A multi-rate sampled-data observer for nonlinear systems under asynchronous sampling is developed in this work. The proposed multi-rate observer is based on a continuous-time design coupled with inter-sample output predictors for the sampled measurements. The sampled-data system with the multi-rate observer forms a hybrid system and it is shown that the error dynamics of the overall system is input-to-output stable with respect to measurement errors, by applying the Karafyllis-Jiang vector small-gain theorem. This sampled-data design also offers robustness with respect to perturbations in the sampling schedule. The performance of the proposed method is evaluated through a chemical batch reactor example.

A systematic method for the design of disturbance-decoupled linear residual generators for fault detection and isolation (FDI) in nonlinear systems is developed. Necessary and sufficient conditions for the existence of linear residual generators for nonlinear systems are derived. As long as these conditions are satisfied, we obtain explicit design formulas for the residual generator, with eigenvalue assignment. The proposed formulation and results provide a nonlinear generalization of standard FDI methods for linear systems. The method is applied to three case studies: a bio reactor, a continuous stirred tanked reactor (CSTR) and a process network.

In safety-critical chemical reactors with potential hazards, reaction kinetics and heat transfer parameters are usually known, and a mathematical model is available. It is then meaningful to base fault detection and isolation algorithms on the first-principles model as opposed to statistics, so that physically meaningful residual signals are generated from material and/or energy balances not closing, leading to reliable fault diagnosis. Additionally, to maintain the safety of the entire system, it is necessary to take appropriate control action based on the mathematical model and the identified faults, to minimize their impact and thus ensure safe operation. In the present work, these ideas will be formulated and illustrated through a continuous stirred-tank reactor case study involving the liquid-phase oxidation of alkylpyridine with hydrogen peroxide. The proposed fault tolerant control strategy monitors the DSM (distance of the system state from the boundary of the dynamic safe set) and the estimate of the fault size, and when they cross a certain limit as a result of an abnormal event, the manipulated input is switched. Simulation results show the effectiveness of the proposed fault tolerant control strategy in dealing with cooling system failure.