# Early Fault Detection and Operator-Based MIMO Fault-Tolerant Temperature Control of Microreactor
###### Abstract  
A microreactor is a chemical reaction device that mixes liquids in a very narrow channel and continuously generates reactions. They are attracting attention as next-generation chemical reaction devices because of their ability to achieve small-scale and highly efficient reactions compared to the conventional badge method. However, the challenge is to design a control system that is tolerant of faults in some of the enormous number of sensors in order to achieve parallel production by numbering up. In a previous study, a simultaneous control system for two different temperatures was proposed in an experimental system that imitated the microreactor cooled by Peltier devices. In addition, a fault-tolerant control system for one area has also been proposed. However, the fault-tolerant control system could not be applied to the control system of two temperatures in the previous study. In this paper, we extend it to a two-input, two-output fault-tolerant control system. We also use a fault detection system that combines ChangeFinder, a time-series data analysis method, and One-Class SVM, an unsupervised learning method. Finally, the effectiveness of the proposed method is confirmed by experiments. microreactor; fault detection method; operator theory; nonlinear control; right coprime factorization; fault-tolerant control +
Footnote †: journal: Applied sciences  
production, the number of sensors and actuators is expected to increase due to numbering up. As the number of devices in a system grows, the likelihood of individual component failure also increases, but it is impractical to repair each time a fault occurs. To avoid such economic losses, it has become common for redundant sensors and actuators to be implemented in plants. Therefore, even if some of the systems fail, such redundant equipment can be used to realize the control system with redundant operation against faults. A control system with redundancy against fault is called a fault-tolerant control system. However, from the viewpoint of safety, the system that can quickly identify the equipment in which the fault has occurred is required [11; 12]. In addition, the use of time-series data to detect faults in production plants has been attracting attention. As production plants become larger and include more sophisticated systems as a result of advances in science and technology, the labor and cost involved in monitoring them has become an issue. Therefore, the construction of a system that senses each condition and automatically analyzes the data will enable real-time fault detection without human intervention [13]. ChangeFinder is a data analysis method that has been attracting attention for its ability to capture changes in behavior (change-points) in a time series rather than the data values themselves, and to calculate a score for the likelihood of a change-point in the time-series data. If time-series data show stationarity during normal conditions, the change-points detected by ChangeFinder may be equipment anomalies [14]. In a previous study, the fault-tolerant control system based on operator theory considering Bounded-Input Bounded-Output (BIBO) stability was proposed for minor temperature sensor faults in microreactors, aiming to continue control even in the event of the fault [15]. The fault-tolerant control system based on operator theory that takes into account BIBO stability has been proposed for the purpose of maintaining control even in the event of minor faults in temperature sensors of microreactors. Operator theory is a nonlinear control theory that expresses inputs and outputs in terms of maps (operators) [16]. Nonlinear control theory makes it possible to design control systems without linear approximation. However, fault detection is required in general fault-tolerant control systems because the control loop is switched between faulty and normal conditions. Prior research has applied One-Class SVM, which is unsupervised learning, and proposed fault detection that does not require a signal at fault in advance.