Delays in fault detection and isolation

Various types of faults arise in industrial processes owing to malfunction of internal components of a process as well as those in measurement sensors and control actuators attached to the process. Over the last three or four decades industrial automation has been increasingly fueled by various technological developments including the availability of highly complex electronic equipment and the overwhelming progress in computer technology. This has led not only to the development of complex control systems but also to higher demand of reliable and secure control systems° Thus it has become imperative that any fault that occurs be detected and identified automatically without severely disturbing the yield the process generates. This has stimulated over the last two decades an extensive study of fault detection and isolation methods. As discussed in a survey paper by Willsky, [5], one faces three different types of tasks or layers in the area of fault detection and isolation, (1) fault detection, (2) fault isolation, and (3) fault estimation. Fault detection consists of designing a residual generator that produces a residual signal enabling one to make a binary decision as to whether a fault occurred or not. Fault isolation imposes a stronger requirement. When one or more faults occur, the residual signal must enable us not only to detect that there are faults occurring in the system, but it must also enable us to identify (isolate) which faults have occurred. Finally, fault estimation is the determination of the extent of failure. The latter is done by trying to reconstruct the fault signals. A number of fundamental problems that arise in fault estimation, i.e. in estimating the fault signals have been studied recently by us [1 ]. We also studied fault detection and fault isolation in the paper [2]. However, an issue which, as far as we know, has not been studied in this context is to estimate and minimize the time it takes after a fault occurs to actually detect the fault on the basis of the residual signal. For discrete-time systems, the notion of using a fixed delay in estimating a fault signal has been introduced in [1 ]. That is, at time step k, one obtains the estimate of the fault signal at k g where g is a fixed nonnegative integer. This clearly weakens the solvability conditions. In [2] we looked into using this delay for fault detection and isolation and we noted this does not weaken the solvability conditions. However, this is due to a fundamental aspect of our problem formulation° In fault detection we required the residual signal to be nonzero if a fault occured and otherwise to be zero. However, we did not impose any constraint on the time between the occurence of a fault and the moment that the residual signal becomes nonzero indicating that a fault has occured. Obviously in many applications this delay in detecting a fault can be quite dangerous and therefore this delay should be as small as possible.