A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes

Abstract

This paper presents a methodology for the robust detection, isolation and compensation of control actuator faults in particulate processes described by population balance models with control constraints and time-varying uncertain variables. The main idea is to shape the fault-free closed-loop process response via robust feedback control in a way that enables the derivation of performance-based fault detection and isolation (FDI) rules that are less sensitive to the uncertainty. Initially, an approximate finite-dimensional system that captures the dominant process dynamics is derived and decomposed into interconnected subsystems, each influenced directly by a single manipulated input. A robustly stabilizing bounded feedback controller is then designed for each subsystem leading to (1) an explicit characterization of the fault-free behavior of each subsystem in terms of a time-varying bound on an appropriate Lyapunov function, and (2) an explicit characterization of the robust stability region. Using the fault-free bounds as thresholds for FDI, the detection and isolation of faults in a given actuator is accomplished by monitoring the evolution of the system within the stability region and declaring a fault if the threshold is exceeded. The thresholds are linked to the achievable degree of asymptotic uncertainty attenuation and can therefore be properly tuned by tuning the controllers. The robust FDI scheme is integrated with a controller reconfiguration strategy that preserves closed-loop stability following FDI. Finally, the implementation of the fault-tolerant control architecture on the particulate process is discussed and the proposed methodology is applied to a simulated model of a continuous crystallizer with a fines trap.