Robust diagnosis and fault‐tolerant control of distributed processes over communication networks

Abstract

This paper develops a robust fault detection and isolation (FDI) and fault-tolerant control (FTC) structure for distributed processes modeled by nonlinear parabolic partial differential equations (PDEs) with control constraints, time-varying uncertain variables, and a finite number of sensors that transmit their data over a communication network. The network imposes limitations on the accuracy of the output measurements used for diagnosis and control purposes that need to be accounted for in the design methodology. To facilitate the controller synthesis and fault diagnosis tasks, a finite-dimensional system that captures the dominant dynamic modes of the PDE is initially derived and transformed into a form where each dominant mode is excited directly by only one actuator. A robustly stabilizing bounded output feedback controller is then designed for each dominant mode by combining a bounded Lyapunov-based robust state feedback controller with a state estimation scheme that relies on the available output measurements to provide estimates of the dominant modes. The controller synthesis procedure facilitates the derivation of: (1) an explicit characterization of the fault-free behavior of each mode in terms of a time-varying bound on the dissipation rate of the corresponding Lyapunov function, which accounts for the uncertainty and networkinduced measurement errors and (2) an explicit characterization of the robust stability region where constraint satisfaction and robustness with respect to uncertainty and measurement errors are guaranteed. Using the fault-free Lyapunov dissipation bounds as thresholds for FDI, the detection and isolation of faults in a given actuator are accomplished by monitoring the evolution of the dominant modes within the stability region and declaring a fault when the threshold is breached. The effects of network-induced measurement errors are mitigated by confining the FDI region to an appropriate subset of the stability region and enlarging the FDI residual thresholds appropriately. It is shown that these safeguards can be tightened or relaxed by proper selection of the sensor spatial configuration. Finally, the implementation of the networked FDI-FTC architecture on the infinite-dimensional system is discussed and the proposed methodology is demonstrated using a diffusion-reaction process example.

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

“…Finally, the reconfiguration of control actuators can be carried out on the basis of the new stability regions (which account for the measurement errors). The reader is referred to Ghantasala and El-Farra (2008) for an example of how such an approach is implemented in the context of transport-reaction processes.…”

Fault-tolerant control of sampled-data nonlinear distributed parameter systems

“…Major bottlenecks in the design of fault-tolerant control systems for distributed parameter systems include the infinite-dimensional nature of these systems, as well as their complex dynamics characterized by nonlinearities and uncertainties. Recently, we developed in [7], [8], [9], [10] a framework for the integration of model-based fault detection, isolation and control system reconfiguration for distributed processes modeled by nonlinear parabolic PDEs with control constraints and actuator faults. The framework brings together tools from infinite-dimensional systems, model reduction, nonlinear and robust control, as well as hybrid system theory.…”

A two-tier architecture for networked process control

“…Using a switched system formulation, the maximum allowable update period between the sensors of each unit and the local controllers of its neighbors has been explicitly characterized. In addition to these works, fault diagnosis and faulttolerant control methods that account for network-induced measurement errors have been developed in Ghantasala and El-Farra (2008). In terms of other research work pertaining to the control problem studied in this paper, we note that most of the available results on MPC of systems with delays deal with linear systems (e.g., Jeong and Park, 2005;Liu et al, 2007).…”