## 4 Case Study of Industrial Control Systems
### Design Optimization and Discussion  
Based on the simulation results from the previous section, this part presents a targeted optimization of the PLC design, guided by the resilience assessment framework. Figure 12: PLC performance curves at \(\lambda=10\) s, \(30\) s, and \(1\) min. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Resilience States** & **Parameters** & **Values** \\ \hline Undetectable failure & A & 1 \\  & R & 0 \\ \hline Detectable failure & A & 0.8 \\  & R & 0.1 \\ \hline \multirow{2}{*}{Degraded} & A & 0.6 \\  & R & 0.3 \\ \hline \multirow{2}{*}{Available} & A & 0 \\  & R & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The values of A and R in different resilience stages. Given the evaluation results and practical design constraints such as latency, hardware cost, and system complexity, we prioritize enhancing the recovery rate to improve overall resilience. Thus, we propose an architectural optimization focused on context backup and rollback strategies during runtime. Specifically, the software execution process is modified to periodically save key runtime contexts and define rollback points. At these points, the state of the CPU is recorded to enable recovery in case of execution anomalies. Upon detection of a fault by the lightweight mimetic scheduler, the faulty CPU core is interrupted, and a targeted software cleansing is performed according to a predefined exception handling logic. The CPU then rolls back to its most recent saved context and re-synchronizes with the other cores before rejoining the mimetic voting process. Figure 13 illustrates the operation of this mechanism. In the MCU, each heterogeneous core may request to update the application's global state after computation. The scheduler collects modification requests from all three cores within a preset time window, conducts majority voting to determine the correct state, and updates the global application state accordingly. After this, a synchronization signal is broadcast to all cores, prompting them to perform a unified state reload, completing the state recovery process. This mechanism effectively shortens the downtime associated with individual core failures, improving the overall system recovery responsiveness. To evaluate the impact of the design optimization, recovery tests were conducted on both the original and the improved PLC implementations. The results indicate that the average recovery rate increased by approximately 60%, reflecting a substantial enhancement in the system's responsiveness to internal disruptions. Based on this updated recovery capability, the degradation-phase recovery parameter \(R\) is reset and the full resilience assessment process from Section 4.2 is repeated. Figure 13: Context backup and cleaning recovery diagram of diverse-redundant MCU. As illustrated in Figure 14, the revised resilience curves show a notable reduction in the area under the degradation phase, alongside improved system robustness and faster recovery. These improvements are particularly evident in scenarios with persistent disruptions, where the system maintained a higher performance baseline and returned to nominal operation more quickly. It is worth noting that beyond the differences in recovery time and strategies demonstrated through the resilience curve comparisons in this section, the proposed evaluation framework and process offer considerable flexibility for customization. Key components of the framework--including the definition of resilience phases, the modeling of adverse conditions, the parameter normalization strategies, and the model formulation of the cyber layer--can be adapted to suit different system contexts and application domains. This flexibility enables the framework to be extended or tailored for a wide range of CPS configurations and resilience design needs. In summary, the design optimization guided by the proposed resilience evaluation framework led to significant performance gains. The degradation zone was markedly reduced, system robustness improved, and overall resilience enhanced.