Control Strategies for Flight in Extreme Turbulence - AIAA ARC

Control Strategies for Flight in Extreme Turbulence Mujahid Abdulrahim∗†

Abdulghani Mohamed‡ and Simon Watkins§

Prioria Robotics, Inc., Gainesville, FL, USA

RMIT University, Melbourne, VIC, Australia

I.

Introduction

The spatial and temporal variations in wind velocity which cause atmospheric turbulence are exacerbated by the topographic and temperature gradients often present at low altitudes. Such gradients exist within the atmospheric boundary layer, which is the region proximate to the ground in which the wind speed varies from near-zero at ground level to the nominal wind speed around 300 m above the ground. With few exceptions for aircraft such as medical evacuation helicopters and crop dusters, low altitude turbulence is a transient problem for manned aircraft in the brief flight phases of take-off and landing. For small unmanned aircraft, however, the entirety of the flight typically exists within an altitude band characterized by high turbulence intensity. Small fixed-wing aircraft operating at slow airspeeds are particularly sensitive to turbulence which can generate large disturbances that affect attitude and flight path stability. UAV control laws are often developed in the absence of significant turbulence, since flight tests are often conducted at remote test ranges and on days with benign atmospheric conditions. The environment in which these control laws are developed does not necessarily reflect the expected operating conditions. For new aircraft designs, airworthiness safety review boards may permit flight only in test areas away from structures and population centers. Flight test engineers usually schedule tests for days with calm winds to improve the quality of the aerodynamic and dynamic data measurements. The result of both the expansiveness of typical UAV test sites with the quiescence of the wind conditions is flight at low turbulence intensity which fails to provide sufficient excitation to evaluate the disturbance rejection capability of control systems. The objective of the current research is to study how the design of control law parameters affects the attitude stability and flight path tracking accuracy of fixed wing aircraft operating in extreme turbulence. Turbulence is replicated in three large wind tunnels which provide continuous, mixed turbulence at high intensity and with length scales similar to the characteristic dimensions of the test aircraft. The UAVs flown in the wind tunnel test sections are self-powered and untethered, flown using remotely piloted inputs to the flight control system.

II. II.A.

Overview of Experiments

Aircraft

The aircraft used for all experiments is a highly-agile monoplane design with large control surfaces and conventional configuration. The aircraft is intended for recreational aerobatics but is particularly suited for studying turbulence sensitivity since the airframe shape provides minimal coupling between the states and high control effectiveness. Figure 1 shows the a top view of the aircraft during a wind tunnel flight in the RMIT wind tunnel. II.B.

Instrumentation

Figure 2 shows the installation of the avionics near the center of gravity of the aircraft. Pilot command are transmitted to the radio receiver near the wing root trailing edge. This receiver transmits control channel ∗ Senior

Controls Engineer, Prioria Robotics, Inc., Gainesville, Florida, USA Fellow, RMIT University, Melbourne, VIC, Australia, AIAA Member. [email protected] ‡ Research Fellow, RMIT University, Melbourne, VIC, Australia § Professor, RMIT University, Melbourne, VIC, Australia † Visiting

1 of 15 American Institute of Aeronautics and Astronautics

Figure 1. Highly-Agile Aircraft Design Used in Wind Tunnel Flight Experiments

data to the flight controller via serial protocol. The flight controller uses the pilot commands to change the control mode, gains, and input reference commands to the attitude and angular rate control loops. Actuator commands are sent as typical pulse-width modulation waveforms, except that the update frequency is varied between 50 Hz and 200 Hz throughout the experiments. Flight data showing the state of the aircraft and control loops is transmitted via serial protocol to a commercially-available data logger which records the flight data to a Micro SD card.

Figure 2. Flight Data Instrumentation and Control Hardware Showing: (L to R) Spektrum Receiver, OpenLog Data Logger, and DataNinja Autopilot

Figure 3 shows the right angle of attack vane that was used for some of the flight testing. The vane is of simple design and is made with inexpensive materials and sensors. The vane is supported by a shaft which rotates in a fixed aluminum tube/sleeve. A linear hall effect sensor with analog output is positioned proximate to a neodymium magnet mounted on the end of the rotating shaft. As the shaft rotates, the magnetic field direction and intensity measured by the sensor produces an output which is proportional to rotation angle. The rotating shaft is supported only by the fixed tube, rather than bushings or bearings. Measurement errors can occur if the magnet moves toward the hall effect sensor rather than simply rotating about the shaft axis. The length of the fixed tube helps mitigate undesired motion of the magnet due to freeplay between the shaft and the tube.


Figure 3. Miniature Angle of Attack Vane Showing Installation on Wingtip (Left) and Design Details (Right)

II.C.

