(305b) Multi-Rate Sampled-Data Fault Detection and Fault-Tolerant Control of Hybrid Process Systems

With the increasing emphasis on safety and reliability in industrial process operation and the susceptibility of process control systems to malfunctions in the control actuators and measurement sensors, the problems of fault detection and fault-tolerant control have become the focus of considerable attention in both the academic and industrial communities. While an extensive and growing body of research work already exists on these topics, the majority of existing methods are developed for purely continuous processes. For hybrid processes wherein discrete events are superimposed on the underlying continuous dynamics, however, results have been more limited, primarily due to the difficulty of handling the strong and inherent interactions between the continuous dynamics and discrete events. It is now well understood that these interactions need to be explicitly taken into account in the development of the fault detection and fault-tolerant control methods for hybrid systems. An effort to address this problem was initiated in [1] where an integrated approach for fault detection and monitoring of a class of nonlinear hybrid processes with control actuator faults, uncertain continuous dynamics and uncertain mode transitions was developed. A key idea was the design of a bank of dedicated mode observers using unknown input observer theory to identify the active mode at any given time and distinguish between faults, mode transitions and uncertainties.

In addition to the challenges posed by the combined discrete-continuous dynamics for fault detection in hybrid systems, there are a number of practical implementation issues that must also be addressed in the fault-tolerant control system design. One such issue is the sampled-data constraint which arises due to the increasing use of networked and/or digital control systems in process operations. The information is often collected and transmitted at a certain rate which is dependent on the capabilities of the particular digital control device, the measurement system, and/or the communication medium. The lack of continuous information transfer between the control system components restricts the ability of the control system to accurately monitor and regulate the process. In most practical applications, the discrete sampling constraint impacts not only the sensor-controller interface, but extends to the controller-actuator interface as well. Furthermore, the control system typically makes use of multiple outputs which may be subject to different sampling rates. For example, in chemical reactors, the composition and density measurements typically need several minutes of analysis, while the temperature can be measured at a relatively fast rate. Moreover, the importance of the measurement collected is another factor that can trigger the use of multi-rate sampling. It is reasonable to apply a fast sampling rate to the sensors placed at certain critical locations in the process (e.g., where frequent monitoring and tight control are required), while reducing the sampling rates of the other sensors in order to reduce cost and optimize energy resource consumption.

In this work, we develop a framework for fault detection and fault-tolerant control for hybrid process systems with sensor-controller and controller-actuator communication constraints and multi-rate sampling. To compensate for the lack of continuous measurements from the sensors, an inter-sample model predictor of each mode of the hybrid system is embedded within the corresponding feedback controller to provide estimates of the measurements between sampling instants, and the states of the model are updated by the actual measurements when they become available from the sensors. Owing to the different sampling rates of the different sensors, the updates are not performed in a synchronized fashion. A sample-and-hold scheme is used on the controller-actuator link, which means that the controller outputs are implemented for a certain period of time before the next controller outputs are transmitted. An augmented system is constructed using a switched system formulation, and its dynamics are analyzed to obtain explicit closed-loop stability conditions (in terms of sampling periods and model uncertainty) for each mode in the absence of faults. The fault-free behavior of each model is then used as the basis for the design of a time-varying alarm threshold for actuator fault detection. To ensure stability in the event of faults, the control system must be reconfigured by using another set of healthy fall-back actuators. The key consideration here is that the fall-back actuator configuration must be chosen with the stability of the future operating modes in mind. Specifically, the fall-back configuration should be available to the subsequent modes, and -- more importantly -- the stability conditions for the future operating modes with the fall-back actuator configuration being used must be satisfied given that the operative sampling periods and inter-sample model predictors are fixed. Finally, the fault detection and reconfiguration capabilities of the fault-tolerant hybrid control system are illustrated using a simulated model of a hybrid chemical process.

References:

[1] Hu, Y. and N. H. El-Farra, "Robust Fault Detection and Monitoring of Hybrid Process Systems with Uncertain Mode Transitions," AIChE Journal, 57, 2783–2794, 2011.