## 5 Simulation and Experimental Results
### Experimental Model
#### 5.3.3 Experimentation Result for SLFM  
The standard flexible link manipulator provided by [39] is fitted with a strain gauge sensor resulting in an analog signal proportional to the deflection of the arm end-point and servo motor sensor, which provides an angular position of arm as described in Figures 8 and 9. In this experimentation, only one sensor output is measured, which is a servomotor angular orientation (\(\theta\)), and remaining states \((\alpha,\dot{\theta},\dot{\alpha})\) are measured by EGESO along with disturbances. MATLAB [41] software is used for simulation purpose considering ode4 (Runge-Kutta) solver for differential calculations with a sample time of 0.001 s.  
Figure 11: Simulation result of control signal for controlling \(\theta\).  
Figure 10: Simulation result of output tracking \(\theta\) and arm end-point deflection \(\alpha\).  
In order to stress the effect of the difference in real-time control efforts, multilevel fixed set-points trajectory with disturbances is adopted. The servo motor gear angle \(\theta\) for the selected trajectory is shown in Figure 15. On the zoomed portion, the proposed controller offers a smooth response without overshoot as compared to other techniques, which leads to less chattering in \(\theta\). Furthermore, it was also considered to have the desired requirement of less arm end-point deflection (\(\alpha\)), and it is observed that the proposed scheme works effectively to satisfy the desired requirement in Figure 16.  
Figure 12: Simulation result of sliding surface \(\sigma\).  
Figure 13: Simulation result of actual and estimated states after reach phase elimination.  
Disturbance of small impulse added manually at time \(t=35\) s, and it is observed that the proposed controller is not giving much overshoot compared to other techniques.  
The motor (actuator) response for controlling servo motor gear angle \(\theta\) is shown in Figure 17. Compared to other techniques, the amplitude order of the proposed control signal is very low.  
The sliding surface response is shown in Figure 18 and it is observed that chattering in sliding surface is of very low order, which is nearly approaching zero.  
\begin{table}
\begin{tabular}{l l l l l l l} \hline \hline \multirow{2}{*}{**Controller**} & \multirow{2}{*}{**Set-Point (\(r\)) Radian**} & \multicolumn{3}{c}{**Error Indices**} \\ \cline{3-8}  & & **IAE** & **ISE** & **ITAE** & **ITSE** & **Control Efforts (\(u\))** \\  & **Output (\(y\))** & & \(\begin{pmatrix}\mathbf{10^{-2}}\end{pmatrix}\) & \(\begin{pmatrix}\mathbf{10^{-3}}\end{pmatrix}\) & \(\begin{pmatrix}\mathbf{10^{-2}}\end{pmatrix}\) & \(\begin{pmatrix}\mathbf{10^{-3}}\end{pmatrix}\) & **in ITAE** \\ \hline GESOBC & error = y \(-\) 0.523 rad & 29.50 & 88.51 & 54.59 & 37.66 & 1.885 \\ EGESOBC & error = y \(-\) 0.523 rad & 28.69 & 91.29 & 60.27 & 34.91 & 1.663 \\ LESOSMC & error = y \(-\) 0.523 rad & 34.22 & 91.02 & 89.72 & 47.24 & 4.825 \\ Proposed scheme & error = y \(-\) 0.523 rad & 25.11 & 78.97 & 42.06 & 23.29 & 1.650 \\ \hline \hline \end{tabular}
\end{table}
Table 4: Comparison of performance indices for simulation results of SLFM.  
Figure 14: Simulation result of error dynamics.  
Figure 15: Experimental result of output tracking \(\theta\).