Linearised Model of Surface-Mounted Permanent Magnet Synchronous Motor for Stability and Speed Enhancement

Abstract

This paper presents a linearised model of the Surface-Mounted Permanent Magnet Synchronous Motor (SPMSM) to enhance stability studies and facilitate control system design. The SPMSM is widely used in various industrial applications due to its high efficiency and performance. However, its non-linear behaviour poses challenges for analysis and control. A state-space model of the SPMSM is derived and linearised at a chosen operating point, with key motor parameters such as L_d = L_q = 0.0171 H, R = 5.29 Ω, and λm = 0.321 Wb. Simulation results demonstrate that the linearised model accurately captures the behaviour of the non-linear system across various input conditions. The step response showed stable, well-damped behaviour with all state variables (current, speed, and position) settling within a few milliseconds. The impulse response analysis confirmed the system’s rapid return to equilibrium, with overshoot levels kept below 5%, indicating good damping. The Bode plot revealed a smooth frequency response, with gain margins and phase margins indicating a stable system. The pole-zero map confirmed that all poles lie in the left-half plane, ensuring system stability. These results validate the linearised model as a reliable tool for stability analysis and control design in SPMSM applications.