Rotor Position Detection Under Low Carrier Ratio Conditions Based on a Sliding Mode Observer

In high-speed permanent magnet synchronous motor (PMSM) drive systems, low switching frequencies increase discretization errors in conventional sliding mode observers (SMOs). This results in greater harmonics in the estimated stator currents and back electromotive force (EMF), thereby degrading the accuracy of speed and position estimation. This paper investigates steady-state position errors of conventional SMOs under low carrier ratios. The analysis reveals that the primary causes are model discretization errors and quasi-sliding mode motion errors. To address these issues, exact discrete voltage equations are derived in the two-phase stationary reference frame. Subsequently, an improved discrete-domain SMO is developed, incorporating a redesigned back-EMF computation method to enhance speed and position estimation accuracy. Furthermore, to improve dynamic performance under high-speed operating conditions, an adaptive quadrature phase-locked loop (AQPLL) is introduced. This method employs a stochastic gradient descent (SGD) algorithm for online parameter tuning, expanding the bandwidth for faster transient response while maintaining noise immunity at low speeds. The proposed method is validated through experiments on a low-inductance PMSM, demonstrating high estimation accuracy, reduced transient errors, and robust performance under parameter mismatches at a carrier ratio as low as 7.