A robust nonlinear position observer for synchronous motors with relaxed excitation conditions

A robust, nonlinear and globally convergent rotor position observer for surface-mounted permanent magnet synchronous motors was recently proposed by the authors. The key feature of this observer is that it requires only the knowledge of the motor's resistance and inductance. Using some particular properties of the mathematical model it is shown that the problem of state observation can be translated into one of estimation of two constant parameters, which is carried out with a standard <i>gradient algorithm</i>. In this work, we propose to replace this estimator with a new one called dynamic regressor extension and mixing, which has the following advantages with respect to gradient estimators: (1) the stringent persistence of excitation (PE) condition of the regressor is <i>not necessary</i> to ensure parameter convergence; (2) the latter is guaranteed requiring instead a non-square-integrability condition that has a clear physical meaning in terms of signal energy; (3) if the regressor is PE, the new observer (like the old one) ensures convergence is exponential, entailing some robustness properties to the observer; (4) the new estimator includes an additional filter that constitutes an additional degree of freedom to satisfy the non-square integrability condition. Realistic simulation results show significant performance improvement of the position observer using the new parameter estimator, with a less oscillatory behaviour and a faster convergence speed.

本文作者近期提出了一种针对表贴式永磁同步电机（surface-mounted permanent magnet synchronous motors）的鲁棒、非线性且全局收敛的转子位置观测器（rotor position observer）。该观测器的核心特性在于，仅需知晓电机的电阻与电感参数。借助数学模型的若干特殊性质，本文证明状态观测问题可转化为两个恒定参数的估计问题，并通过标准梯度算法（gradient algorithm）完成该估计任务。在本研究中，我们提出采用一种名为动态回归器扩展与混合（dynamic regressor extension and mixing）的新型估计器替代原有的梯度类估计器，相较于梯度估计器，该新型估计器具备以下优势：(1) 无需满足回归器严格的激励持续（persistence of excitation, PE）条件即可保证参数收敛；(2) 仅需满足非平方可积性条件即可保证参数收敛，该条件在信号能量层面具备清晰的物理意义；(3) 若回归器满足激励持续条件，则新型观测器（与原观测器一致）可保证指数收敛，从而为观测器赋予一定的鲁棒特性；(4) 新型估计器包含一个额外的滤波器，该滤波器可作为额外自由度以满足非平方可积性条件。实际仿真实验结果表明，采用新型参数估计器的转子位置观测器性能得到显著提升，具体表现为振荡更少、收敛速度更快。