(646e) Constrained Sensor Fault-Tolerant Control of Distributed Process Systems

The majority of research studies on fault-tolerant process control have focused on spatially homogeneous processes modeled by systems of ordinary differential equations; yet, many chemical processes, such as transport-reaction processes and fluid flows, are characterized by inherent spatial variations and are more suitably modeled by systems of partial differential equations. The need to develop fault-tolerant control methods for distributed parameter systems has motivated a number of recent works in this area (see, for example, [1-3]). The focus of these studies, however, has been on the diagnosis and handling of control actuator faults. Sensor faults, on the other hand, are equally critical in terms of their influence on the overall process stability and performance, and require attention in the fault-tolerant control system design, especially as dense deployments of sensor networks are increasingly used in industrial systems. The measurement errors introduced by sensor malfunctions can deteriorate the overall control quality and may result in more catastrophic effects and economic losses if not explicitly handled. Systematic methods for handling sensor faults in distributed control systems remain lacking at this stage.

In this paper, we focus on the control of distributed process systems modeled by highly dissipative PDEs subject to sensor faults, control constraints and external disturbances. The key objective is to design a fault-tolerant control system that guarantees graceful degradation in process performance under sensor faults. To this end, we first obtain, via model reduction techniques, a suitable finite-dimensional model that captures the dominant dynamics of the infinite-dimensional system, and use it to investigate the closed-loop stability properties under different actuator and sensor configurations. The stability properties are influenced by the control constraints which limit the set of initial conditions starting from where stability can be achieved (the stability region), as well as the disturbances and sensor faults which constrain the set of terminal states that the system can be steered to in finite time (the terminal region). Using Lyapunov analysis techniques, an explicit characterization of the stability and terminal regions for each actuator and sensor configuration is obtained in terms of the constraints, and the available bounds on the sizes of the disturbances and sensor faults. This characterization is then used to devise switching strategies that ensure minimal deterioration in the size of the terminal region under a given sensor fault. The idea is to identify the location of the closed-loop state relative to the stability and terminal regions following fault detection, and have the supervisor either switch to an actuator configuration that recovers the fault-free terminal region (thus maintaining operation under the faulty sensor) if feasible, or switch to a new sensor configuration with a larger, but still acceptable, terminal region. Precise conditions for the implementation of the proposed switching strategies on the infinite-dimensional system are derived using singular perturbation techniques. Finally, the theoretical results are illustrated using a diffusion-reaction process example.

References:

[1] El-Farra, N. H. and S. Ghantasala, "Actuator fault isolation and reconfiguration in transport-reaction processes", AIChE J., 53, 1518-1537, 2007.

[2] Armaou, A. and M. Demetriou, "Robust detection and accommodation of incipient component faults in nonlinear distributed processes", AIChE J., 54, 2651-2662, 2008.

[3] Ghantasala, S. and N. H. El-Farra, Robust actuator fault isolation and management in constrained uncertain parabolic PDE systems, Automatica, 45, 2368-2373, 2009.