(204e) Sensor Fault Accommodation Strategies in Multi-Rate Sampled-Data Control of Particulate Processes

Fault-tolerant control of particulate processes is a fundamental problem in agricultural, chemical, food, mineral, and pharmaceutical industries. This problem is significant since malfunctions in the control system components or process equipment can negatively impact the particle size distribution of and thus harm the end product quality. This problem has received limited attention, especially compared to the significant body of research work on the synthesis and implementation of feedback control systems on particulate processes (e.g., see [1] for some results and references in this area).

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 and uncertain dynamics of particulate processes. An effort to address these problems was initiated in [2] where a methodology for the detection and handling of control actuator faults was developed based on low-order models that capture the dominant process dynamics. The results were generalized in [3] to address the problems of fault isolation and robustness to model uncertainty. 

Various implementation issues arise in the design of any fault-tolerant control system. These include discrete and multi-rate sampling of the output measurements, as well as the possibility of sensor faults. Measurement availability is constrained by inherent limitations on data collection, processing and transmission capabilities of the measurement sensors. In particulate processes, sensor measurements of the dispersed and the continuous phase variables are typically available at discrete times. The control system may also make use of multiple outputs subject to different sampling rates. For instance, the dispersed phase properties may be collected using light scattering techniques whereas properties of the solute concentration in the continuous phase may be obtained from a refractometer. Ignoring these factors in process monitoring and controller design may erode the performance of the fault-tolerant control system. Hence, it is crucial that these be explicitly accounted for in designing the monitoring and control systems.

Furthermore, fault-tolerant control systems need to consider the type of fault that occurs to ensure proper handling. Faults are classified as sensor, actuator, or component faults depending on where they appear in the system. While existing fault-tolerant control methods for distributed parameter systems have focused largely on actuator and component fault diagnosis and compensation (e.g., see [4]-[5]), sensor faults are commonly encountered in practice and need to be accounted for. This can be achieved through either passive or active fault-tolerant control techniques, as opposed to component faults which are typically handled via fault accommodation [5].

In this work, we develop a model-based framework for fault-tolerant control of multi-rate sampled-data particulate processes with sensor faults based on a suitable finite-dimensional
approximation of the infinite-dimensional system. The model is used in designing a stabilizing observer-based output feedback controller with an inter-sample model predictor that compensates for the discrete availability of multi-rate measurements. A closed-loop stability analysis is conducted leading to an explicit characterization of the interdependencies linking the stabilizing sensor sampling rates to the size of the model uncertainty, the controller and observer design parameters, and the choice of the control configuration. The stability conditions are used to obtain, for each control configuration, a region of stability in terms of the feasible sampling periods, which is then used to predict the behavior of the sampled-data closed-loop system under a certain set of operating conditions and devise accordingly either passive or active sensor fault compensation schemes. The proposed fault-tolerant control framework is illustrated using a simulated model of a non-isothermal continuous crystallizer.

References:

[1] Christofides, P.D. (2002). Model-Based Control of Particulate Processes. Kluwer Academic Publishers, Netherlands.

[2] El-Farra, N.H. and Giridhar, A. (2008). Detection and management of actuator faults in controlled particulate processes using population balance models. Chem. Eng. Sci., 63(5), 1185 – 1204.

[3] Giridhar, A. and El-Farra, N.H. (2009). A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes. Chem. Eng. Sci., 64(12), 2963 – 2977.

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

[5] Napasindayao, T. and El-Farra, N.H. (2012). Fault detection and accommodation in particulate processes with delayed, sampled measurements. In Proceedings of the 8th IFAC Symposium on Advanced Control of Chemical Processes, 172–177. Singapore.