# Early Fault Detection and Operator-Based MIMO Fault-Tolerant Temperature Control of Microreactor
## 7 Simulation Results  
In this chapter, the effectiveness of the proposed control and fault detection systems is verified by simulation. Simulations were performed using MATLAB 2023b. One-Class SVM used ocsvm function. ChangeFinder and real-coded genetic algorithms were self-developed. In the simulation, a normally distributed noise with mean 0 and variance 0.0005 is added to \(y_{n}\) assuming the measurement noise of the temperature sensor. The target temperature is (outside temperature - reference input). Simulations were performed for the following two cases. The parameters are also shown in Table 3.  
1. Part W\({}_{1}\) increased 3.2 \({}^{\circ}\)C from 500 s and Part W\({}_{3}\) increased 3.6 \({}^{\circ}\)C from 500 s.
2. Part W\({}_{3}\) increased 0.2 \({}^{\circ}\)C from 500 s.  
Part W\({}_{1}\) Increased 3.2 \({}^{\circ}\)C from 500 s and Part W\({}_{3}\) Increased 3.6 \({}^{\circ}\)C from 500 s  
Figure 11 shows the results of temperature control using the proposed control system. Figure 12 also shows the results of the real-time fault classification. Figure 11b shows that the value of the fault sensor fluctuates due to the faults that occurred during the 500 s. However, as Figure 11a shows, the temperature of the controlled object continues to track the reference input. The control input jumps up at 500 s due to the sensor fault. However, it returns to the appropriate input by switching to the fault-tolerant control system.  
Discussing the results for Figure 12a, ChangeFinder's change-point score jumped at 503 s, 3 s after the fault. Figure 12b shows that One-Class SVM detected the fault at 500 s, the control cycle in which the fault data were first measured; One-Class SVM detected the fault before ChangeFinder's score jumped. Thus, ChangeFinder contributed little to fault detection. In addition, there were no false positives.  
Figure 11: Simulation results under condition where Part W\({}_{1}\) increased 3.2 \({}^{\circ}\)C from 500 s and Part W\({}_{3}\) increased 3.6 \({}^{\circ}\)C from 500 s: (**a**) temperature. (**b**) Measurements of faulty sensors. (**c**) Control input.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Symbol** & **Description** & **Value** & **Unit** \\ \hline \(T_{n}\) & smoothing scale & 10 & – \\ \(T_{0}\) & Outside temperature (initial temperature) & 26 & \({}^{\circ}\)C \\ \(dt\) & Control cycle & 1 & s \\ \(T_{F}\) & Fault occurrence time & 500 & s \\ \(B\) & Time constant of a fault element & 0.2 & s \\ \(A_{1}\) & Fault element amplitude of PartW\({}_{1}\) & \(-\) & \({}^{\circ}\)C \\ \(A_{3}\) & Fault element amplitude of PartW\({}_{3}\) & \(-\) & \({}^{\circ}\)C \\ \(r\) & Oblivion coefficient & 0.03 & \(-\) \\ \(r_{1}\) & Reference input of PartW\({}_{1}\) & 3.7 & \({}^{\circ}\)C \\ \(r_{2}\) & Reference input of PartW\({}_{3}\) & 4 & \({}^{\circ}\)C \\ \(k\) & SDAR model order & 1 & \(-\) \\ \(B_{n}\) & Design parameter & 0.9999 & \(-\) \\ \(n_{w_{n}}\) & Design parameter & 50 & \(-\) \\ \(k_{C_{r}}\) & Proportional gain of \(C_{w_{n}}\) & 0.0140 & \(-\) \\ \(k_{C_{i}}\) & Integral gain of \(C_{w_{n}}\) & 0.0003 & \(-\) \\ \(k_{M_{r}}\) & Proportional gain of \(M_{w_{n}}\) & 0.0140 & \(-\) \\ \(k_{M_{i}}\) & Integral gain of A \(M_{w_{n}}\) & 0.0003 & \(-\) \\ \(n_{a_{n}}\) & Design parameter & 50 & \(-\) \\ \hline \hline \end{tabular}
\end{table}
Table 3: Condition parameters of simulations.