465691 Fault Estimation and Performance-Based Accommodation in Multi-Rate Sampled-Data Process Systems
Fault-tolerant control of sampled-data systems has been the focus of prior work  where a model-based framework was developed for fault detection and reconfiguration of a control system with sampled and delayed measurements. This was implemented in the context of control actuator faults. While reconfiguration of the control system is a viable option for fault handling, it is not always an ideal go to solution for fault handling in situations where the availability of component redundancy is either costly on intrinsically limited by process design considerations. The ability of the system to operate satisfactorily in the faulted control configuration is a worthwhile pursuit as was demonstrated in  where a stability-based fault accommodation strategy was developed. These results where subsequently generalized in  to include fault estimation capabilities through an optimization-based approach to aid in the implementation of the fault accommodation framework mentioned prior.
A key aspect of previous works is that all states in the system were assumed to be sampled at the same rate. In many practical situations, however, limitations on the measurement capabilities of different sensors may result in a significant gap between the sampling rates, and in such cases a synchronized sampling mechanism may not be the best choice . Moreover, the importance of the measurement collected is another factor that can trigger the use of multi-rate sampling. It is reasonable to apply a fast sampling rate to the sensors placed at certain critical locations in the process (e.g., where frequent monitoring and tight control are required), while reducing the sampling rates of the other sensors in order to reduce cost and optimize energy resource consumption. A more robust framework for fault-tolerant control would therefore be to allow for the possibility of sampling each state at a different rate. However, to date there has not been any rigorous assessment or characterization of the stability properties of multi-rate sampled-data systems in the context of fault-tolerant control, nor has there been any thorough assessment of performance-based accommodation for multi-rate sampled systems. These are important gaps that the current work aims to address.
Motivated by these considerations, we present in this work a combined data-based and model-based framework for the detection and accommodation of control actuator faults in process systems with multi-rate sampled measurements. A key feature of this contribution is to explicitly incorporate performance based fault accommodation into the framework, which would allow for post accommodation performance to be characterized and determine if the accommodation measure is sufficient or if more drastic measures must be taken to ensure the desired quality of the process output. Initially, a model-based controller is designed and its closed-loop stability and performance properties are explicitly characterized in terms of the model and controller design parameters, the sensor sampling rates and the magnitudes of the faults. The model is used to compute the control action, and its states are updated at different times whenever the measurements become available from the sensors. A data-based moving-horizon parameter estimation scheme, which takes the available sampled data from the process, is developed and used to estimate the severity of the faults and to identify their locations. Owing to the different sampling rates of the states, the data set used for fault estimation contains missing data. To address this problem, suitable propagation models are incorporated in the fault diagnosis unit to provide estimates of the missing states based on the available measurements, which are then used in solving the optimization problem. The fault accommodation logic will then determine an appropriate response while using this estimated fault values to meet some baseline performance needed by the process, whilst ensuring stability. The fault accommodation logic is based on the parametrization of the closed-loop stability region and the performance metric obtained at the controller design stage as a function of the fault size, the controller design and model parameters as well as the frequency of each of the sampled measured states. Finally, the developed framework is illustrated using a simulated chemical process example.
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