# 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  
In the second set of experiments, the method is applied to the drum water level control of the CFB boiler. The effectiveness of the algorithm is verified by the boiler equipment of the Quzhou special equipment inspection center. The traditional MFAC and PID controls are added, and the regulation time, MSE, and MAE are comparatively analyzed. The operation of the CFB boiler can be divided into three processes: fuel combustion, flue gas heat transfer, and water vaporization. (1) Combustion process: The fuel is sent into the furnace by the coal hopper through the coal feeder, the coal feeding air, and the coal seeding air. When the coal reaches the combustion temperature, it burns and moves backward. (2) Heat transfer process: The combustion of fuel releases heat, and the flue gas has a strong radiation heat transfer with the water pipe in the furnace. Then, the flue gas enters the tail flue, exchanges heat with the economizer and preheater, and is finally discharged from the chimney. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Methods** & **MFAC** & **MFAC-OER** \\ \hline Rise time (s) & 5 & 3 \\ Adjust time (s) & 22 & 10 \\ MAE & \(2.62\times 10^{-2}\) & \(9.05\times 10^{-3}\) \\ MSE & \(9.12\times 10^{-3}\) & \(2.82\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Several performance indexes of each control method. Figure 3: Two control methods’ system output error curves: (**a**) MFAC output error curve; and (**b**) MFAC-OER output error curve. 3. Vaporization process: It is the process of steam generation, including water cycle and steam-water separation. The chemically treated water is deoxygenated by the deaerator and preheated by the economizer to enter the drum. The CFB boiler process flow is shown in Figure 4.  
The main control goal of the steam-water system of the CFB boiler is to track the steam load requirements according to the feed water flow of the boiler, control the steam temperature within a certain range, and ensure the safe, stable, and energy-saving operation of the boiler and turbine. According to the characteristics of the steam-water system, it can be controlled in two aspects, that is, the drum water level control and main steam temperature control. In the steam-water system of the CFB boiler (in the dotted box of Figure 4), water flows out from the water supply device, and the steam drum is removed after moderate heating by the economizer. In addition, the water supply device also supplies water to the desuperheater, so that the temperature change of the main steam is not too large. The main steam passes through the steam-water separation device and the superheater, and finally becomes the finished steam through the desuperheater [28,29]. Figure 5 is a simplified flow chart of the steam-water system in the dotted box in Figure 4 [21]. Figure 4: The block diagram of the CFB boiler water system. Figure 5: The simplified block diagram of the CFB boiler water system. In CFB boilers, the drum water level represents the balance between the boiler load and water supply. Therefore, in order to ensure the stability and efficiency of the boiler, it is very important to keep the water level within a reasonable working area. The virtual line frame in Figure 5 is the drum water level part of the steam-water system. The purpose of the drum water level control is to:  
1. Keep the drum water level within a reasonable operating area. If the water level is too high and exceeds the normal level, it will lead to a problem in the steam-water separation process. In addition, if the steam carries too much water, it will bring too much dirt to the superheater wall and turbine blades, and even the blades will be damaged by the impact of the water flow. If the water level is too low, it will lead to an abnormal water circulation process, which will destroy the normal operation of the whole system [30]. 2.