## 5 Simulation Result Analysis
### No Disturbance  
In this case, the model of the system has been simulated without incorporating external disturbance. The accompanying Figure 3 shows a comparison of previously existing techniques with the proposed method in trajectory tracking, the error plots, and control signal. In Figure 3, when no disturbance is given to the system, the minimized plots (a) and (b) display performance of IADRC, NLADRC, ADRC, and the proposed method while reference trajectory tracking for shoulder and elbow joints. The minimized plots (c) and (d) depict the error trajectory generated during reference tracking. The control signal required by the controllers is illustrated in the minimized plots (e) and (f). Minimum values of ITSE, ISE, ITAE, and IAE indicate the proposed method performs better in terms of trajectory tracking for ULRRE and can be observed from Table 3.  
In Figure 4, when constant disturbance with \(-20\%\) parameter variation is given to the system, the minimized plots (a) and (b) display the performance of IADRC, NLADRC, ADRC, and the proposed method while reference trajectory tracking for shoulder and elbow joints. The minimized plots (c) and (d) depict the error trajectory generated during reference tracking. The control signal required by the controllers is illustrated in the minimized plots (e) and (f). \begin{table}
\begin{tabular}{l c c c c c} \hline \hline
**Upper Limb Parameters** & **Parameter** & **Actual Value** & \(\mathbf{-20\%}\) & \(\mathbf{+20\%}\) & **Units** \\ \hline Limb and exoskeleton masses & \(m_{1}\) & 2.25 & 1.8 & 2.7 & kg \\  & \(m_{2}\) & 1.47 & 1.176 & 1.764 & kg \\ Limb lengths & \(L_{1}\) & 0.34 & 0.272 & 0.408 & m \\  & \(L_{2}\) & 0.25 & 0.2 & 0.3 & m \\ Center of mass & \(L_{\mathrm{c1}}\) & 0.17 & 0.136 & 0.204 & m \\  & \(L_{\mathrm{c2}}\) & 0.125 & 0.1 & 0.15 & m \\ Mass moment of inertia & \(l_{1}\) & 0.2505 & 0.2004 & 0.3006 & kg\(\cdot\)m\({}^{2}\) \\  & for exoskeleton and limbs & \(l_{2}\) & 0.0925 & 0.074 & 0.111 & kg\(\cdot\)m\({}^{2}\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Parameters of the ULRRE. Figure 3: Sinusoidal trajectory tracking comparison of ADRC, NLADRC, IADRC, and the proposed method for the shoulder and elbow joints with a reference without disturbance. In Figure 5, when constant disturbance with +20% parameter variation is given to the system, the minimized plots (a) and (b) display the performance of IADRC, NLADRC, ADRC, and the proposed method while reference trajectory tracking for shoulder and elbow joints. The minimized plots (c) and (d) depict the error trajectory generated during reference tracking. The control signal required by the controllers is illustrated in the minimized plots (e) and (f). The ITSE, ISE, ITAE, and IAE of the proposed method have values 7.529, 13.61, 15.73, and 18 with \(-\)20% parameter variation and 7.534, 13.61, 13.74, and 18 for the shoulder joint with \(+\)20% parameter variation, respectively, which are minimum as compared IADRC, NLADRC, and ADRC. Minimum values of ITSE, ISE, ITAE, and IAE indicate the proposed method performs better in terms of trajectory tracking for ULRRE and can be observed from Table 5.  
Figure 4: Sinusoidal trajectory tracking comparison of ADRC, NLADRC, IADRC, and the proposed method for the shoulder and elbow joints with \(-\)20% parameter variation and constant disturbance. Figure 5: Sinusoidal trajectory tracking comparison of ADRC, NLADRC, IADRC, and the proposed method for the shoulder and elbow joints with +20% parameter variation and constant disturbance.