Comment on steroid hormones and disease activity during pregnancy in systemic lupus erythematosus

Abstract

The problem of implementing fault‐tolerant control to nonlinear processes with input constraints subject to control actuator failures is considered, and an approach predicated upon the idea of integrating fault‐detection, feedback and supervisory control is presented and demonstrated. To illustrate the main idea behind the proposed approach, availability of measurements of all the process state variables is initially assumed. For the processes under consideration, a family of candidate control configurations, characterized by different manipulated inputs, is first identified. For each control configuration, a Lyapunov‐based controller that enforces asymptotic closed‐loop stability in the presence of constraints, is designed, and the constrained stability region, associated with it, is explicitly characterized. A fault‐detection filter is used to compute the expected closed‐loop behavior in the absence of faults. Deviations of the process states from the expected closed‐loop behavior are used to detect faults. A switching policy is then derived, on the basis of the stability regions, to orchestrate the activation/deactivation of the constituent control configurations in a way that guarantees closed‐loop stability in the event that a failure is detected. Often, in chemical process applications, not all state variables are available for measurement. To deal with the problem of lack of process state measurements, a nonlinear observer is designed to generate estimates of the states, which are then used to implement the state feedback controller and the fault‐detection filter. A switching policy is then derived to orchestrate the activation/deactivation of the constituent control configurations in a way that accounts for the estimation error. Finally, simulation studies are presented to demonstrate the implementation and evaluate the effectiveness of the proposed fault‐tolerant control scheme, as well as to investigate an application in the presence of uncertainty and measurement noise. © 2006 American Institute of Chemical Engineers AIChE J, 2006