The fault detection problem in nonlinear systems using residual generators

In this chapter we study the fault detection problem using residual generators based upon high gain nonlinear observers in a differential algebraic framework. We analyze the stability of the residual generator when a fault occurs. We also consider two faults types: constant and time-varying faults. It is shown that under some mild conditions over the aforementioned faults the residual is different from zero. The high reliability required in industrial processes has created the necessity of detecting abnormal conditions while processes are operating. These conditions are called faults and it is important to detect and to isolate them in the early stages. The fault is a term which means degradation of the process or degradation in equipment performance because of changes in the process physical characteristics, process inputs or environmental conditions. A fault in a process is considered as a not-allowable deviation which can be detected by an appropriated signal evaluation. State observers are suitable structures to evaluate this change. The difference between the measured outputs of the process and the observer is the so-called residual value which is used to detect the fault. In this chapter we consider the fault detection problem with a residual generator approach using high gain nonlinear observers in a differential algebraic framework. We study two types of faults: constant and time-varying faults. The differential algebraic approach allows us to define the concept of algebraic observability [3, 4, 5, 6] and supplies state estimation through observers designed for systems described by differential algebraic equa-The chapter is organized as follows. Section 1.2 presents some differential algebra basic definitions. In Section 1.3, we present the residual generation problem and the residual generator stability using the uniform ultimate boundedness (UUB) theorem [2]. Section 1.4 presents two fault cases. A numerical example is given in Section 1.5.