构造性自适应观测器设计方法研究及其在故障诊断中的应用
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摘要
状态估计和参数估计在故障诊断、自适应控制、容错控制等领域有着广泛的应用,自适应观测器就是通过状态和参数的联合估计达到该目标的一类递归算法本论文主要围绕自适应观测器的设计问题展开,探讨了一类构造性自适应观测器设计方法,并将其应用于动态系统的故障诊断。主要研究工作如下：
1.针对现有的自适应观测器没有考虑状态方程和输出方程同时含有未知参数的情况,用构造性方法对状态方程和输出方程同时含有未知参数的连续线性时变系统设计了一种带指数遗忘因子的自适应观测器,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。与应用于增广系统进行自适应估计的Kalman滤波器相比,自适应观测器方法有着简单的收敛性条件和数值仿真上易于实现的优点。数值仿真结果表明该自适应观测器具有良好的快速收敛性、跟踪性及抗干扰性等期望性能。
2.将上文设计的连续线性时变系统自适应观测器推广到离散线性时变系统,针对状态方程和输出方程同时含有未知参数的多输入多输出离散线性时变系统,用构造性方法设计了一种自适应观测器,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。数值仿真表明该自适应观测器具有收敛性、跟踪性及抗干扰性等期望性能。
3.基于高增益观测器和自适应估计理论,针对状态方程和输出方程同时含有未知参数的一类一致能观的单.输出非线性系统,用构造性方法设计了一种联合估计状态和未知参数的自适应观测器。该自适应观测器的参数估计采用时变增益矩阵,结构形式及参数设置简单。给出了使该自适应观测器满足全局指数收敛性的持续激励条件,并在理论上简洁地证明了该自适应观测器的全局指数收敛性。数值仿真结果表明该自适应观测器具有期望的性能,如快速收敛性、跟踪性等。
4.进一步将上文单输出非线性系统的自适应观测器设计推广到一类更一般的多输出非线性系统,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。仿真表明该自适应观测器可以快速跟踪未知参数的变化。
5.一般情况下,残差是变量测量值和它的数学解析值之间的解析冗余,故障的发生会引起系统的残差发生改变。基于模型的故障诊断方法是通过对测量信号处理技术生成残差的,本质上是对包含所需属性的原始数据的一种转换,因此依赖于残差的设计。本文基于前一部分已设计的自适应观测器对线性时变系统的加性故障设计残差,并在理论上分析残差的性质。该残差同时考虑了执行机构故障和传感器故障。数值仿真表明所设计的残差对被监视的故障是敏感的。
6.汽车在行驶过程中，主动悬架系统是影响乘客舒适程度和安全的最重要部件之一，而悬架系统经过长时间使用,容易老化导致性能降低,有必要对零件的老化系数进行估计，以便控制策略中考虑参数的变化。本文基于主动悬架系统全系统非线性状态方程,构造自适应观测器以实现系统未测状态和零件老化系数的实时估计。仿真表明,该自适应观测器能够迅速的跟踪元件老化系数的变化,实现悬架系统关键元器件的故障诊断。
Joint estimation of states and parameters in state-space systems is of practical importance for fault diagnosis and for adaptive control. Recursive algorithms designed for this purpose are usually known as adaptive observers. In this dissertation a class of adaptive observers in a constructive manner is discussed and the main contributions are described as follows:
1. Previous works on globally convergent adaptive observers do not consider unknown parameters in both state equations and output equations. In this dissertation for continuous-time multiple-input multiple-output linear time-varying systems with unknown parameters in both state and output equations, an adaptive observer with exponential forgetting factor is designed in a constructive manner and its global exponential convergence is formally established under appropriate assumptions. Compared to the Kalman filter, the advantages of the proposed adaptive observer reside both in its simpler convergence condition and in its more efficient numerical implementation. A numerical example is presented to illustrate the performance of the adaptive observer.
2. For discrete-time multiple-input multiple-output linear time-varying systems with unknown parameters in both state and output equations, an adaptive observer is designed in a constructive manner. In order to establish the global exponential convergence for simultaneous estimation of states and unknown parameters, a persistent excitation condition is required. A numerical example is presented to illustrate the performance of the adaptive observer.
3. For a class of single output uniformly observable nonlinear systems with unknown parameters in both state and output equations, an adaptive observer is designed in a constructive manner based on the techniques of high gain observer and adaptive estimation. The high gain adaptive observer for joint state and unknown parameter estimation is conceptually simple. The new algorithm makes use of a time varying gain matrix for unknown parameter estimation, which simplifies the initialization and parameter tuning. In order to establish the global exponential convergence of the adaptive observer, a persistent excitation condition is required. Consequently, the global exponential convergence for simultaneous estimation of states and unknown parameters is formally established following a simple procedure. A numerical example is presented to illustrate the performance of this adaptive observer.
4. Furthermore a more general adaptive observer for nonlinear multi-input-multi-output (MIMO) systems is developed and a persistent excitation condition is obtained in order to establish the global exponential convergence of the adaptive observer. A numerical example is presented to illustrate the performance of this adaptive observer.
5. A residual is a transformation of raw data with some desired properties for the purpose of fault diagnosis. Typically, model-based methods for fault diagnosis rely on the design of residuals which are signals computed from available sensor measurements with the aid of a mathematical model of the monitored system. Based on the developed adaptive observer in this dissertation, residuals are generated for fault diagnosis in linear time-varying systems. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their insensitivity to the faults to be ignored. The residuals presented in this dissertation extend the results of previous works by simultaneously taking into account both actuator and sensor faults. A numerical example is presented to illustrate the performance of these residuals.
