(523g) Data-Based Fault Identification and Accommodation in Sampled-Data Controlled Particulate Processes

Fault-tolerant control of particulate processes is a fundamental problem encountered in a wide range of industries, including the agricultural, chemical, food, mineral, and pharmaceutical industries. This problem is significant given that malfunctions in the control system or process equipment can negatively impact the particle size distribution of interest and thus harm the desired end product quality. Major bottlenecks in the design of model-based fault-tolerant control systems for particulate processes include the infinite-dimensional nature of the process model as well as the complex and uncertain dynamics of particulate processes. An effort to address these problems was initiated in [1]-[2]  where a methodology for the detection, isolation and handling of control actuator faults in particulate processes was developed based on low-order models that capture the dominant process dynamics. A number of subsequent studies were carried out to account for various implementation issues that arise in the design of fault-tolerant control systems, including the discrete and delayed availability of output measurements [3], and the presence of multi-rate sampling and sensor faults [4].

In both studies, fault detection was achieved by designing a fault-free time-varying alarm threshold off-line and later comparing this with values of the residual for the entire duration of the process. However, the scheme for fault detection was stability-based, leaving ``small" malfunctions that do not lead to instability to go undetected. In designing this threshold, there are competing design requirements that need to be considered. For example, there is the need to tighten the threshold for timely fault detection; however, an extremely tight bound may result in false alarms. It was also assumed in those studies that a fault identification scheme was already in place which was able to determine the nature and location of the fault. This information was utilized in determining the appropriate response for fault accommodation. After each fault, a new alarm threshold for fault detection had to be calculated and used since the closed-loop system will have different stability properties after each fault accommodation event.

In this work, our aim is to address some of these limitations by integrating within the fault-tolerant control methodology a fault identification mechanism that allows for immediate detection of faults and/or malfunctions while determining its location and magnitude. One key element of the proposed scheme is that it can still be used for fault identification even after fault accommodation. This allows for timely fault detection in the event of consecutive system faults. This is an advantage over the previous detection schemes where a new alarm threshold had to be calculated after every fault accommodation event. This recalculation may result in delays in the fault detection preceding a fault. Timely or even instantaneous fault identification is important even for faults that do not immediately result in an unstable behavior since these malfunctions may later on result in poor process performance or even instability. In addition, rapid detection will also allow for systematic scheduling of plant maintenance and equipment repair or replacement.

Motivated by the above considerations, we develop in this study a model-based framework for the integrated detection, identification and accommodation of actuator faults in sampled-data particulate processes described by complex population balance equations. Initially, model reduction techniques are applied to derive a finite-dimensional model to be used in designing a stabilizing sample-and-hold state feedback controller. This controller uses past values of the state measurements in between sampling times. The controller then utilizes updated state measurements when sensor readings are received at discrete times. Through a stability analysis, an explicit characterization of the behavior of the closed-loop system is obtained as a function of the controller design parameters, the update time, and the actuator health. This characterization is then used as a metric in determining the appropriate post-fault response once a fault is detected. Fault identification is carried out by solving a data-based moving-horizon optimization problem. Data from the fault identification scheme are used in the fault accommodation which involves modifying the controller design parameters based on the stability plots generated from the stability analysis. Finally, the proposed fault-tolerant control framework is applied to a simulated model of a non-isothermal continuous crystallizer and is shown to effectively handle simultaneous and consecutive faults.

References:

[1] N. H. El-Farra and A. Giridhar, "Detection and management of actuator faults in controlled particulate processes using population balance models," Chemical Engineering Science, 63: 1185-204, 2008.

[2] A. Giridhar and N. H. El-Farra, "A unified framework for detection, isolation and compensation of actuator faults in uncertain particulate processes," Chemical Engineering Science, 64: 2963-2977, 2009.

[3]  T. Napasindayao and N. H. El-Farra, "Fault detection and accommodation in particulate processes with sampled and delayed measurements,"
Industrial & Engineering Chemistry Research, 52:12490-12499, 2013.

[4] T. Napasindayao and N. H. El-Farra, "Sensor fault accommodation strategies in multi-rate sampled-data control of particulate processes," In Proceedings of the 10th IFAC Symposium on Dynamics and Control of Process Systems, Mumbai, India, pp. 379-384, 2013.