(357d) Sampled-Data Fault-Tolerant Control of Nonlinear Distributed Processes

The development of systematic methods for the detection and handling of faults in distributed process systems is a fundamental problem whose technological significance encompasses a large number of practical applications including transport-reaction processes and fluid flow systems. Traditionally, most of the research work in process control dealing with the problems of fault detection and fault-tolerant control has focused on spatially homogeneous processes modeled by systems of ordinary differential equations. In recent years, a number of efforts have been initiated towards the development of fault detection and compensation methods for distributed parameter systems modeled by partial differential equations (PDEs). Examples include methods for fault detection and accommodation based on approximate linear or nonlinear models (e.g., [2],[1]), as well as reconfiguration-based fault-tolerant control of nonlinear distributed processes [4]. Recently, in [3],[5] a unified framework was developed for the integration of model-based fault diagnosis and control system reconfiguration for distributed processes modeled by nonlinear parabolic PDEs with control constraints and actuator faults. Practical implementation issues such as handling plant-model mismatch and the lack of complete state measurements across the spatial domain were investigated and addressed in [6].

In addition to model uncertainty and constraints, a key issue that needs to be accounted for in the practical implementation of monitoring and fault-tolerant control systems is the lack of continuous measurements. In practice, measurements of the process outputs are typically available from the sensors at discrete time instances. The frequency at which the measurements are available is dictated by the sampling rate which is typically constrained by the inherent limitations on the data collection and processing capabilities of the measurement sensors. The limitations on the frequency of measurement availability imposes restrictions on the implementation of the feedback controller and can also erode the diagnostic and fault-tolerance capabilities of the fault-tolerant control system if not explicitly accounted for at the design stage. An effort to address this problem was initiated in [7] where an actuator fault detection and reconfiguration scheme for sampled-data distributed processes modeled by linear systems of parabolic PDEs was developed. A key idea was to include within the control system an approximate model of the dominant process modes to provide the observer with estimates of the output measurements between sampling times, and to update the state of the model using the actual measurements whenever they become available from the sensors. By exploiting the linear structure of the process and the controllers, both necessary and sufficient conditions for closed-loop stability were obtained leading to an exact characterization of the minimum allowable sampling rate. When this architecture is implemented on a nonlinear process, the maximum allowable sampling period predicted by linearization-based analysis can guarantee stability only for sufficiently small initial conditions, thus restricting the operating region of the process. Since many chemical processes are characterized by strong nonlinear dynamics and the need to be operated over large regions of the operating space, it is important to develop fault-tolerant control systems that account explicitly for the nonlinearities, both in the design of the control law and the fault diagnosis scheme.

Motivated by these considerations, we present in this work a fault detection and fault-tolerant control architecture for highly dissipative systems of nonlinear PDEs with actuator faults and limited state measurements that are sampled at discrete time instances. The architecture consists of a family of nonlinear output feedback controllers, observer-based fault detection filters that account for the discrete sampling of measurements, and a switching law that orchestrates the transition from the faulty actuator configuration to a healthy fall-back following fault detection. An approximate model that captures the dominant process dynamics is embedded in the control system to provide the observer with estimates of the output measurements between sampling instances. The state of the model is then updated using the actual measurements at discrete time instances. By analyzing the behavior of the estimation error between sampling times, and exploiting the stability properties of the compensated model, a sufficient condition for practical stability and ultimate boundedness of the sampled-data nonlinear closed-loop system is derived in terms of the sampling rate, the plant-model mismatch, the controller design parameters and the spatial placement of the control actuators and measurement sensors. The stability condition is used to obtain estimates of (1) the maximum allowable sampling rate that guarantees both stability and residual convergence in the absence of faults, and (2) the size of achievable ultimate bound. This characterization is then used as the basis for deriving appropriate fault detection and actuator reconfiguration rules. Finally, the proposed methodology is demonstrated through an application to the problem of suppressing wavy behavior in falling liquid films modeled by the Kuramoto-Sivashinsky equation.

References:

[1] Armaou, A. and M. Demetriou, ``Robust Detection and Accommodation of Incipient Component and Actuator Faults in Nonlinear Distributed Processes,'' AIChE J. 54:2651-2662, 2008.

[2] Baruh, H., ``Actuator Failure Detection in the Control of Distributed Systems,'' J. Guidance, Control, and Dynamics, 9:181-189, 1986.

[3] El-Farra, N. H., ``Integrated Fault Detection and Fault-Tolerant Control Architectures for Distributed Processes,'' Ind. & Eng. Chem. Res., 45:8338-8351, 2006.

[4] El-Farra, N. H. and P. D. Christofides, ``Coordinating Feedback and Switching for Control of Spatially-Distributed Processes,'' Comp. & Chem. Eng., 28:111-128, 2004.

[5] El-Farra, N. H. and S. Ghantasala, ``Actuator Fault Isolation and Reconfiguration in Transport-Reaction Processes,'' AIChE J., 53: 1518-1537, 2007.

[6] Ghantasala, S. and N. H. El-Farra, ``Actuator Fault Isolation and Compensation in Constrained Uncertain Parabolic PDES Systems,'' Automatica, provisionally accepted, 2009.

[7] Ghantasala, S. and N. H. El-Farra, ``Actuator Fault Detection and Reconfiguration in Distributed Processes with Measurement Sampling Constraints,'' Proceedings of American Control Conference, to appear, St. Louis, MO, 2009.