(17a) Model Based Fault Detection and Isolation for Non-Linear Systems with Disturbance Decoupling

One of the most widely studied schemes in the area of model based fault diagnosis and isolation (FDI) is the observer-based fault diagnosis approach that comprises of a virtual reconstruction of the system using a process model which is simulated on a computer (De Persis and Isidori, 2001; Ding, 2008; Du and Mhaskar, 2014; Du et al., 2013; Frank, 1990; Frank and Ding, 1997; Mhaskar et al., 2006). The estimates of the virtual system follow the outputs of the real system in the absence of faults, and show an evident deviation in the presence of faults. Any deviation is expressed in terms of residuals which can then be used for fault diagnosis. Since perfect modeling of the real system is impossible due to model uncertainties or disturbances, it is essential that the residuals generated are disturbance-decoupled, i.e. unaffected by disturbances.

Motivated by the above considerations, the goal of this study is to design a fault diagnosis scheme for non-linear systems using an observer/ residual generator, driven by the output of the process, that gives an output (the residual) which is (i) unaffected by disturbances (ii) zero in the absence of faults and initialization errors (iii) non-zero in the presence of faults. In addition to the above conditions, it is desired that the residual asymptotically decays to zero in the presence of initialization errors and absence of faults. To this end, we study the problem of using linear residual generators for non-linear systems, as this would provide a facile way to guarantee asymptotic stability via eigenvalue assignment. Necessary and sufficient conditions for the existence of linear residual generators for non-linear systems are derived, which are a direct generalization of the standard linear results in Ding (2008). Our results lead to a concrete design method of a linear disturbance-decoupled residual generator with stability guarantees, for nonlinear process systems.

The applicability of our proposed method is illustrated through three case studies: (i) a bio-reactor with potential fault in the feeding system, in the presence of uncertainty in the growth rate, (ii) a non-isothermal CSTR with potential faults in the cooling system and in the concentration sensor, in the presence of uncertainty in the reaction rate, and (iii) a process network consisting of four CSTRs and a flash separator. Simulation results show the effectiveness of the proposed method in detecting and isolating faults. An additional advantage of the proposed method is that it provides guidance on the choice of measurements that are required for fault detection and diagnosis, by specifying the degrees of freedom for selecting the appropriate sensors

References

De Persis, C., Isidori, A., 2001. A geometric approach to nonlinear fault detection and isolation. IEEE transactions on automatic control 46, 853-865.

Ding, S.X., 2008. Model-based fault diagnosis techniques: design schemes, algorithms, and tools. Springer Science & Business Media.

Du, M., Mhaskar, P., 2014. Isolation and handling of sensor faults in nonlinear systems. Automatica 50, 1066-1074.

Du, M., Scott, J., Mhaskar, P., 2013. Actuator and sensor fault isolation of nonlinear process systems. Chemical Engineering Science 104, 294-303.

Frank, P.M., 1990. Fault diagnosis in dynamic systems using analytical and knowledge-based redundancy: A survey and some new results. Automatica 26, 459-474.

Frank, P.M., Ding, X., 1997. Survey of robust residual generation and evaluation methods in observer-based fault detection systems. Journal of process control 7, 403-424.

Mhaskar, P., Gani, A., El‐Farra, N.H., McFall, C., Christofides, P.D., Davis, J.F., 2006. Integrated fault‐detection and fault‐tolerant control of process systems. AIChE Journal 52, 2129-2148.