(317a) Robust Performance-Based Fault Detection, Isolation And Compensation In Uncertain Particulate Processes

Particulate processes are widely used in a number of important processing industries including agricultural, chemical, food, minerals, and pharmaceuticals. It is now well understood that the Particle Size Distribution (PSD) in these processes provides a critical link between the product quality and the process operating variables, and that the ability to effectively manipulate the PSD is essential to controlling the quality of the end product. These realizations have motivated significant research work on the design of model-based feedback control systems for particulate processes to achieve PSDs with desired characteristics (e.g., see [1], [3] for recent results and references). Despite the significant and growing body of research work on this topic, the problems of fault detection and fault-tolerant control of particulate processes have not been investigated. For particulate processes involved in the production of specialty chemicals where the ability to meet stringent product specifications is critical to the product utility, the erosion of control authority caused by control system failures can result in off-spec products and lead to substantial production losses if such faults are not properly diagnosed and handled in the control system design.

One of the key challenges that arise in model-based fault diagnosis of particulate processes is the infinite-dimensional nature of particulate process models which are typically obtained through the application of population, material and energy balances and consist of systems of nonlinear partial integro-differential equations that describe the evolution of the PSD, coupled with systems of nonlinear ordinary differential equations that describe the evolution of the state variables of the continuous phase. The infinite-dimensional nature of population balance models precludes their direct usage for the synthesis of practically implementable controllers or fault diagnostic filters which need to be designed on the basis of appropriate low-order models to be suitable for practical implementation. This requires that the fault diagnosis filters be designed and implemented in a way that allows discriminating between approximation errors and faults. To address this problem, we recently developed in [2] a methodology for the detection and handling of actuator faults in single-input particulate processes on the basis of appropriate reduced-order models that capture the dominant process dynamics. The fault detection task was addressed by means of a filter that simulates the behavior of the fault-free, reduced-order model and using the discrepancy from the behavior of the actual process as a residual signal. Failure compensation, on the other hand, was accomplished through a switching mechanism that reconfigures the control system based on the stability regions of the constituent control configurations in a way that preserves closed-loop stability in the event of fault detection. Using regular perturbation theory, appropriate fault detection thresholds and control reconfiguration criteria that account for model reduction and state estimation errors were derived for the implementation of the control architecture on the particulate process.

For particulate processes with several manipulated inputs, it is important not only to detect that a fault has occurred but also to identify its location in order to avoid the unnecessary shut down of possibly healthy actuators following fault detection. This requires that a fault isolation scheme that identifies the faulty inputs within the operating set be incorporated into the fault-tolerant control architecture. Another important issue that must be accounted for in the design of model-based fault diagnosis and fault-tolerant control systems is the presence of model uncertainty. Population balance models that describe particulate processes are inherently uncertain due to the presence of unknown, or partially known, process parameters as well as time-varying exogenous disturbances which, if not properly accounted for, can adversely affect all the components of the fault-tolerant control architecture; e.g., degrading the stability and performance properties of the feedback controller, corrupting the fault diagnosis process leading to false alarms and poor supervisory control. Typically, unless the filter is re-designed to achieve uncertainty decoupling, the residual will be sensitive to both the uncertainty and the faults, leading to false alarms. One way to decouple the effect of uncertainty on the residual is to re-design the fault detection filters using the unknown-input observer principle [4]. This approach, however, is complicated by the strong nonlinear dynamics of particulate processes (e.g., owing to complex growth, nucleation, agglomeration and breakage mechanisms, and the Arrhenius dependence of nucleation laws on solute concentration in crystallizers).

Motivated by these considerations, we present in this work a methodology for the robust detection, isolation and compensation of actuator faults in multi-variable particulate processes described by population balance models with control constraints, time-varying uncertain variables and actuator faults. The main idea is to shape the fault-free closed-loop system response via robust feedback control in a way that facilitates the design of dedicated fault detection and isolation (FDI) filters whose residuals are practically insensitive to the uncertainty. This is achieved as follows. Initially, a low-order model that captures the dominant process dynamics is derived using the method of weighted residuals. The approximate model is used to design a set of robust nonlinear feedback controllers that enforce robust stability with an arbitrary degree of asymptotic attenuation of the effect of uncertainty on the outputs of the closed-loop system. To facilitate fault isolation, the manipulated inputs are chosen such that each controlled output is directly influenced by a single input. A set of dedicated FDI filters that replicate the fault-free closed-loop behaviors of the approximate model outputs in the absence of uncertainty are constructed. The input/output pairings ensure that each residual is dedicated to one only input. To decouple the effect of uncertainty on the residual, a bound that captures the size of the fault-free residual in the presence of uncertainty is derived and used as a threshold for robust fault detection. A key feature of this bound is that it is a function of the achievable degree of asymptotic uncertainty attenuation and can be made arbitrarily small by properly tuning the robust controller. Essentially, by controlling the degree of uncertainty attenuation, the asymptotic closeness between the process and FDI filter outputs (i.e., the residual size) can be made as small as desired in the absence of faults, and thus practically insensitive to the uncertainty. The robust FDI filters are integrated with a controller reconfiguration strategy that orchestrates the transition from the faulty actuators to a well-functioning fall-back configuration following FDI. Appropriate FDI criteria are derived for the implementation of the fault-tolerant control architecture on the particulate process to ensure its robustness with respect to model reduction errors. Using regular perturbations theory, the criteria are expressed in terms of optimized residual thresholds that capture the closeness of solutions between the fault-free reduced and full-order models. Finally, the proposed approach is applied to the problem of robust fault-tolerant control of the Crystal Size Distribution in a continuous crystallizer with a fines trap.

References:

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

[2] El-Farra, N. H. and A. Giridhar, ``Detection and Management of Actuator Faults in Controlled Particulate Processes Using Population Balance Models," Chem. Eng. Sci., in press, 2007.

[3] Larsen, P., D. Patience and J. B. Rawlings, ``Industrial Crystallization Process Control," IEEE Contr. Syst. Mag., 26: 70-80, 2006.

[4] Watanabe, K. and D. M. Himmelblau, ``Instrument fault detection in systems with uncertainties," Inter. J. Syst. Sci., 13: 137-158, 1982.