## 6 Simulation Analysis and Experimental Verification
Figure 8:3 Sine response with SMC (sgn) (experimental). Figure 8:4 Sine response with SMC (sat) (experimental). After analyzing the experimental results of the step response and sine response, it can be found that the experimental results and simulation results of different control algorithms have the same change trend. According to the change of control error and high-frequency chattering in Table 2, it can be seen that AFSMC has the best control effect. In order to further verify the feasibility and effectiveness of AFSMC algorithm in the actual polishing process, different control algorithms are used for polishing experiments, and the blade surface polishing quality is observed. The blade material is TC4, and the length, width, and thickness are 80 mm, 30 mm, and 1 mm, respectively. The abrasive of the flap wheel is SiC, the granularity is P600, and the initial diameter is 16 mm. Due to the small polishing force, the dry polishing method was used in this experiment. The surface roughness of the blade before polishing is 0.821 mm-1.214 mm. The flap wheel polishing experiment of the blade is shown in Figure 8:5 \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline  & \multicolumn{1}{c}{**Response**} & \multicolumn{1}{c}{**PID**} & \multicolumn{2}{c}{**SMC**} & \multirow{2}{*}{**AFSMC**} \\ \cline{4-6}  & & & & **Sgn(s)** & & **Sat(0.02)** & \\ \hline \multirow{3}{*}{simulation result} & \multirow{2}{*}{Control error} & Step & 5.12 & 1.97 & 3.02 & 1.12 \\  & & Sin & 5.48 & 2.12 & 3.23 & 1.21 \\ \cline{2-6}  & \multirow{2}{*}{Chattering extent} & & & & & \\ \hline \multirow{3}{*}{experimental result} & \multirow{2}{*}{Control error} & Step & 5.26 & 2.15 & 3.14 & 1.28 \\  & & Sin & 5.83 & 2.34 & 3.46 & 1.37 \\ \cline{1-1} \cline{2-6}  & \multirow{2}{*}{Chattering extent} & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Comparison of simulation and experimental results of different control algorithms. Figure 21: Sine response with AFSMC (experimental). Figure 23a shows the Infinite Focus G4 automatic zoom 3D surface measuring instrument for blade surface roughness measurement [36,37], which can perfectly combine the topography measurement and roughness measurement in the same system, with the highest vertical resolution of 10 mm. During the roughness measurement, 5 points are randomly measured on the blade surface, and the average value is calculated as the final measurement result. A microanalysis of the blade surface is shown in Figure 24.  
Figure 23: Blade surface quality inspection equipment. Figure 22: Flap wheel polishing experiment of blisk blade. The 3D coordinate measuring machine is used to measure the form and position accuracy error of the blade as shown in Figure 23b. The polished blade is divided into 5 sections to measure the error of the blade profile, and the test results are obtained after scanning and data processing, as shown in Figure 25 [38,39]. Three measuring points are sampled at different sections of the blade basin and back, and the normal error of the measuring points is used to represent the form and position accuracy error of the polished blade. The form and position accuracy errors and surface roughness of the polishing experiments are shown in Figure 26. The experimental results show that the AFSMC algorithm can effectively reduce the surface roughness by 50% and improve the form and position accuracy by 42%, which can also ensure the precise control of polishing force.