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One of the central problems at the interface of process control and operations is the development of systematic methods for the diagnosis and handling of faults. The motivation for studying this problem stems in part from the vulnerability of automated industrial processes to malfunctions in the control actuators, measurement sensors and process equipment, as well as the increased emphasis placed on safety, reliability and profitability in the operation of industrial processes. Despite the substantial and growing body of literature on this problem, most of the previous research work in this area has focused on spatially homogeneous processes modeled by systems of ordinary differential equations. Yet, there are many important industrial processes such as transport-reaction and particulate processes that are characterized by spatial variations and are more appropriately modeled by Partial Differential Equations (PDEs). Major bottlenecks in the design of fault diagnosis and fault-tolerant control systems for distributed processes include the infinite-dimensional nature of the models that describe the dynamics of these processes, as well as the complex nonlinearities and uncertainties that characterize these models.

To overcome these problems, the central objective of this research project has been the development of a general, yet practical, methodology for the integration of fault diagnosis and fault management in distributed processes by bringing together tools from model reduction, nonlinear and robust control techniques, and hybrid system theory. Exploiting the inherently low-dimensional dynamic behavior of certain classes of distributed parameter systems, we have been able to formulate and solve the problem on the basis of appropriate low-order models that are suitable for the design of practically implementable control and diagnosis algorithms, and are amenable to rigorous stability and performance analysis. The diagnosis and control algorithms have been successfully applied to simulated models of both transport-reaction and particulate processes.

(a) Fault detection, isolation and reconfiguration in transport-reaction processes

In this direction, our research efforts have focused on the development of integrated fault detection and isolation (FDI) and fault-tolerant control (FTC) architectures for transport-reaction processes modeled by highly dissipative nonlinear PDEs with control constraints and control actuator faults. Specifically, we initially developed a model-based fault-tolerant control architecture that brings together model-based fault detection, spatially distributed feedback and supervisory control to orchestrate switching between different actuator configurations following fault detection. The architecture was subsequently generalized to address the problem of actuator fault isolation and incorporate performance considerations in the control reconfiguration logic. Practical implementation issues such as the availability of only a limited number of measurements were accounted for by incorporating a nonlinear state estimation scheme into the control structure and modifying the FDI and switching logics accordingly. The problem of designing integrated FDI-FTC architectures that are robust with respect to model uncertainty and measurement errors was also studied and addressed using a performance-based approach that unites FDI and robust control techniques and leads naturally to an explicit characterization of the state-space regions where robust FDI is feasible under uncertainty and constraints. Finally, the issue of discrete measurement sampling and its impact on the monitoring and reconfiguration capabilities of the fault-tolerant control system were investigated. The problem was addressed using an inter-sample model predictor that provides the controller with estimates of the process states when measurements are not available from the sensors. The theoretical results were successfully applied to simulated models of diffusion-reaction processes and non-isothermal tubular reactors with recycle.

(b) Fault detection, isolation and compensation in particulate processes

In addition to transport-reaction processes, our work has also focused on the design of integrated FDI-FTC systems for particulate processes described by population balance models with control constraints, uncertain dynamics, actuator faults and limited measurements. This problem is motivated by the need to minimize the impact of control system failures on the achievable particle size distribution, which is critical to maintaining the desired end product quality in particulate processes. The developed methodology focused initially on fault detection issues in single-input particulate processes and was later generalized to multi-input processes to incorporate fault isolation capabilities and account explicitly for the presence of model uncertainty. The algorithms were applied successfully to simulated models of continuous crystallizers with and without a fines trap.

In addition to being the first studies in process control to address the fault diagnosis and fault-tolerant control problems for distributed processes in an integrated fashion, a key feature of our approach is the explicit linkage, via singular or regular perturbation techniques, between the detection and isolation tasks, on the one hand, and the structure of the PDE, on the other. This linkage enabled the derivation of robust alarm thresholds that guard against false alarms when implementing the reduced-order model-based FDI-FTC architectures on the infinite-dimensional system.

Our work in this area has been recognized by several awards to my doctoral student, Sathyendra Ghantasala, who has been working on this project over the past couple of years and has been partially supported by this grant. These awards include (1) Best Presentation In Session Awards at the 2007 and 2009 American Control Conferences, (2) Student travel awards from the American Automatic Control Council (2009 and 2007), the UC Davis Graduate Student Association (2009), the UC Davis Office of Graduate Studies (2008) and the AIChE Computing and Systems Technology Division (2007) to participate in various professional meetings and present results from our work on this project. Sathyendra is currently in the final stages of writing his thesis and is expected to obtain his Ph.D. in Chemical Engineering before the end of this year. In addition to graduate student support, funds from this grant were also used to pay for the travel of the principle investigator to the relevant professional meetings and to provide summer compensation.