Observer-based Robust Fault Detection Design Of Linear Time-invariant Uncertain Systems

As the development of science technology and production level, scale of modern control system became larger and more complicated. The possibility of fault arising in the system is also increasing. In order to improve the reliability and security of the system, it is becoming urgent to building a fault detection system. Which is used to monitor the system states, detect the faults, in order to avoid catastrophic accidents.Observer based fault detection is an effective way in model based fault detection theory. Because mathematical model is different form actual system, it contains modeling error and unknown inputs, this article mainly studied the design of observer based fault detection for LTI (linear time invariant) system with model uncertainty.In recent ten years, the design of observer based fault detection for LTI system with model uncertainty largely adopted BMI (Bilinear matrix inequality) algorithm. The flaw of those methods is solutions easily fall into local optimal solution. In order to fix this situation, A reference residual model design under the optimal index, that is giving the fault detection rate and lower the false alarm rate, is proposed with no uncertainty is considered. Then based on model matching technique, the robust fault detection problem is then presented via a linear matrix inequality (LMI) formulation, the optimal solution can be obtained by a convex LMI. An example demonstrates the proposed approach effectively guarantee residual’s sensitivity to fault and improve the fault detection performance.In some control system cases, the model uncertainty are real structured uncertainties, which can not be treated as norm bounded complex uncertainties. Cause it will introduce some conservative results in the parameter solution. Which might lead the robust fault detection system to fail to pick up the fault signals. Based on this situation, this article introduced the structured singular value theory, which is useful for analysis and synthesis of systems which have structured uncertainty. By some mathematical tactics, the problem of design an observer based robust fault detection system with real structured uncertainty was transfonned into a robust stability problem. And the solution is given by BMI algorithm in the end. An example is employed to illustrate its effectiveness.