Test Case 3: Internal and External Disturbances

Test Case 3 includes sensor and actuator random noise as well as turbulence. It also includes a 15 kts gust on final approach when the aircraft reaches an altitude of 400 ft. This test is the most critical because it represents a worst case scenario. Figure 5.18 shows the vertical navigation results. The aircraft starts at the trim condition at cruise altitude and begins a 300 fpm descent to prevent over-speeding. After the airspeed is below the flap operating airspeed, the flaps are deployed manually by the pilot. When the flaps are deployed, the aircraft initiates a 500 fpm descent to the target altitude of 1500 ft. The

airplane then performs an ILS approach down to 200 ft. It can be seen that the autopilot maintained altitude tracking through different airspeeds, altitudes, and flap configurations in the presence of internal and external disturbances.

Figure 5.18. Vertical navigation results for the SR22 aircraft.

Figure 5.19 shows the pitch angle tracking by the adaptive autopilot. It can be seen that the pitch angle follows the reference model closely. This shows that the blended output does, in fact, track the original output of interest (the pitch angle). It can be seen that the autopilot adapts appropriately to changes in configuration. Figure 5.20 shows the time history of the longitudinal adaptive gains. As predicted by the theory, all adaptive gains remained bounded. Unlike the disturbance free case, the configuration changes are not as noticeable in the adaptive gains. The horizontal navigation results are shown in Figure 5.21.

Figure 5.19. Pitch angle tracking results for the SR22 aircraft.

Figure 5.20. Longitudinal adaptive gains time history for the SR22 aircraft.

Figure 5.21. Horizontal navigation results for the SR22 aircraft.

The aircraft navigates appropriately through all the waypoints to position itself to start the ILS approach. After the ILS starts, the aircraft aligns itself with the runway while following the glideslope. The localizer error for the last 400 seconds of the flight is shown in Figure 5.22.

Figure 5.22. Localizer error time history for the SR22 aircraft.

The autopilot is able to align the aircraft with the runway. When the gust hits at 400 ft (890 seconds into the flight), the aircraft is displaced from the localizer. The autopilot is able to bank the aircraft to remain within the operating distance of the ILS transmitter and realigns the aircraft with the runway. The bank angle tracking is shown in Figure 5.23.

Figure 5.23. Bank angle tracking results for the SR22 aircraft.

The bank angle tracks the reference model closely. The bank angle response has a higher frequency once the ILS approach starts, but the bank angle remains close to the reference model. The lateral adaptive gains are shown in Figure 5.24.

Once again, as predicted by the theory, all adaptive control gains remained bounded. After the test scenario was completed successfully by the autopilot on the aircraft used for design, the autopilot was transferred, without modification, to a different GA aircraft. The following section describes the autopilot transfer process and results.

Figure 5.24. Lateral adaptive gains time history for the SR22 aircraft.

Autopilot Transfer Results

The autopilot was transferred to a Ryan Navion nonlinear simulator. The model was then linearized to verify that the blended outputs are minimum phase and have a nonzero high frequency gain. The longitudinal transfer function from elevator to blended pitch angle was found to be:

5 4 3 2

6 5 4 3 2

( ) 25.54 94.03 2978 6729 4303 336.4

( ) 35.32 635.8 2152 4393 307.1 245.3

b

Similarly, the lateral transfer function from aileron deflection to blended bank angle was found to be:

5 4 4 3 4 2 4 2 4

6 5 4 3 2

( ) 25.54 164.2 1.365 10 1.53 10 3.215 10 1.35 10

( ) 38.07 720.4 3494 3590 6882 75.23

b

Table 5.4 shows the zeros and the high frequency gain for each of these transfer functions.

Table 5.4. Zeros and high frequency gain of blended outputs in the Navion aircraft.

Transfer

Function Zeros High Frequency

Gain addition, the zeros of the blended outputs do not coincide with the reference model poles.

It is expected that, by blending the outputs in this manner, the blended outputs will track the original outputs at low frequencies, allowing the generic conventional controller to navigate the aircraft through the test case scenario while being subjected to internal and external disturbances.

After it was verified that the mathematical requirements of the adaptive controller were satisfied in the new aircraft, Test Case 3 was run. The simulation was started from a trim condition at 6000 ft and 110 kts and stopped at 200 ft. Figure 5.25 shows the vertical navigation results.

It can be seen that the autopilot successfully navigated the aircraft from cruise altitude to 200 ft. The autopilot was able to adapt to changes in altitude, airspeed, and configuration. The glideslope was also followed. To do this, the adaptive autopilot tracked the reference model pitch angle. The results are shown in Figure 5.26.

Figure 5.25. Vertical navigation results for the Navion aircraft.

Figure 5.26. Pitch angle tracking results for the Navion aircraft.

The pitch angle was tracked correctly throughout the test scenario. The blended output converged to the pitch angle, allowing the pitch angle to track the reference model.

The longitudinal adaptive gains are shown in Figure 5.27

Figure 5.27. Longitudinal adaptive gains time history for the Navion aircraft.

The adaptive gains remained bounded throughout the simulation. The horizontal navigation results are shown in Figure 5.28.

Figure 5.28. Horizontal navigation results for the Navion aircraft.

The aircraft was navigated successfully through all the waypoints. The localizer was then used to align the aircraft with the runway. Figure 5.29 shows the time history of the localizer error from the start of the ILS at 1500 ft until the end of the simulation. It can be seen that the autopilot successfully aligned the aircraft with the runway.

Figure 5.29. Localizer error time history for the Navion aircraft.

The bank angle tracking is shown in Figure 5.30. It can be seen that the bank angle follows the reference model closely. Once again, the ILS demands higher frequency bank angle commands, but the autopilot is able to track adequately.

Figure 5.30. Bank angle tracking results for the Navion aircraft.

Figure 5.31 shows a time history of the lateral adaptive gains. Once again, as predicted by the theory, the adaptive gains remain bounded.

Figure 5.31. Lateral adaptive gains time history for the Navion aircraft.

The results show that the autopilot was able to adapt to both aircraft. Without a priori knowledge of each aircraft’s dynamics, the autopilot adapted quickly enough to perform its intended functions successfully. Changes of aircraft configuration were also handled appropriately. The autopilot was robust enough to operate in the presence of both internal and external disturbances. It was also capable of performing an ILS approach, and to maintain positive control of the aircraft after being disturbed by a 15 kts gust.