(268c) Fault Detection and Isolation in Nonlinear Hybrid Process Systems

Safety and reliability are primary concerns in the operation of chemical processes. The continued increase in the size and complexity of modern industrial plants, together with the increased reliance on automation, poses challenges in meeting these objectives because of the increased likelihood of faults, such as malfunctions in process equipment and failures of control instrumentation, which if not accounted for can undermine the stability and integrity of the entire system. Not surprisingly, the development of systematic methods for the detection, isolation and handling of faults in chemical processes has been the subject of numerous research efforts within both the academic and industrial circles in process control. An examination of the existing literature on these topics, however, shows that the overwhelming majority of existing methods have been developed for purely continuous processes. Yet, many chemical processes that are characterized by strong interactions between continuous dynamics and discrete events, and are more appropriately modeled by hybrid systems [1]. The distinguishing feature of a hybrid system is its multi-modal structure characterized by switching between a finite number of continuous dynamical subsystems. The continuous dynamics often arise from the underlying physical laws such as mass, momentum, and energy conservation, and are typically modeled by continuous-time differential equations. The discrete events, on the other hand, can be the result of inherent physico-chemical discontinuities in the continuous dynamics, transitions between different operating regimes, the use of discrete actuators and sensors in the control system, or the use of logic-based switching for supervisory and safety control.

One of the key issues in the design of model-based fault detection schemes for hybrid systems is handling the switched dynamics which requires the design of a hybrid observer that reconstructs both the continuous and discrete variables and ensures residual convergence under switching. Another key consideration is the ability of the fault detection scheme to discriminate effectively between process and/or control system faults on the one hand, and the discrete transitions that take place between the continuous modes on the other. An effort to address these issues was initiated in [2] where a hybrid monitoring scheme that discriminates between actuator faults and mode transitions was developed using tools from unknown input observer theory and results from switched system stability. Given that the diagnostic filters in this scheme are designed to only detect faults within the continuous modes, a residual exceeding the specified threshold indicates that some fault has occurred in one or more actuators of the operating mode but cannot pinpoint the location of the fault. This in turn necessitates that the supervisor shut down all the actuators of the active control configuration upon fault detection, including possibly healthy actuators, and switch to an appropriate fall-back configuration whose entire set of actuators are well functioning to ensure fault-tolerance. To avoid the unnecessary shut down of healthy actuators, a fault isolation scheme that identifies the faulty actuators within the active configuration needs to be incorporated into the hybrid monitoring structure. The ability to distinguish between faults in different actuators depends to a large extent on the structure of the input operator which describes the channels through which the different inputs influence the process evolution.

Motivated by these considerations, we develop in this work an architecture for actuator fault detection and isolation in hybrid processes modeled by switched nonlinear systems. The architecture consists of (1) a set of dedicated FDI filters that detect and isolate the faults within the continuous modes, (2) a set of mode observers that locate the active mode at any given time, and (3) a supervisor that switches between the FDI filters as the process transitions from one mode to another. Initially, an invertible coordinate transformation is used to transform the dynamics of each mode into a form in which evolution of each output is excited by only one input and decoupled from the rest. Next, a set of dedicated FDI filters, each replicating the fault-free behavior of a given output using measurements of the others, is constructed, and the discrepancy between the evolution of the fault-free and actual outputs are used as residuals. The specific way in which the actuators influence each output ensures that the residual of each filter is dedicated to faults in only one actuator and can therefore be used to discern the fault or health status of that actuator at any given time. Conditions for the convergence of the fault-free residuals under switching are also derived to ensure that the residuals are insensitive to the mode transitions. To correctly identify which mode is active at any given time, a set of mode observers that recreate the expected behavior of each mode using both input and output measurements are constructed. By proper choice of the controller and observer design parameters, we ensure that the residuals of the mode observers are decoupled from the faults within each mode, and are thus sensitive only to the mode location. The implementation of the monitoring scheme proceeds by running the mode observers in parallel with the process for all times and analyzing the residuals' pattern. At any given time only the observer estimating the states of the active mode will return a zero residual. A mode transition is marked by a change of the zero residual to a non-zero value. Once a mode transition is detected and the active mode is identified, the supervisor switches to the corresponding bank of FDI filters to assess the fault or health status of the actuators in that particular mode. Finally, the design and implementation of the proposed monitoring scheme are demonstrated using a chemical process example.

References:

[1] Christofides, P. D. and N. H. El-Farra, Control of Nonlinear and Hybrid Process Systems: Designs for Uncertainty, Constraints and Time-Delays, 446 pages, Springer-Verlag, Berlin, Germany, 2005.

[2] El-Farra, N. H., ``Model-based Fault Detection and Monitoring of Uncertain Hybrid Process Systems," AIChE Annual Meeting, Paper 557v, Philadelphia, PA., 2008.