基于H∞滤波的无刷直流电机状态和参数估计

State and Parameter Estimation of Brushless DC Motor Based on H∞Filter

反电动势是无刷直流电机调速控制中必不可少的参数。针对噪声统计特性未知的情况,建立了在两相定子静止坐标系下的状态空间模型,将电机系统的反电动势、电流、反电动势和电机参数(L和R)作为增广的状态向量,采用扩展H∞滤波算法进行状态估计。构造非线性函数的雅可比矩阵和状态误差的李雅普诺夫函数,设计了表征相邻采样时刻非线性函数的雅可比矩阵之间关系的满秩矩阵,借助随机过程有界定理,给出了该算法的估计误差有界的充分条件。仿真结果表明,无刷直流电机匀速或加速运行时,扩展H∞滤波具备良好的收敛性,估计的反电动势等参数精度高,可实现电机的精准控制。

The back electromotive force(EMF)is an essential parameter in the speed control of brushless DC motor.The pa⁃per presents a method of back EMF estimation based on extended H∞filter which the statistical characteristics of noise are unknown,by establishing an augmented model under the stationary coordinate system of two-phase stator,the back EMF,the stator current,inductance and resistance as the state vector.A Lyapunov function of the state error and Jacobian matrices of nonlinear function is constructed,and a full-rank matrix is designed to index the change of the Jacobian matrices.Based on the boundedness of the ran⁃dom process,sufficient conditions for the estimated error of the algorithm are given.The simulation results show that,the extended H∞filter can always have good convergence speed and high precision of parameters estimation whenever the motor is running at a constant or accelerated speed,which can realize the precise control of the motor.