Fault diagnosis for distributed parameter systems using the modulation functions

对工艺过程要求的增加导致了复杂控制系统的应用。因此，故障诊断对于保证各工艺过程的安全运行显得越来越重要。集总参数系统的故障诊断已经有了很多研究成果，而分布参数系统的故障诊断仍然是一个活跃的研究领域。因此，大多数方法依赖于基于观察者的技术。当然，这样做的缺点是DPS或由此产生的无限维观测器都必须近似。在任何情况下，所得到的故障诊断系统都具有较大的阶数，以保持相关的近似误差足够小。这就阻碍了故障诊断方法的实现。本课题组提出了一种新的具有恒定故障的抛物型系统故障诊断方法，该方法克服了上述缺点。主要思想是推导出仅依赖于已知输入和输出信号的故障的代数表达式。该故障检测方程是将所谓的调制函数方法应用于DPS的结果。由此可以看出，调制函数是由实现分布参数信号模型的设定点转移问题而产生的。因此，故障检测问题可以追溯到DPS的前馈控制问题。对于后者，最近在文献中发展了强有力的方法。因此，新方法使得它们也可以用于解决故障检测问题。本研究项目的主要目的是将先前获得的结果扩展到DPS故障诊断的一般和系统方法。因此，必须考虑时变故障、干扰和模型不确定性。随后，计划将这些结果推广到其他类型的DPS，如双曲系统、双调和系统或分数系统。为了扩大故障诊断方法在实际问题中的适用性，本项目还研究了具有更高空间域和复杂几何结构的DPS问题。所得的理论结果将在模拟和实验装置中得到验证。

Increasing requirements for technological processes lead to the application of sophisticated control systems. Therefore, fault diagnosis gains more and more importance to ensure the safety of various technological processes. Many results for the solution of this problem can be found for lumped parameter systems, whereas the fault diagnosis of distributed parameter systems (DPS) is still an area of active research. Thereby, most approaches rely on observer-based techniques. This, of course, has the disadvantage that either the DPS or the resulting infinite-dimensional observer has to be approximated. In any case, the resulting fault diagnosis system has a large order to keep the related approximation error sufficiently small. This hinders the implementation of such fault diagnosis methods. In the proposer's research group, a new method for the fault diagnosis for parabolic systems with constant faults was developed, that does not suffer from these shortcomings. The main idea is to derive an algebraic expression for the fault that only depends on known input and output signals. This fault detection equation results from applying the so-called modulation function approach to the DPS. With this, it can be shown that the modulation function follows from realizing a set-point transition problem for a distributed parameter signal model. As a consequence, the fault detection problem can be traced back to a feedforward control problem for DPS. For the latter powerful methods were recently developed in the literature. Hence, the new approach makes it possible that they also become available for solving fault detection problems.The main objective of this research project is the extension of the previously obtained results to a general and systematic approach for the fault diagnosis of DPS. Thereby, time-varying faults, disturbances, and model uncertainties have to be taken into account. Subsequently, the extension of these results to other classes of DPS such as hyperbolic, biharmonic or fractional systems is planned. In order to enlarge the applicability of fault diagnosis methods for real world problems the project also investigates DPS with higher spatial domains and complex geometry. The obtained theoretical results will be verified in simulations as well as by utilizing experimental setups.