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Delta算子描述不确定离散故障检测系统$H_\infty$滤波器设计

林瑞全,张玉   

  1. 福州大学电气工程与自动化学院, 福州 350116
  • 出版日期:2015-01-25 发布日期:2015-04-08

林瑞全,张玉. Delta算子描述不确定离散故障检测系统$H_\infty$滤波器设计[J]. 系统科学与数学, 2015, 35(1): 65-74.

LIN Ruiquan,ZHANG Yu. DESIGN OF ${\bm H}_{\bf \infty}$ FILTER FOR DELTA OPERATOR-FORMULATED UNCERTAIN DISCRETE-TIME FAULT DETECTION SYSTEMS[J]. Journal of Systems Science and Mathematical Sciences, 2015, 35(1): 65-74.

DESIGN OF ${\bm H}_{\bf \infty}$ FILTER FOR DELTA OPERATOR-FORMULATED UNCERTAIN DISCRETE-TIME FAULT DETECTION SYSTEMS

LIN Ruiquan ,ZHANG Yu   

  1. College of Electrical Engineering and Automation, Fuzhou University, Fuzhou 350108
  • Online:2015-01-25 Published:2015-04-08

考虑故障检测对象参数发生加性范数有界摄动的情况, 基于线性矩阵不等式(LMI)方法, 对一类由Delta算子描述的不确定离散故障检测系统的鲁棒$H_\infty$故障检测滤波器设计问题进行研究.通过构建增广系统, 利用Lyapunov函数理论和Schur补定理, 把$H_\infty$故障检测滤波器存在的充分条件转化为LMI形式.通过求解数值算例并作对比分析, 表明考虑对象参数发生摄动所设计的鲁棒$H_\infty$ 故障检测滤波器能正确有效地检测到故障信号, 而不考虑对象参数发生摄动所设计的$H_\infty$ 故障检测滤波器将不能正确有效地检测到故障信号.

With consideration that the parameters of the Delta operator-formulated uncertain discrete-time systems are of additively norm-bounded uncertainty, based on linear matrix inequality (LMI) method, a design method of robust $H_\infty$ fault detection filter for the uncertain Delta operator-formulated discrete-time systems is discussed in this paper. By constructing an augmented system, with Lyapunov function theory and Schur complement lemma, a sufficient condition for the existence of the robust $H_\infty$ fault detection filter is given in LMI form. A numerical example is used to illustrate the effectiveness of the proposed approach. The contrastive analysis results show that with the designed method, the fault signal can be correctly detected when the parameters of the fault detection systems are of variations, while the fault signal can't be correctly detected if the variations are not considered when the fault detection filter is designed.

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[1] 林瑞全,郑先娜. 基于Delta算子离散化方法的质子交换膜燃料电池[J]. 系统科学与数学, 2017, 37(12): 2317-2326.
[2] 林瑞全,张涛,翟少琼. 基于Delta算子离散化方法的永磁同步电机${\bm H}_\infty$控制系统[J]. 系统科学与数学, 2017, 37(1): 1-9.
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