具有不可测量前提变量的离散T-S模糊系统H∞/H−故障检测
1. 大连交通大学, 理学院, 辽宁大连 116028
2. 大连交通大学, 自动化与电气工程学院, 辽宁大连 116028
| 摘 要： | 本文研究了一类具有不可测量前提变量的离散非线性系统的故障诊断问题，该系统为Takagi-Sugeno (T-S)模型，所研究的T-S结构可以通过使用含有局部非线性规则来减少模型中的规则数量，从而简化了计算的过程。在设计故障检测观测器时，主要考虑未知输入信号的因素，同时为了最小化不确定性对系统性能的影响，最大化执行器故障对生成残差的影响。描述残差对故障灵敏度的H-性能指标和残差对未知输入鲁棒性的H∞性能指标，将鲁棒故障检测观测器的设计问题描述为满足H∞/H-的优化设计问题。不可测量前提变量与可测量前提变量的情况相比，它可以表示更大的非线性系统。然后给出满足故障检测观测器的存在条件，提出一种新的迭代线性矩阵不等式（LMI）算法和运用凸优化技术来求解最优观测器增益矩阵。最后通过数值算例来验证该方法的有效性，利用这种方法设计的故障检测观测器对故障的灵敏度高，对未知输入的鲁棒性强。 |
| 关 键 词： | 离散时间的T-S模糊系统; 不可测量的前提变量; 故障诊断; H∞/H-性能指标 |
| DOI： | 10.57237/j.se.2023.05.001 |
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收稿日期: 2023-06-13
接受日期: 2023-07-14
在线出版日期: 2023-10-09
H∞/H− Fault Detection for Discrete T-S Fuzzy Systems with Unmeasurable Premise Variables
1. School of Science, Dalian Jiaotong University, Dalian 116028, China
2. School of Electric Engineering and Automation, Dalian Jiaotong University, Dalian 116028, China
| Abstract: | In this paper, we study the fault diagnosis problem for a class of discrete nonlinear systems with unmeasurable premise variables, which are Takagi-Sugeno (T-S) models. The studied T-S structure can simplify the computation by using rules containing local nonlinearities to reduce the number of rules in the model. In designing the fault detection observer, the main consideration is the unknown input signal, while maximizing the effect of actuator failure on the generated residuals in order to minimize the impact of uncertainty on the system performance. The H- performance index of residual-to-fault sensitivity and the H∞ performance index of residual-to-unknown-input robustness are described, and the design problem of a robust fault detection observer is described as an optimal design problem satisfying H∞/H-. The unmeasurable premise variables are compared to the case of measurable premise variables, which can represent larger nonlinear systems. Then, a new iterative linear matrix inequality (LMI) algorithm and convex optimization technique are proposed to solve the optimal observer gain matrix by giving the existence conditions of the fault detection observer. Finally, the effectiveness of the method is verified by numerical examples, and the fault detection observer designed by this method is highly sensitive to faults and robust to unknown inputs. |
| Keywords: | Discrete-Time T-S Fuzzy System; Non-measurable Premise Variables; Fault Diagnosis; H∞/H- Performance Index |
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