【作者】 吴小雪；

【导师】 刘贺平；

【作者基本信息】 北京科技大学 ， 控制科学与工程， 2023， 博士

【摘要】 二维系统与现代过程控制密切相关,在多维信号处理、多维数字滤波、热处理、重复处理等领域有广泛应用。由于二维系统具有丰富的工程应用背景,至今仍是控制领域的研究热点之一。在工程实践中,二维系统同样有着可靠性和安全性的需要,同样面临着故障带来的严重威胁。另一方面,实际控制系统的性能往往需要在有限频域内进行描述。若不考虑系统本身发生的故障或者外部输入信号的有限频特性而采用全频方法进行处理,容易造成设计上的不准确和保守性。因此,二维系统的有限频域内的故障检测问题具有重要的研究价值。由于二维系统自身复杂性,相比于一维系统,其故障检测问题上更具挑战性。本文针对二维Roesser系统、二维Fornasini-Marchesini(FM)系统,分别研究了有限频故障估计、有限频故障检测以及同时故障检测与控制问题,给出了相应的设计方法,具体内容如下:(1)针对二维Roesser系统,分别采用两种方法设计故障估计滤波器。所设计的故障估计滤波器可满足给定的有限频性能指标,在故障检测的同时可以重构故障的特征。借助于二维广义KYP引理来描述故障和干扰的有限频特征,避免了现有方法采用加权函数所带来的复杂度和不准确性。在此基础上,为二维Roesser系统设计了新的残差评价函数和阈值。最后,在数值算例中,将所提出的故障估计方法应用于热交换器模型中,以验证其实用性,且与现有方法相比较,所采用的新的残差评价函数和阈值可以有效地避免故障漏报和误报。(2)针对具有传感器故障的二维FM系统,设计了有限频故障检测滤波器。利用二维广义KYP引理,将有限频性能指标转化为矩阵不等式条件,并采用构造切平面的方法解决了设计过程中出现的非凸问题,进而给出滤波器的设计条件。在数值算例中,和现有方法进行比较,验证了所提出方法具有一定的优越性。(3)针对二维FM系统,设计了有限频故障估计滤波器。利用二维广义KYP引理来描述故障的有限频特征,结合矩阵不等式技术,给出故障估计滤波器的设计条件。与现有方法相比,所设计的故障估计滤波器,在实现故障检测功能的同时,可重构故障的特征。在数值算例中,将所提出的方法应用于平稳随机场模型的故障检测,以验证所提方法相对于现有方法具有更低的故障漏报率和误报率。(4)针对二维FM系统,设计了同时故障检测滤波器/控制器。针对故障和干扰的有限频特性,设计满足有限频性能指标的故障检测滤波器/控制器,在实现故障检测目标的同时还可以兼顾控制性能。借助于二维广义KYP引理,将有限频性能指标转化为矩阵不等式条件,并给出两步算法求解所得到的非凸条件。与现有方法相比,集成设计方法具有更好地扰动抑制能力,故障灵敏性也更强。最后,将所提出的方法应用于带钢轧制过程,以验证其实用性。(5)针对具有时滞的二维FM系统,设计了有限频故障估计滤波器。首先推导出了具有时滞的二维FM系统的广义KYP引理。在此基础上,给出二维时滞FM系统的有限频故障估计滤波器设计条件。与现有方法相比,该设计条件在实现故障检测功能的同时,还可以重构故障的特征。最后,用数值算例验证了该故障估计方法的实用性。更多还原

【Abstract】 Two-dimensional systems are closely related to modern process control,which have been widely used in multi-dimensional signal processing,multi dimensional digital filtering,heat treatment,repetitive processing,etc.Therefore,two-dimensional systems are a research hot spot in the field of control.In engineering applications,two-dimensional systems face the threat of faults,and thus the reliability and security should be paid attention to.On the other hand,the performance of control systems often needs to be described in the finite-frequency domain.It can be easy to cause inaccuracy and conservatism if we adopt the full frequency approach and do not take into account the finite-frequency characteristics of faults or external signals.Therefore,the finite-frequency fault detection of two-dimensional systems has an important research value.In addition,due to their structural complexity,the fault detection of two-dimensional systems faces more challenges compared with one-dimensional systems.In this thesis,we investigate the problems of finite-frequency estimation,finite-frequency fault detection,and simultaneous fault detect and control of two-dimensional Roesser systems and Fornasini-Marchesini(FM)systems.The main contributions of this thesis are listed as follows:(1)Two finite-frequency fault estimation filter design methods are developed for the two-dimensional Roesser systems.The designed fault estimation filter can meet the prescribed finite-frequency performance criteria,and can be used to detect faults and reconstruct their features simultaneously.By using the two-dimensional generalized KYP lemma to describe the finitefrequency characteristics of faults and disturbances,the complexity and uncertainty caused by the weighting function can be avoided.On this basis,a new residual evaluation function and a threshold are also designed for two-dimensional Roesser systems.Finally,the proposed fault estimation method is applied to the heat exchanger model to verify its practicability.Compared with the existing methods,it is verified that the new residual evaluation function and threshold can effectively detect faults.(2)A finite-frequency fault detection filter is designed for two-dimensional FM systems subjected to sensor faults.By using the two-dimensional generalized KYP lemma,the finite-frequency performance criteria can be transformed into a matrix inequality condition.Then,a tangent plane is constructed to solve the non-convex problem in the design process,and the design conditions for the finite-frequency fault detection filter are developed.Finally,a numerical example shows the advantages of this method compared with the existing methods.(3)A finite-frequency fault estimation filter is designed for twodimensional FM systems.By using the two-dimensional generalized KYP lemma and the matrix inequality technique,the finite-frequency characteristics of faults are described and the design conditions of the fault estimation filter are given.The designed fault estimation filter can detect faults as well as reconstruct the feature of faults.In the numerical example,the proposed method is applied to the fault detection of the stationary random field model,and compared with the existing methods,it is verified that this method has lower false alarm rate.(4)An integrated fault detection filter and controller is designed for twodimensional FM systems.A fault detection filter/controller is designed to satisfy the finite-frequency performance criteria,which can achieve the goal of fault detection as well as satisfy the control performance.By using the two-dimensional generalized KYP lemma,the finite-frequency performance criteria is transformed into a matrix inequality condition,and a two-step algorithm is proposed to solve this non-convex condition.Compared with the existing methods,the integrated design method has better disturbance attenuation and better fault sensitivity.Finally,the proposed method is applied to the strip rolling process to verify its effectiveness.(5)A finite-frequency fault estimation filter is designed for two-dimensional FM systems with time delay.Firstly,the generalized KYP lemma is derived for the two-dimensional time-delay FM system,and then the design condition of the fault estimation filter is given on the basis of this lemma.Compared with the existing methods,the designed fault estimation filter can not only realize the function of fault detection,but also reconstruct the characteristics of the faults.Finally,numerical examples verify the practicability of the fault estimation method.更多还原