Failure detection and localization in linear continuous dynamical systems

In this paper, the detection and localization of possible continuous control system failures are investigated in continuous and discrete domains, respectively. Only such failures that manifest themselves as abrupt variations in the coefficients of the system governing differential equations are considered. The local and global failure detectabilities of different system variables are defined. Based on these definitions, the paper shows that instantaneous failure detection is possible only by observing the failure-induced jumps in some continuous system variables under the noise-free conditions. If noise is present, a robust way of failure detection is to average the observed variables before making any decisions. Consequently, a residual-based failure detection scheme is derived. It comprises essentially a hypothesis testing on the mean of the window-averaged residuals between the output of the system and that of the model. After the possible occurrence of the failure being detected, under the noise-free conditions, the failure location can be traced in terms of the changed coefficients of the system differential equations by simply solving a set of linear algebraic equations in the discrete domain. If the data are noisy, least-squares type of algorithms can be used to increase the robustness of the failure localization. Two examples of continuous systems subject to possible failures are simulated to demonstrate the direct and residual-based failure detection schemes.