(552f) Fault Estimation and Performance-Based Accommodation in Multi-Rate Sampled-Data Process Systems

Fault handling is a critical component of modern-day process control systems. When left unchecked, faults in process elements such as measurement sensors and control actuators can lead to substantial loss of product quality and in some cases instabilities and safety hazards. The critical nature of this problem has led to a significant body of research work on the topic of fault-tolerant control (e.g., see [1]-[4]). Classically, this problem has been addressed in the context of a conventional feedback control setting where continuous measurements of the states are assumed to be available for the controller to utilize in driving the process to the desired operating point. However, with real-time operation practices this is generally not the case, and measurements of the state variables are limited in availability by the measurement sensors and/or the resources of the sensor-controller communication medium. Discretely sampled-data systems are commonly found in industrial processes as continuous measurement of system data often proves logistically or technologically prohibitive. In sampled-data systems, the stability of the closed-loop system is critically dependent on the rate at which the sampled measurements are taken.

Fault-tolerant control of sampled-data systems has been the focus of prior work [5] 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 [6] where a stability-based fault accommodation strategy was developed. These results where subsequently generalized in [7] 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 [8]. 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.

References:

[1] M. Blanke, M. Kinnaert, J. Lunze, and M. Staroswiecki, Diagnosis and Fault-Tolerant Control. Berlin, Germany: Springer, 2003.

[2] R. Isermann, Fault-Diagnosis Systems: An Introduction from Fault Detection to Fault Tolerance. Berlin, Germany: Springer, 2005.

[3] Y. Zhang and J. Jiang, â??Bibliographical Review on Reconfigurable Fault-Tolerant Control Systems,â? Annu. Rev. in Contr., vol. 32, pp. 229â??252, 2008.

[4] P. Mhaskar, J. Liu, and P. D. Christofides, Fault-Tolerant Process Control: Methods and Applications. London, England: Springer-Verlag, 2013.

[5] Y. Sun and N. H. El-Farra, â??Model-Based Fault Detection and Fault-Tolerant Control of Process Systems with Sampled and Delayed Measurements," Proceedings of 18th IFAC World Congress, pp. 2749-2754, 2011.

[6] T. Napasindayao and N. H. El-Farra, â??Fault Detection and Accommodation in Particulate Processes with Sampled and Delayed Measurements,â? Ind. Eng. Chem. Res., 52, 12490â??12499, 2013.

[7] T. Napasindayao and N. H. El-Farra, â??Model-based Fault-Tolerant Control of Uncertain Particulate Processes: Integrating Fault Detection, Estimation and Accommodation,â? Proceedings of 9th IFAC Symposium on Advanced Control of Chemical Processes, pp. 872-877, 2015.

[8] J. Wang, T. Chen, and B. Huang, â??Multi-rate Sampled-Data Systems: Computing Fast-Rate Models,â? J. Proc. Contr., vol. 14, pp. 78â??88, 2004.