Estimation and fault diagnosis for non-linear system with time-varying faults and measurement noises: Application on two CSTRs in series

A continuously stirred tank reactor (CSTR) is largely used in water treatment and in chemical and biological processes. It is characterized by a complex non-linear behaviour. Operating large reactors in industry can be expensive, so a common trick used to reduce costs is to operate multiple CSTRs in series. Consequently, the CSTR is usually exposed to faults and noises. This paper addresses the design of a robust observer for estimation and fault diagnosis strategy on two CSTRs in series. The considered system is affected simultaneously by time-varying actuator and sensor faults with measurement noises. The Takagi-Sugeno multimodel approach is proposed to transform the non-linear model into an interpolation of several linear sub-models with non-measurable premise variables. The purpose of this brief is to provide the state and the fault estimation for the considered system using a proportional multiple integral (PMI) unknown input observer. The exponential stability conditions are studied with the Lyapunov theory and L2 optimization and formulated in terms of linear matrix inequalities. In addition, a comparative study with a PMI observer is conducted. Finally, the proposed observer is used for time-varying fault detection and isolation.