在建立永磁同步电机(PMSM) Delta算子离散化模型的基础上,利用线性矩阵不等式(LMI)方法对PMSM的$H_{\mathrm{\infty }}$控制问题进行研究.以LMI 形式给出了PMSM $H_{\mathrm{\infty }}$控制器参数存在的充分条件,通过求解LMI得出PMSM $H_{\mathrm{\infty }}$控制器参数.最后对PMSM $H_{\mathrm{\infty }}$控制系统的稳定性问题进行分析,并给出负载和给定转速发生变化时PMSM $H_{\mathrm{\infty }}$控制系统的速度响应曲线.结果表明,快速采样时基于Delta 算子离散化方法所设计的$H_{\mathrm{\infty }}$控制器不但能保证PMSM闭环系统的稳定性,而且能较好的改善PMSM的跟随给定和抗干扰能力.

Delta operator model of PMSM is firstly built, based on linear matrix inequality (LMI) method, $H_{\mathrm{\infty }}$ control problem for PMSM is then discussed in this paper. A sufficient condition for the existence of the designed $H_{\mathrm{\infty }}$ controller is given in LMI form. The parameters of the designed controller can be obtained by solving the LMIs. Finally, the stability problem of PMSM $H_{\mathrm{\infty }}$ control system is analyzed, the speed response curves of the closed-loop system are given when the setting load and the giving speed are changed respectively. The analysis results show that when the sampling time is smaller, the designed $H_{\mathrm{\infty }}$ controller based on Delta operator ensures the PMSM closed-loop system asymptotically stable and the PMSM performance of exactly tracking and anti-interference can be enhanced.