# Adaptive Robust Fuzzy Impedance Control of an Electro-Hydraulic Actuator
## 6 Experimental Results  
Experiments were conducted to validate the performance of the proposed ARFIC. The drive cylinder and the load cylinder were both controlled by servo valves. Four pressure sensors were utilized. A position sensor was used to obtain the displacement and velocity of the drive cylinder. A data acquisition card was employed to collect data and output control inputs. The control strategy was implemented in the MATLAB Simulink Realtime environment with a 1 kHz control rate.  
Firstly, ARC (without impedance control) was tested. Table 3 lists the parameters of the electro-hydraulic system. Tables 4 and 5 list controller parameters. Figure 5 shows the desired velocity trajectory, \(\dot{x}_{d}=0.02\sin\left(\frac{\pi}{5}t+\frac{3\pi}{2}\right)+0.03\) m/s. \(u_{L}=-2\) V is the servo valve command  
Figure 5: Desired velocity trajectory.  
Figure 6: Tracking errors of ARC.  
Figure 7: Control input of ARC.  
Next, ARFIC was verified when the velocity command was constant at 0.02 m/s and 0.04 m/s. The parameters of the fuzzy impedance rule were chosen according to Table 6. ARFIC was tested compared with ARC (without impedance control), to validate the effectiveness of fuzzy impedance control. A step-like signal was applied to the servo valve which controls the load cylinder. A pressure sensor was used to measure the load force in experiments.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**Symbol** & **Value** & **Unit** \\ \hline \(v_{\text{max}}\) & 0.05 & m/s \\ \(v_{\text{min}}\) & 0.01 & m/s \\ \(F_{L\text{max}}\) & \(6\times 10^{4}\) & N \\ \(F_{L\text{trimin}}\) & 2000 & N \\ \(m_{\text{max}}\) & 850 & Ns\({}^{2}\)/m \\ \(m_{\text{min}}\) & 350 & Ns\({}^{2}\)/m \\ \(b_{\text{cmax}}\) & \(1\times 10^{6}\) & Ns/m \\ \(b_{\text{cmin}}\) & \(1\times 10^{5}\) & Ns/m \\ \hline \hline \end{tabular}
\end{table}
Table 6: Parameters of the fuzzy impedance rule.  
Figure 8: Parameter estimations of ARC: (**a**) estimation of \(\theta_{1}\); (**b**) estimation of \(\theta_{2}\); (**c**) estimation of \(\theta_{3}\).  
As shown in Figure 9a, the velocity command was 0.02 m/s, and the load command changed in a step-wise manner from \(-1\) V to \(-0.7\) V then to \(-1\) V. The regulated velocity commands are shown in Figure 9b, which guaranteed an expected impedance behavior when load command change occurred. A smooth smaller velocity command was produced by fuzzy impedance control in ARFIC. The load force of ARFIC was kept in a close range, as shown in Figure 9d. Tracking errors with respect to unregulated or regulated velocity command are shown in Figure 9c. Both ARFIC and ARC achieved accurate velocity tracking. ARFIC showed a great ability to handle load change through velocity adjustment.  
Fuzzy impedance control worked when the deviation of load force exceeded 10% of the nominal value in experiments. It can be seen that dynamic balance behavior was achieved with a fuzzy logic-based impedance control. To validate the effectiveness of ARFIC further, some other load and velocity commands were tested. Similarly, in all kinds of cases, ARFIC demonstrated accurate velocity tracking and impedance regulation between velocity and force. The experiment results are shown in Figures 10-12. A smooth regulated velocity command was generated when the load force was beyond the regular range. ARFIC could keep the load force in a close range, comparing with ARC.  
Figure 11: Tracking performance with a 0.04 m/s velocity command and \(-1.6\) V \(\sim-2.2\) V \(\sim-1.6\) V load command: (**a**) load command; (**b**) velocity commands; (**c**) velocity tracking errors; (**d**) load forces.  
Figure 10: Tracking performance with a 0.02 m/s velocity command and \(-1\) V \(\sim-2\) V \(\sim-1\) V load command: (**a**) load command; (**b**) velocity commands; (**c**) velocity tracking errors; (**d**) load forces.