# Fault Diagnosis for a Class of Robotic Systems with Application to 2-DOF Helicopter
## 5 Results
### Experimental Results  
To validate the proposed scheme, a test on a physical real-time helicopter was performed. The experimental platform shown in Figure 5 and its corresponding schematic diagram in Figure 6 which shows the communication and data directly between the devices and the software. First of all, it is necessary to control the system to carry out the detection of faults. Because the 2-DOF system is in a closed loop, is possible to implement a PID control. The experimental platform consists of two motors, a lift motor that causes the pitch motion, and a tail motor, which produces the yaw motion. DC motors with a nominal voltage of 12 volts. The platform parameters are shown in Table 4. The Labview software was used as a programming platform, it contains the control law to stabilize the system and the algorithm to fault diagnosis; the SCB-68A board from National Instruments(r) and an Arduino(r) Mega 2560 board with 56 input/output pins were used as an interface for communication between the physical system and the software. For the power part, a SparkFun(r) Monster Moto Shield H-bridge was used with a voltage capacity of 16 volts, 30 amps of current and 20 KHz of PWM frequency. The sensing was carried out by two rotary optical encoders, one placed at the base of the platform, which allows the yaw angle to be measured, \(\psi\), and the other placed in the center of the platform which measures pitch angle \(\phi\).  
The information of the angles and angular velocities of pitch and yaw are obtained through the SCB-68A board, the fault detection and control algorithm processes the information and feeds back the controlled signal to the interface consisting of two devices, the SCB-68A board and the Arduino(r) Mega 2560, which transforms the signal to PWM; taking the PWM signal as input, the power device supplies the motors with voltage. The data acquired is processed in the Matlab(r) software to obtain the graphs of the behavior of the residuals.  
To produce faults in the physical system, external signals to the system were injected into both sensors and actuators, one at a time. Is important to mention that the produced faults in each of the physical tests, were in a proportion of 50 % with respect to the output.  
The threshold of the normalized residual evaluation is presented in each of the cases in which the faults occur. The threshold for sensor failure is \(\pm 5\) and the threshold for actuators failure is \(\pm 10\), these values were chosen based on the structure and dynamics of the decoupled equations.  
Figure 4: Response of residual to the fault \(f_{a1}\).  
Figure 8: Normalized residual evaluation in case 2 (fault at sensor 1, \(f_{s1}\)).  
Figure 7: Response of residual to the sensor fault \(f_{s1}\).  
Figure 9: Response of residual to the sensor fault \(f_{s2}\).  
Actuator Fault 2. Figures 13 and 14 show the response to residual to the actuator fault \(f_{a2}\). Where the residuals \(r_{1}\) and \(r_{2}\) response to this fault. The residuals are different from zero, indicating sensitivity to the fault while the \(r_{3}\) remains very close to zero indicating insensitivity to the fault.  
Figure 11: Response of residual to the actuator fault \(f_{a1}\).  
Figure 12: Normalized residual evaluation in case 4 (fault at actuator 1, \(f_{a1}\)).  
Figure 10: Normalized residual evaluation in case 3 (fault at sensor 2, \(f_{s2}\)).