在建立质子交换膜燃料电池(PEMFC)供气系统数学模型的基础上,采用Delta算子离散化方法对PEMFC 的供气系统过氧比$H_{\mathrm{\infty }}$控制器的设计问题进行研究,通过求解线性矩阵不等式(LMI)得出其$H_{\mathrm{\infty }}$控制器参数.在此基础上,把基于Delta算子离散化方法所设计的$H_{\mathrm{\infty }}$ 控制器性能与基于传统Z 变换方法所设计的控制器性能进行分析比较.结果表明:快速采样时,相比传统Z变换方法,基于Delta算子方法所设计的PEMFC 过氧比$H_{\mathrm{\infty }}$ 控制器不但能更好保证系统的稳定性,具有更好的抗干扰性,可以克服负载变化对PEMFC性能的影响,实现过氧比的有效控制,而且其控制性能趋近于基于连续系统方法所设计的$H_{\mathrm{\infty }}$控制系统的性能.

In this paper, the mathematical model of the air supply system of proton exchange membrane fuel cell (PEMFC) is established, the oxygen excess ratio $H_{\mathrm{\infty }}$ controller of PEMFC is then designed by using Delta operator discretization method, and the controller parameters can be obtained by solving the linear matrix inequality (LMI). Based on the above, the performance of the $H_{\mathrm{\infty }}$ controller based on the Delta operator discretization method and the performance of the controller based on the traditional Z transform method are compared. The results show that the PEMFC $H_{\mathrm{\infty }}$ controller based on Delta operator method can not only guarantee the stability and anti-interference of the system, be resistant to the affection of load variations, the oxygen excess ratio of PEMFC can be effectively controlled, but also its control performance approaches to that of the $H_{\mathrm{\infty }}$ control system based on the continuous system method. } \EKeywords{PEMFC, Delta operator, $H_{\mathrm{\infty }}$ control, oxygen excess ratio control, LMI.