(710g) Fault Detection and Fault-Tolerant Control of Particulate Processes with Sampled and Delayed Measurements

The development of systematic methods for fault detection and fault-tolerant control of particulate processes is a fundamental problem whose practical
significance encompasses a wide range of important processing industries including agricultural, chemical, food, minerals, and pharmaceuticals. A key motivation for studying this problem is the fact that the loss of control authority due to control system failures can impact the particle size distribution, and ultimately harm the end-product quality if faults are not properly diagnosed and handled. Major bottlenecks in the design of model-based fault-tolerant control systems for particulate processes include the infinite-dimensional nature of the process model as well as the complex nonlinear and uncertain dynamics of particulate processes. An effort to address these problems was initiated in [1] where a methodology for the detection and handling of actuator faults in particulate processes was developed on the basis of appropriate low-order models that capture the dominant process dynamics. These results were subsequently generalized in [2] to address the problems of fault isolation and model uncertainty.

Beyond the problems of nonlinearities and uncertainty, there is a host of practical implementation issues that need to be accounted for in the design of the fault-tolerant control system, including the issues of measurement sampling and delays. In particulate processes, measurements of the principal moments of the particle size distribution (obtained, for example, using light scattering techniques) and measurements of the continuous phase variables (e.g., solute concentration and temperature in a crystallizer) are typically available from the sensors at discrete time instances and are delayed. The frequency and times at which the measurements are received by the control system are constrained by the inherent limitations on the data collection, processing and transmission capabilities of the measurement sensors. These limitations impose restrictions not only on the implementation of the controller but also on the ability to accurately monitor the process evolution, which in turn can erode the diagnostic and control system reconfiguration capabilities of the fault-tolerant control system if not explicitly accounted for in the monitoring and control system design.

In this work, we develop a model-based framework for actuator fault detection and reconfiguration in particulate processes modeled by population balance equations with discretely-sampled and delayed measurements. Initially, model reduction techniques are used to derive an approximate finite-dimensional system that captures the dominant dynamics of the particulate process. An observer-based output feedback controller is then designed on the basis of this system to stabilize the process in the absence of faults. To compensate for the lack of continuous measurements, an inter-sample model predictor is included within the control system to provide the observer with an estimate of the process output when measurements are not available from the sensors. The model state is then updated when measurements are received at discrete times. To compensate for the measurement delay, the control system includes a propagation unit that uses the low-order model together with the past values of the control input to calculate an estimate of the current output from the received delayed measurements. This estimate is then used to update the inter-sample model predictor which, together with the controller, generates the control signal for the process. By formulating the closed-loop system as a combined discrete-continuous system, an explicit characterization of the minimum allowable sampling rate that guarantees stability in the absence of faults is obtained in terms of the plant-model mismatch, the controller and observer design parameters, the size of the measurement delay, and the choice of the control configuration. The characteristic fault-free closed-loop behavior obtained from this analysis is used as the basis for deriving appropriate rules for fault detection and control system reconfiguration. The idea is to use the state observer as a fault detection filter and compare its output with the estimate of the current plant output generated by the propagation unit at the sampling times. The discrepancy is used as a residual and compared against a time-varying alarm threshold obtained from the stability analysis to determine the fault or health status of the control actuators. Once a fault is detected in the operating control configuration, the control system is prompted to switch to one of the feasible fall-back control configurations under the given measurement sampling rate and delay to preserve stability and minimize performance deterioration. Finally, the proposed fault-tolerant control framework is illustrated using a simulated model of a continuous crystallizer with a fines trap.

References:

[1] El-Farra, N. H. and A. Giridhar, ``Detection and Management of Actuator Faults in Controlled Particulate Processes Using Population Balance Models,'' Chem. Eng. Sci., 63:1185-1204, 2008.

[2] Giridhar, A. and N. H. El-Farra, ``A Unified Framework for Robust Fault Detection, Isolation and Compensation in Uncertain Particulate Processes,'' Chem. Eng. Sci., 64:2963-2977, 2009.