非光滑三明治系统状态估计与故障预报研究

Non-smooth sandwich systems widely exist in mechanical system, electronic system and communication system. In order to estimate the states of the system and detect the fault of the system more accurate, it is necessary to construct special types of state estimation observer and fault detection observer for the special systems. Based on the characteristics of the sandwich system with hysteresis, a non-smooth state-space function will be constructed in terms of the key term separation principle and switching functions. Then, a non-smooth observer which can switch among the different operating zones automatically according to the change of the operation conditions will be proposed based on the obtained non-smooth state-space model. The convergence theorem and its proof of the proposed non-smooth observer will be given as well. Under the consideration of the model uncertainties and disturbances of the system, by introducing the concept of general disturbance vector, spectrum analysis of the residuals, and zeros assignment, the research will focus on the development of the state estimation and fault detection observers for the non-smooth sandwich systems with dead zone, backlash and hysteresis. . Some innovations and breakthroughs in the observer construction theory and fault detection field for complex nonlinear system are expected to be obtained by finishing this study. The research results are expected to provide novel theories and techniques in the real application for state estimation and fault detection of non-smooth sandwich systems which widely exist in the engineering applications.

非光滑三明治系统广泛存在于机械系统、电路系统和通信系统中，针对这类特殊系统构建特殊的状态估计观测器和故障预报观测器来实现准确的状态估计和故障预报意义重大。本项目拟根据迟滞非光滑三明治系统的特点，采用关键项分离原理和切换函数，建立描述该类系统的非光滑状态空间方程。据此，构造能够随系统工作区间变化而自动切换的迟滞非光滑观测器，并给出相应的收敛定理及其证明。在考虑模型不确定性和干扰的情况下，通过引入广义干扰向量概念，结合残差频谱分析和观测器零点配置方法，研究构建死区、间隙和迟滞三明治系统的鲁棒状态估计观测器和鲁棒故障预报观测器。.本项目的研究，可望在复杂非线性系统观测器设计理论、复杂非线性系统故障预报方法等方面有所创新和突破，获得有学术意义实用价值的研究成果，为工程实践中广泛存在的非光滑三明治系统的状态估计和故障预报提供新的理论与技术。

背景：.在电路系统、通讯系统和工业机电系统中都广泛存在着死区、间隙、迟滞三种典型非光滑非线性环节。而且，在实际系统中这些非光滑非线性环节往往夹在两个线性环节之间，构成为非光滑三明治系统。在过去的建模中，往往忽略了这些非光滑非线性特性，而用线性系统简化该类系统。然而，这样的简化处理必然造成模型的不准确，给后面的观测器构建带来不利影响。因此，通过努力将这些客观存在的特性都考虑进去，构建更为准确的数学模型来描述非光滑三明治系统,在此基础上构建观测器对这类非光滑三明治系统进行准确的状态估计和故障预报是很有应用价值的研究工作。.主要研究内容、重要结果和科学意义：.1.根据非光滑三明治系统的特性，由分离原则，通过引入切换函数和切换项，提出并分别建立了带死区三明治系统、带间隙三明治系统和带迟滞三明治系统的非光滑状态空间方程，为构建非光滑观测器提供基础。.2.根据前面提出的非光滑状态空间方程，构造了一种非光滑状态估计观测器以估计这类系统的状态。在分析清楚死区、间隙、迟滞三者逻辑关系的基础上，依次完成了死区、间隙和迟滞三明治系统的非光滑状态估计观测器设计工作。仿真和实验结果都表明：与传统的观测器相比，项目提出的非光滑状态估计观测器获得了更快和更准确的状态估计效果。.3.对非光滑状态估计观测器的收敛性进行了深入分析。分别给出了相应非光滑状态估计观测器的收敛定理和相应证明。.4.针对三明治系统特点，定义“广义干扰”，并最小化广义干扰到状态估计误差传递函数的范数指标来设计鲁棒观测器的增益矩阵，从而使得观测器的状态估计误差对广义干扰不敏感，实现三明治系统鲁棒状态估计。.5.在考虑三明治系统模型误差和干扰的情况下，构建鲁棒故障预报观测器对非光滑三明治系统进行故障预报。鲁棒故障预报观测器的增益矩阵是通过零点配置和最小化基准区间观测器的范数指标的方法来确定。因此，鲁棒故障预报观测器的残差只对故障敏感。