# Implementation of Fault-Tolerant Control for
## 6 Experimental Results
### Experimental Results
#### 6.3.2 Multiple Faults  
The effectiveness of the proposed fault-tolerant control in the case of multiple faults was also investigated. The desired faults occurred after 10 sand are assumed to be  
\[\left\{\begin{array}{l}\tau_{1}^{t}=\tau_{1}+f_{1}(t)\;t>5000\\ \tau_{2}^{t}=(1-\rho_{2}(t))\tau_{2}+f_{2}(t)\;t>5000\\ \tau_{3}^{t}=(1-\rho_{3}(t))\tau_{3}\;t>5000\end{array}\right. \tag{56}\]  
where \(f_{1}(t)=30\), \(\rho_{2}(t)=0.4\sin(\pi t/2400)\), \(f_{2}(t)=-60\sin(\pi t/2400)\), and \(\rho_{3}(t)=-0.7\).  
The overall results of this experiment are similar to the previous results from the simulations and the single fault experiments. The fault estimation capability is still at the same level as that of the single fault case, as seen in Figure 13. The trajectory tracking performances of the two algorithms can be said to have behaviors similar to those seen in Figure 14. AFTC-SSMC showed the smaller trajectory tracking errors, especially after the faults occurred at 10 s, demonstrating the fault-tolerant characteristics, even in this multiple faults case. In Figure 14a,b, it can be seen that the picking phenomenon due to the slow response of the AFTC strategy was reduced by using the synchronization technique. And the synchronization joint errors were shown in Figure 15.  
Figure 14: The error at joints with multiple faults. (**a**) Joint 1; (**b**) Joint 2; (**c**) Joint 3.  
Figure 12: The synchronization error with a single joint fault occurring at Joint 2. (**a**) Joint 1; (**b**) Joint 2; (**c**) Joint 3.  
Figure 13: Fault estimation results with multiple faults. The aqua and pink dashed lines are upper and lower thresholds, respectively. (**a**) Joint 1; (**b**) Joint 2; (**c**) Joint 3.  
**Remark 2**.: _In this section, the experimental results were discussed. The resulting tracking trajectory errors were shown with single and multiple faults. In a real system, the uncertainties and disturbances have a higher magnitude than that of the simulation environment. Due to the limitation of selection parameters in a real system, the robot system with PFTC-SMC failed when multiple faults occurred. Therefore, in these experimental results, only the results of AFTC-SMC and the proposed AFTC-SSMC were presented. As mentioned in Section 1, the synchronization technique does not show effectiveness in an open-chain system such as a serial robot manipulator. Therefore, before a fault occurs, both controllers have a similar accuracy level. After a fault occurs, due to the slow response of AFTCs, the controller without the consideration of the synchronization error showed a high picking value at the joint fault. The proposed controller with a constraint within the synchronization technique quickly responded to the occurrence of faults before the system had the feed-back information from fault estimation. Hence, AFTC-SSMC showed better performance than AFTC-SMC. However, in a real system, due to the limitation of adjustment controller parameters, the error at joints without faults were slightly increased when compared with those of AFTC-SMC by the synchronization technique. This characteristic may be a disadvantage of this proposed controller. However, the AFTC-SSMC still showed an acceptable performance at these actuators._