## 6 Simulation Analysis and Experimental Verification  
MATLAB and C++ is used to compile the simulation program, which is based on PID, SMC(sgn), SMC(sat), AFSMC, and dynamic model of pressure control system. The polishing force tracking control signal and the step signal are set as \(r_{\mathrm{sin}}(t)=60\sin(\pi t)\) and \(r_{\mathrm{st}}(t)=60\), respectively. The polishing experiment uses Advantech IPC-610L as the controller, and the control program is written based on C language, including the sampling time sequence, the A/D program, and the pressure sensor measurement program. PCL818L, PCL730, and PCL726D/A are produced by Advantech Technology Corporation (Kunshan, China), which are used for data acquisition, conversion, and output. The collected data are analyzed, processed, and displayed by the LabWindows/CVI platform. After feedback, the IPC sends out command signals to control the pneumatic servo system and finally realizes the real-time adjustment of the polishing force. The simulation results of the step response are shown in Figures 6-9, and the simulation results of the sine response are shown in Figures 10-13. The simulation results of the step response and sine response of PID are shown in Figures 6 and 10, and the average value of control error is 5.30N. Compared with the other three control algorithms, the PID algorithm has the largest control error. The simulation results of the step response and sine response of the SMC(sgn) are shown in Figures 7 and 11, with an average control error of 2.045N. Compared with the PID control algorithm, the control error of the SMC(sgn) algorithm is obviously reduced. However, from the aspect of control input, SMC(sgn) can easily generate high-frequency chattering, which not only affects the accuracy of control but also increases energy consumption, causes system oscillation or instability, and damages controller components. SMC(sat) (s) is proposed to reduce high-frequency chattering caused by SMC(sgn). Figures 8 and 12 show the simulation results of the step response and sine response of the SMC(sat), with an average control error of 3.125N. SMC(sat) effectively reduces high-frequency chattering, but the average control error does increase. Figures 9 and 13 show the simulation results of the step response and sine response of the AFSMC, with an average control error of 1.165N. Compared with PID, SMC(sgn), and SMC(sat), the control errors of AFSMC are reduced by 78.0%, 43.0%, and 62.7%, respectively, and the high-frequency chattering of the system is also significantly reduced. Experimental results of the step response are shown in Figures 14-17, and experimental results of the sine response are shown in Figures 18-21. Figures 14 and 18 show the experimental results of the step response and sine response of the PID, with an average control error of 5.545N. Figures 15 and 19 show the experimental results of the step response and sine response of the SMC(sgn), with an average control error of 2.245N. Figures 16 and 20 show the experimental results of the step response and sine response of the SMC(sat), with an average control error of 3.30N. Figures 17 and 21 show the experimental results of the step response and sine response of the AFSMC, with an average control error of 1.325N. Compared with PID, SMC(sgn), and SMC(sat), the control errors of AFSMC are reduced by 76.1%, 40.9%, and 65.9%, respectively. Figure 6: Step response with PID (simulation). Figure 8: Step response with SMC (sat) (simulation). Figure 7: Step response with SMC (sgn) (simulation). Figure 10: Fine response with PID (simulation). Figure 9: Step response with AFSMC (simulation). Figure 11: Sine response with SMC (sgn) (simulation). Figure 12: Sine response with SMC (sat) (simulation). Figure 14: Step response with PID (experimental). Figure 13: Sine response with AFSMC (simulation). Figure 16: Step response with SMC (sat) (experimental). Figure 8:0 Step response with SMC (sgn) (experimental). Figure 8:1 Step response with AFSMC (experimental). Figure 8:2 Fine response with PID (experimental).