# Design of Hybrid Phase Sliding Mode Control Scheme for Lower Extremity Exoskeleton
## 3 Experimental Results and Discussion
### Simulation and Comparison Experiments  
In this section, the simulation experiment is implemented, and the performance of the proposed control algorithm is studied by simulation platform. The following primary analysis is completed: First, this work verifies the effectiveness of the sliding mode control method combined with the extended state observer for the lower extremity exoskeleton. Secondly, the smoothing method solves the time requirement concerning the pneumatic muscle contraction and relaxation. Thirdly, the result shows that the motion characteristic of pneumatic artificial muscles meets the control requirement for the exoskeleton movement. Add un-modelled uncertainties to the nominal model parameters, and the total uncertain disturbances are related to system information and selected as \(d=m\text{sgn}(q)+nq\), where \(m=diag(2,2),n=diag(0.2,0.2)\). The desired trajectory of lower extremity exoskeleton in the gait cycle are obtained by VICON three-dimensional gait analysis system:  
\[q_{d}=\left\{ \begin{array}{rl}q_{hip}=0.017(82.24-21.38\cos(5.06t)+8.347\sin( 5.06t)+5.319\cos(10.12t)\\ -3.161\cos(10.12t)-0.535\cos(15.18t)-2.624\sin(15.18t))\\ q_{base}=0.017(25.08-7.049\cos(5.18t)-21.46\sin(5.18t)-16.29\cos(10.39t)\\ +13.220\sin(10.39t)+1.332\cos(15.55t)+4.175\sin(15.55t))\end{array} \right. \tag{25}\]  
The system initial state \(x_{0}=\left[ \begin{array}{rrrr}1.2&0.15&-0.5&0.5\end{array} \right]\). The swing phase and the stance phase controller gains are \(k_{gsv}=\left[ \begin{array}{rr}100&0\\ 0&100\end{array} \right]\), \(k_{gst}=\left[ \begin{array}{rr}20&0\\ 0&20\end{array} \right]\) respectively. The conventional controller (16) sets \(\eta=\left[ \begin{array}{rr}5&0\\ 0&5\end{array} \right]\), while the new one(17) can be set as \(\eta=\left[ \begin{array}{rr}0.1&0\\ 0&0.1\end{array} \right]\). To avoid peaking phenomenon, the initial value of the ESO is set to be the same as the initial value of the system states and disturbances. To ensure the stability of the system, \(\bar{A}\) in Equation (8) need to be guaranteed for Hurwitz, that is  
\[\alpha_{1}=\left[ \begin{array}{rr}6&0\\ 0&6\end{array} \right],\alpha_{2}=\left[ \begin{array}{rr}10&0\\ 0&10\end{array} \right],\alpha_{3}=\left[ \begin{array}{rr}6&0\\ 0&6\end{array} \right] \tag{26}\]  
In the actual test of the lower extremity exoskeleton motion, the phase switching time is determined by the phase detector we mention ahead. Assuming there are twice switching in 2 s, and gait switching signal is shown in Figure 9. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Number** & \(m_{i}\) **/(kg)** & \(I_{i}\) **/(nm)** & \(r_{i}\) **/(nm)** \\ \hline
1 & 9.933 & 0.1 & 0.117 \\
2 & 2.269 & 0.1 & 0.352 \\
3 & 1 & 0.469 & 0.093 \\
4 & 1 & 0.372 & 0.2 \\
5 & 1 & 0.05 & 0.15 \\
6 & 29.378 & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Exoskeleton system main parameters. The simulation result can be found in Figures 10-15. The tracking control performance of Hybrid Phase Sliding Mode Control Scheme is shown in Figures 10 and 11, where Figure 10 is the angle tracking curve and Figure 11 is the angular velocity tracking curve of the double joints. The tracking error between \"ESO+SMC\" and desired trajectory is markedly shown in Figure 12. During the gait phase switching, although the tracking error increases, it is small enough to meet the control requirement. Therefore, the results show that the controller, together with an extended state observer, has excellent control performance for the exoskeleton system. Figure 13 shows that the extended state observer has good observation ability for strong disturbances. It can be seen that the exoskeleton system by this method can adapt to a relatively bad environment and still obtain good control performance. The control inputs of the traditional SMC controller (16) and ESO+SMC (17) are shown in Figure 14. The traditional one shows the great effect of chattering while the other eliminates this phenomenon.