6. A full vehicle active suspension system with the nolinear dynamics is considered. The aging coefficients of the components are modeled as unknown parameters. An adaptive observer is designed to estimate the aging coefficients. The simulation result shows the aging coefficients could be estimated rapidly.
1.针对现有的自适应观测器没有考虑状态方程和输出方程同时含有未知参数的情况,用构造性方法对状态方程和输出方程同时含有未知参数的连续线性时变系统设计了一种带指数遗忘因子的自适应观测器,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。与应用于增广系统进行自适应估计的Kalman滤波器相比,自适应观测器方法有着简单的收敛性条件和数值仿真上易于实现的优点。数值仿真结果表明该自适应观测器具有良好的快速收敛性、跟踪性及抗干扰性等期望性能。
2.将上文设计的连续线性时变系统自适应观测器推广到离散线性时变系统,针对状态方程和输出方程同时含有未知参数的多输入多输出离散线性时变系统,用构造性方法设计了一种自适应观测器,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。数值仿真表明该自适应观测器具有收敛性、跟踪性及抗干扰性等期望性能。
3.基于高增益观测器和自适应估计理论,针对状态方程和输出方程同时含有未知参数的一类一致能观的单.输出非线性系统,用构造性方法设计了一种联合估计状态和未知参数的自适应观测器。该自适应观测器的参数估计采用时变增益矩阵,结构形式及参数设置简单。给出了使该自适应观测器满足全局指数收敛性的持续激励条件,并在理论上简洁地证明了该自适应观测器的全局指数收敛性。数值仿真结果表明该自适应观测器具有期望的性能,如快速收敛性、跟踪性等。
4.进一步将上文单输出非线性系统的自适应观测器设计推广到一类更一般的多输出非线性系统,并给出了使该自适应观测器满足全局指数收敛性的持续激励条件。仿真表明该自适应观测器可以快速跟踪未知参数的变化。
5.一般情况下,残差是变量测量值和它的数学解析值之间的解析冗余,故障的发生会引起系统的残差发生改变。基于模型的故障诊断方法是通过对测量信号处理技术生成残差的,本质上是对包含所需属性的原始数据的一种转换,因此依赖于残差的设计。本文基于前一部分已设计的自适应观测器对线性时变系统的加性故障设计残差,并在理论上分析残差的性质。该残差同时考虑了执行机构故障和传感器故障。数值仿真表明所设计的残差对被监视的故障是敏感的。
6.汽车在行驶过程中，主动悬架系统是影响乘客舒适程度和安全的最重要部件之一，而悬架系统经过长时间使用,容易老化导致性能降低,有必要对零件的老化系数进行估计，以便控制策略中考虑参数的变化。本文基于主动悬架系统全系统非线性状态方程,构造自适应观测器以实现系统未测状态和零件老化系数的实时估计。仿真表明,该自适应观测器能够迅速的跟踪元件老化系数的变化,实现悬架系统关键元器件的故障诊断。
Joint estimation of states and parameters in state-space systems is of practical importance for fault diagnosis and for adaptive control. Recursive algorithms designed for this purpose are usually known as adaptive observers. In this dissertation a class of adaptive observers in a constructive manner is discussed and the main contributions are described as follows:
1. Previous works on globally convergent adaptive observers do not consider unknown parameters in both state equations and output equations. In this dissertation for continuous-time multiple-input multiple-output linear time-varying systems with unknown parameters in both state and output equations, an adaptive observer with exponential forgetting factor is designed in a constructive manner and its global exponential convergence is formally established under appropriate assumptions. Compared to the Kalman filter, the advantages of the proposed adaptive observer reside both in its simpler convergence condition and in its more efficient numerical implementation. A numerical example is presented to illustrate the performance of the adaptive observer.
2. For discrete-time multiple-input multiple-output linear time-varying systems with unknown parameters in both state and output equations, an adaptive observer is designed in a constructive manner. In order to establish the global exponential convergence for simultaneous estimation of states and unknown parameters, a persistent excitation condition is required. A numerical example is presented to illustrate the performance of the adaptive observer.
3. For a class of single output uniformly observable nonlinear systems with unknown parameters in both state and output equations, an adaptive observer is designed in a constructive manner based on the techniques of high gain observer and adaptive estimation. The high gain adaptive observer for joint state and unknown parameter estimation is conceptually simple. The new algorithm makes use of a time varying gain matrix for unknown parameter estimation, which simplifies the initialization and parameter tuning. In order to establish the global exponential convergence of the adaptive observer, a persistent excitation condition is required. Consequently, the global exponential convergence for simultaneous estimation of states and unknown parameters is formally established following a simple procedure. A numerical example is presented to illustrate the performance of this adaptive observer.
4. Furthermore a more general adaptive observer for nonlinear multi-input-multi-output (MIMO) systems is developed and a persistent excitation condition is obtained in order to establish the global exponential convergence of the adaptive observer. A numerical example is presented to illustrate the performance of this adaptive observer.
5. A residual is a transformation of raw data with some desired properties for the purpose of fault diagnosis. Typically, model-based methods for fault diagnosis rely on the design of residuals which are signals computed from available sensor measurements with the aid of a mathematical model of the monitored system. Based on the developed adaptive observer in this dissertation, residuals are generated for fault diagnosis in linear time-varying systems. The sensitivity of the residuals to the monitored faults is rigorously analyzed, as well as their insensitivity to the faults to be ignored. The residuals presented in this dissertation extend the results of previous works by simultaneously taking into account both actuator and sensor faults. A numerical example is presented to illustrate the performance of these residuals.
6. A full vehicle active suspension system with the nolinear dynamics is considered. The aging coefficients of the components are modeled as unknown parameters. An adaptive observer is designed to estimate the aging coefficients. The simulation result shows the aging coefficients could be estimated rapidly.
引文
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