system.