改进型平方根无迹卡尔曼曼滤滤波及其在无轴承永磁同步电机无速度传感器运行中的应应用用

Modified square-root unscented Kalman filter and its application to speed sensorless control of bearingless permanent magnet synchronous motor

平方根无迹卡尔曼滤波(SRUKF)解决了标准无迹卡尔曼滤波(UKF)中由于误差协方差阵负定而引起的滤波发散问题,保证了算法的数值稳定性,但仍存在对模型参数变化的鲁棒性差、收敛速度慢及对突变状态的跟踪能力低等缺陷.因此,本文提出一种改进SRUKF滤波,通过引入时变渐消因子和弱化因子,实时修正滤波增益矩阵和误差协方差平方根矩阵,实现残差序列正交,确保SRUKF滤波保持对目标实际状态的准确跟踪.将该算法在无轴承永磁同步电机无速度传感器矢量控制系统中进行仿真研究.结果表明:改进SRUKF非线性近似精度、数值稳定性及滤波精度更高,在系统状态突变或负载扰动时,鲁棒性更强,能够有效实现转速及转子角度的准确估计,确保转子稳定悬浮运行.

The squareroot unscented Kalman filter （SRUKF） algorithm handles the problem of filtering divergence caused by nonpositiveness of the error covariance matrix in conventional unscented Kalman filter （UKF）. However, problems of low robustness to model parameter variation, slow convergence, and undesirable tracking ability to abrupt statechanges remain unsolved. We propose an improved SRUKF by introducing the timevarying fading factor and the diminishing factor to adjust gain matrices and the stateforecast covariance squareroot matrix, in order to realize the orthogonality of the residual sequences and force the SRUKF to track the realstate rapidly. The vector control system for the bearingless permanent magnet synchronous motor （BPMSM） without a speed sensor is set up based on this approach. Simulation results show that the proposed method improves the nonlinear approximation accuracy and raises numerical stability and filtering efficiency; it achieves high robustness to the abrupt statechanges and the load disturbances; it provides precise estimates of the speed and the space position, and ensures the stable operation of the rotor suspension.