We show that the pair (rotor position, resistance) of a nonsalient permanent magnet synchronous motor (PMSM) is not observable in the sensorless setting, namely, when only the electrical signals (voltages and intensities) are measured. However, if the rotation speed ω and the current in rotating frame id are not constantly zero, we prove that there only exist a maximum of six indistinguishable solutions, the resistance being the root of a polynomial of degree six. Besides, in the particular case where ω, id, and iq are constant, we show that the number of possible solutions is reduced to two, with two well-identified possible values for the resistance. Those two solutions can be dissociated if the sign of iq (namely, the mode of use of the motor) is known. Inspired by the nonlinear Luenberger methodology, this property enables us to propose an estimation algorithm, which relies on a one-dimensional minimization of a criterion involving the voltages and intensities filtered at three distinct sufficiently large frequencies. Its performances are tested and illustrated in simulations on real data.

中文翻译：

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无传感器 PMSM 的位置和电阻估计：不可观测系统的非线性 Luenberger 方法


我们表明，在无传感器设置中，即仅测量电信号（电压和强度）时，非凸极永磁同步电机（PMSM）的对（转子位置、电阻）是不可观测的。然而，如果旋转速度 ω 和旋转坐标系 id 中的电流不恒定为零，我们证明最多只存在六个不可区分的解，电阻是六次多项式的根。此外，在 ω、id 和 iq 恒定的特定情况下，我们表明可能的解决方案数量减少到两个，并且有两个明确的可能电阻值。如果已知 iq 的符号（即电机的使用模式），则可以分离这两个解。受非线性 Luenberger 方法的启发，这一特性使我们能够提出一种估计算法，该算法依赖于涉及在三个不同的足够大的频率处过滤的电压和强度的标准的一维最小化。其性能在真实数据的模拟中进行了测试和说明。