# An Improved Model-Free Adaptive Nonlinear Control and Its Automatic Application
## 4 Simulation Experiment and Analysis
### Experiment 2: Circulating Fluidized Bed Boiler Drum Water Level Control
The MFAC-OER drum water level simple control block diagram is shown in Figure 7.  
Figure 8 is the boiler bubble water level output diagram of MFAC-OER, MFAC, and PID. The change of the curve can reflect the respond time of the system. Figure 9 is the corresponding water level output error diagram, which can more intuitively reflect the response of the system. Table 2 is the corresponding performance index, which directly reflects the respond accuracy. From the water output diagram and the corresponding water output error diagram, the FFDL-MFAC-OER method has an effective respond accuracy. The water level error range is between (\(-0.15\) m, \(0.12\) m) (except for the change in working conditions), and has fast tracking characteristics. It is superior to FFDL-MFAC and PID methods, and can effectively suppress the influence of interference, thus maintaining the water level. The performance indicators of Table 2 are analyzed as follows: For the rise  
Figure 6: Circulating fluidized bed boiler water system experiment platform. time, as shown in Table 2, the MFAC-OER is one-third of the PID; in terms of adjustment time, the MFAC-OER method is less than the MFAC method, and is much lower than the PID adjustment time. The value by the MFAC-OER is much smaller than that by the PID, indicating that it has higher accuracy and better stability. In addition, it can be seen from Figures 8 and 9 that the MFAC-OER method can still respond to feedback faster under variable operating conditions. This results in the better tracking of the given boiler bubble water level, which further confirms the effectiveness of the proposed method. Figure 10 shows the water supply input change curves of the MFAC-OER, MFAC, and PID methods, which reflects the input stability. Stable control input change can reduce the energy loss and daily maintenance cost. It is not difficult to see that the water supply maintained by the MFAC-OER method has been in a reasonable working range. The water supply is always stable at 5 m from 0 s to 500 s and 7 m from 500 s to 1000 s, with little change. When the working condition changes (500 s), it can also respond quickly; in MFAC and PID, the water supply of 6 m from 0 s to 500 s and the water supply of 9 m from 500 s to 1000 s has been in a large fluctuation process, which is greatly affected by interference and is prone to being large or even small. If it is too high, exceeding the normal water level will lead to problems in the steam-water separation process; an excessively low water level will lead to an abnormal water cycle. In addition, the frequent adjustment of the water supply will also lead to a greater loss of system components. After a long period of operation, it is proven that the MFAC-OER method of the CFB water level has the following advantages: stable drum water level, sensitive control, high safety and reliability, effectively avoiding the interference of internal and external disturbance factors, and meeting the control requirements. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Methods** & **PID** & **MFAC** & **MFAC-OER** \\ \hline Rise time (s) & 16 & 16 & 6 \\ Adjust time (s) & 55 & 32 & 18 \\ MAE & \(8.69\times 10^{-2}\) & \(5.21\times 10^{-2}\) & \(2.29\times 10^{-2}\) \\ MSE & \(1.05\times 10^{-1}\) & \(5.70\times 10^{-2}\) & \(2.42\times 10^{-2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of several performance indexes of each control method. Figure 9: Three control methods’ system water level output error curves: (**a**) PID water level output error curve; (**b**) MFAC water level output error curve; and (**c**) MFAC-OER water level output error curve.