# An Extended Proxy-Based Sliding Mode Control of Pneumatic Muscle Actuators
## 4 Experiment Studies
### Experimental Results  
To investigate the performance of the proposed method, several experiments have been designed with the reference. First, we compare the control effects of the EPSMC, SMC, PSMC, PID control, and fuzzy control to show the superiority of the proposed method. Then, the ESPMC is applied to the PMA with different loads, by which the robustness of the system would be illustrated.  
Figure 4 shows the tracking performance of the PMA. Figure 5 is the result of the corresponding tracking error. The results of the tracking performance are shown in Table 2 which indicates that the EPSMC behaves best since it can reduce the \"chattering\" phenomenon significantly. Meanwhile, the SMC suffers from the sever \"chattering\", which results in the inaccurate track. The PSMC and PID are model-free control strategies. As long as the suitable control parameters are adjusted, favorable control performance can be achieved, but this is also its deficiency. In physical applications, it takes a lot of time and effort to select the appropriate parameters. Also, the fuzzy controller is heavily dependent on the experience of selecting membership functions and rules and suffers from high computational burden.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Name** & **Type** & **Details** \\ \hline Displacement sensor & GA-75 & Measurementrange: 0–150 mm \\  & & Linearity: \textless{}0:1\% (=0.09\%) \\ \hline Electromagnetic valve & ITV1030-211 BS & Input: 0–5 V \\  & & Output: 0.005-0.5 MPa \\ \hline Relieve-pressure valve & AW20-02 BCG & Regulating range: 0.05–0.85 MPa \\ \hline Pneumatic Muscle & FESTO DMSP-20-200N-RM & Inner diameter: 20 mm \\  & & Rated length: 60–9000 mm \\  & & Lifting force: 0–1500 N \\ \hline Data acquisition board & NIPCI-6025E & 16 AI and 2 AO \\  & & 32 digital I/O buses \\  & & Sampling rate: 200 kS/s \\ \hline Force sensor & TJL-1 & Measurement range: 0–300 N \\  & & Sensitivity: \(2\pm 0.1\) mV/V \\  & & Accuracy: 0.03\% F: S \\ \hline Power supply & Q-120 DE & Input: AC 200 V, 50 Hz \\  & & Output: \(\pm 5\) V, \(\pm 12\) V, \(\pm 24\) V \\ \hline Air compressor & Denair, DW35 & Capacity: 150 L \\  & & Power: 800 W \\  & & Exhaust pressure: 0.8 MPa \\ \hline \hline \end{tabular}
\end{table}
Table 1: List of main equipment in the experiments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Strategy** & **MaxERROR (m)** & **InteERROR (m)** \\ \hline EPSMC & \(1.1\times 10^{-3}\) & \(3.3\times 10^{-4}\) \\ SMC & \(7.9\times 10^{-3}\) & \(2.3\times 10^{-3}\) \\ PSMC & \(5.9\times 10^{-3}\) & \(1.7\times 10^{-3}\) \\ PID & \(2.7\times 10^{-3}\) & \(1.1\times 10^{-3}\) \\ Fuzzy Control & \(4.3\times 10^{-3}\) & \(1.9\times 10^{-3}\) \\ \hline \hline \end{tabular}
\end{table}
Table 2: The tracking performance of different control strategies.  
To further investigate the robustness of the proposed method, the PMA is attached to 0.5 kg, 1.0 kg, and 1.5 kg loads and driven to tracking the same reference. Figures 6 and 7 are the performances of PMA tracking. It is shown that even though the PMA is attached to different loads, the control effect is almost the same. Obviously, as the quality increases, the control effect also deteriorates. This is reasonable because the control parameters are tuned based on the PMA that does not mount any mass. The result is shown in Table 3.  
Figure 4: The tracking performance of the PMA.  
Figure 5: The tracking error of the PMA.