## 2 Methodology
### Real Condition Tracking  
To validate the practical applicability of the proposed EEA-ESKF-MPC strategy, real condition tracking experiments were conducted using operational data from the Distributed Control System (DCS) of a 350 MW supercritical power plant. This test assesses the controller's ability to track setpoints under realistic scenarios, including normal operation, load variations, and disturbance responses, thereby reflecting the complex dynamics of actual plant operations. The results, presented in Figure 7 and Table 4, compare the EEA-ESKF-MPC against the existing power plant controller (typically a PID-based strategy), focusing on pressure, load, and temperature tracking performance. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Case** & **Controller** & **IAE1** & **IAE2** & **IAE3** & **ME1 (MPa)** & **ME2 (MW)** & **ME3 (\({}^{\circ}\)C)** \\ \hline Case 1: & ESKF-MPC & 7.837 & 47.952 & 64.004 & 1.423 & 7.943 & 4.969 \\ Throttle valve & EEA-ESKF-MPC & 7.473 & 47.529 & 37.314 & 1.427 & 7.952 & 4.907 \\ opening degree & EA-ESKF-MPC & 8.437 & 80.076 & 39.514 & 1.428 & 7.973 & 5.036 \\ disturbance (3000 s) & MPC & 8.423 & 59.909 & 63.781 & 1.424 & 7.940 & 5.008 \\ \hline Case 2: Coal feed & ESKF-MPC & 2.973 & 38.490 & 49.850 & 0.405 & 4.413 & 3.186 \\ rate disturbance & EEA-ESKF-MPC & 3.058 & 37.170 & 44.765 & 0.405 & 5.222 & 3.182 \\ (6000 s) & EA-ESKF-MPC & 2.630 & 95.535 & 51.256 & 0.394 & 4.3879 & 3.185 \\ MPC & 3.441 & 52.203 & 47.786 & 0.403 & 3.532 & 3.200 \\ \hline Case 3: Water feed & ESKF-MPC & 9.711 & 116.421 & 76.232 & 1.242 & 14.831 & 5.064 \\ rate disturbance & EEA-ESKF-MPC & 9.540 & 116.083 & 73.964 & 1.240 & 14.850 & 5.043 \\ (9000 s) & EA-ESKF-MPC & 9.571 & 155.878 & 60.759 & 1.241 & 14.669 & 5.041 \\ MPC & 10.987 & 127.995 & 66.853 & 1.242 & 14.664 & 5.049 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Control Performance of Different Controllers under Disturbance Cases. Figure 7: Comparison between the real controller and the proposed controller. (**a**) Pressure; (**b**) load; (**c**) temperature. Figure 7 provides a visual comparison of the control effects. In Figure 7a, the pressure response of the EEA-ESKF-MPC closely tracks the setpoint with minimal deviation, contrasting with the power plant controller's larger fluctuations. Figure 7b shows the load tracking, where the EEA-ESKF-MPC maintains a stable output despite rapid changes, while the power plant controller exhibits noticeable lag and overshoot. Figure 7c highlights the temperature control, with the EEA-ESKF-MPC achieving significantly tighter regulation compared to the power plant controller's oscillatory behavior. Table 4 quantifies these improvements. For pressure control, the EEA-ESKF-MPC reduces the IAE1 to 605.807, a 77.25% improvement over the power plant controller's 2667.670, and the ME1 to 0.923 MPa, a 40.83% reduction from 1.560 MPa. In load control, the IAE2 drops to 4384.299 (a 27.05% decrease from 6010.110), and the ME2 improves to 6.498 MW (a 5.30% reduction from 6.860 MW), indicating enhanced tracking accuracy. The most pronounced improvement occurs in temperature control, where the IAE3 decreases to 8000.564 (a 65.25% reduction from 23025.860), and the ME3 falls to 10.411 \({}^{\circ}\)C (a 75.08% improvement from 41.780 \({}^{\circ}\)C), showcasing exceptional stability and precision. These results underscore the superiority of the EEA-ESKF-MPC in real-world conditions. The adaptive error mechanism, coupled with the neural network-based prediction model (Section 2.2), enables the controller to dynamically adjust to operational variations, effectively mitigating the limitations of the power plant's PID controller, which struggles with the system's nonlinearity and coupling. The significant reductions in IAE and ME across all variables highlight the EEA-ESKF-MPC's ability to minimize cumulative errors and peak deviations, enhancing both dynamic performance and robustness.