Integration of fault diagnosis and control based on a trade-off between fault detectability and closed loop performance

Abstract

This paper presents a novel methodology for simultaneous optimal tuning of a fault detection and diagnosis (FDD) algorithm and a feedback controller for a chemical plant in the presence of stochastic parametric faults. The key idea is to propagate the effect of time invariant stochastic uncertainties onto the measured variables by using a Generalized Polynomial Chaos (gPC) expansion and the nonlinear first principles’ model of the process. A bi-level optimization is proposed for achieving a trade-off between the fault detectability and the closed loop process variability. The goal of the outer level optimization is to seek a trade-off between the efficiency of detecting a fault and the closed loop performance, while the inner level optimization is designed to optimally calibrate the FDD algorithm. The proposed method is illustrated by a continuous stirred tank reactor (CSTR) system with a fault consisting of stochastic and intermittent variations in the inlet concentration. Beyond achieving improved trade-offs between fault detectability and control, it is shown that the computational cost of the gPC model based method is lower than the Monte Carlo type sampling based approaches, thus demonstrating the potential of the gPC method for dealing with large problems and real-time applications.