(305d) Optimal Device Placement for Fault Tolerant Controller Design of Transport-Reaction Processes with Irregular Process Domain

Actuator failures have too often plagued chemical processes, often leading to deteriorating product quality and potentially dangerous process operation, such as runaway conditions. Motivated by the importance of the aforementioned problem, the issue of fault tolerant and fault accommodating controller design has been an active research topic in the chemical engineering community. However, while there has been extensive research from the control community on fault detection and diagnosis of finite dimensional systems using model-based robust and adaptive control techniques, the issue of fault tolerant control for distributed processes has been investigated in the last five years.

In this presentation we address the issue of fault tolerance by explicitly considering the spatial variability that transport-reaction processes naturally enjoy, The underlying idea is to identify actuator locations that while being physically apart they have the same authority on the process states. This is only applicable to distributed parameter systems wherein two or more different locations within the spatial domain of definition can provide the same level of controllability and at the same time the same feedback gain can be applicable to all such locations.  We capitalize on this property of spatially distributed parameter systems to find locations for different groups of actuators with similar controllability levels, and when a given actuator group fails, then simply deactivating the faulty actuator group and activating another actuator group constitutes the fault accommodation policy, while the control signal in this case is not changed.

Therefore the major conceptual contribution of this work is the efficient identification of ``optimal'' actuator locations that have the same level of controllability and design a single feedback controller for the archetypal actuator group. A major hurdle in such a procedure is the complexity of the spatial domain which in general would render the approach computationally infeasible. In principle, the spatial operator eigenfunctions could be combined with the method of weighted residuals to identify an ordinary differential equation (ODE) based approximation of the process description. However, for processes with complex spatial domains such functions cannot be analytically derived. We circumvent this by developing a proper orthogonal decomposition based algorithm that is used to reduce the process description to the ODE form. The algorithm is specifically tailored to account for the statistical nature of the order reduction step and converge to the true optimal actuator locations. An on-line supervisor is subsequently built that includes a fault detection scheme that monitors for possible faults by comparing the plants performance with that of the nominal performance. When a deviation is observed, then a fault is declared. The fault accommodation scheme in this special case does not require a control reconfiguration, but simply the deactivation of the current actuator group and the activation of another healthy actuator group. The profound simplicity of the fault accommodation significantly reduces the costs associated with process supervision with obvious economic and performance savings.