Wind Tunnels

Flight experiments were conducted in several wind tunnels, including: • Wind Engineering Tunnel, Monash University • Automotive Tunnel, Monash University • Industrial Wind Tunnel, RMIT University • Wind Engineering Tunnel, MEL Consultants Each of the tunnels has a test section that is sufficiently-sized to permit untethered flight tests of small unmanned aircraft. These tests are conducted with the vehicle operator standing at the downstream section of the wind tunnel with the airflow velocity set to the desired airspeed. The aircraft is equipped with conventional wheeled landing gear which permits normal take-off from the ground surface of the test section. The aircraft moves upstream briefly to generate sufficient airspeed to climb out of the boundary layer near the surface. Once airborne, the pilot commands roll, pitch, yaw, and thrust to maintain the lateral, longitudinal, and vertical position of the aircraft near the center of the test section. Figure 4 shows the aircraft flying in the wind engineering section of the Monash University wind tunnel. The test cross section is 15 m x 4 m with a streamwise-dimension of 45 m. Turbulence is replicated in the tunnel using jets and collectors in the lower-level return sections and a combination of grids and screens in the inlet area of the upper test section. The scale of the tunnel permits large turbulence length scales with a maximum turbulence intensity of 7%. Figure 5 shows high-frequency 3-axis air-data measurement probes mounted in the automotive test section of the Monash University wind tunnel. The view is from the upstream inlet looking downstream toward the collector and flow deflectors, which route the air toward the upper-level wind engineering section shown in Figure 4. The automotive section is an anechoic, open-jet test section which provides the ability to fly through a significant wind gradient above and to the side of the jet. The turbulence intensity in the automotive section is roughly 1.5%. Figure 6 shows the test aircraft flying in the Industrial Wind Tunnel at RMIT University. The test cross section is 3 m x 2 m, which is the smallest of the wind tunnels used for the study. Large grids placed at the inlet of the test section generate turbulence which becomes continuous and well-mixed by the longitudinal center of the tunnel. This tunnel was used in several configurations with turbulence intensity ranging from 1.5% to 13%.


Figure 4. Wind Engineering Tunnel, Monash University

Figure 5. Automotive Tunnel, Monash University

Figure 7 shows the wind engineering tunnel at MEL Consultants. Ground features generate a velocity gradient which is normally used to simulate the effect of the atmospheric boundary layer on scale building models. For the flight tests, the wind tunnel was used to replicate turbulence with short length scales and a turbulence intensity of 7%. II.D.

Parameter Variations

Table 1 shows a partial configuration range for the series of flight tests which included eight aircraft, four wind tunnels, five wind tunnel configurations, five control architectures, and numerous parameter configurations.

III.

Nominal Aircraft Model

Models of the aircraft lateral response and the actuator dynamics are generated from closed-loop frequency sweep maneuvers flown in conventional flight tests outside the wind tunnel. Figure 8 shows three sets of frequency response data and identified dynamics. The blue lines show the magnitude and phase response of the actuator command to actuator output shaft position. The response shows -1 dB attenuation and -45 deg phase lag near 7 Hz. The red line shows the dynamic response between the measured actuator position and the aircraft roll rate. This response excludes the actuator dynamics, since the input is measured position. The aircraft-only response shows -4 dB amplitude attenuation and -70 deg phase lag by the maximum 4 of 15 American Institute of Aeronautics and Astronautics

Figure 6. Industrial Wind Tunnel, RMIT University

Figure 7. Wind Engineering Tunnel, MEL Consultants

shown frequency. The green line represents the combined actuator and aircraft flight dynamics, measured from actuator command to aircraft roll rate response. The sequential dynamics results in -5 dB magnitude attenuation and -120 deg phase lag at 7H Hz. For each of the measured magnitude and phase responses, a dashed line in the respective color shows the results of a frequency domain system identification using CIFER. The model agreement in both magnitude and phase is excellent. Equation 1 shows the form and parameter values for the identified actuator mdel. The aileron response is represented by a two-state equivalent system in standard form with a natural frequency of 62.7 rad/s (10 Hz) and a damping ratio of 0.77. ω2 + 2ζωs + ω 2 ω = 62.7rad/s

GAil (s) =

s2

(1)

ζ = 0.77 Equation 2 shows the first-order roll convergence dynamic which includes a time delay that is equivalent to the control loop interval.


Table 1. Aircraft and Wind Tunnel Configuration Range During Untethered Flights

MAGNITUDE(DB)

Parameter Mass Control Loop Rate Servo Command Rate Roll, Pitch, & Yaw Inner-Loop Gain Margin Turbulence Intensity Turbulence Length Scale

Minimum 97.8 40 50 3 1.5 0.05

Maximum 130 260 100 9 15 1

Units g Hz Hz dB % m

0 −1

AilC to AilR (Meas)

−2

AilC to AilR (Fit)

−3

AilR to P (Meas)

−4

AilR to P (Fit) Ail to P (Meas)

−5

C

AilC to P (Fit)

−6 1

10

PHASE(DEG)

0 −20 −40 −60 −80 −100 −120 1

10 OLRllSw1_COM_ABCDE_AilC_AilR

Gn:

FREQUENCY 1.09 FREQUENCY(RAD/SEC) (RAD/S)

OLRllSw1_NAV_ABCDE_AilC_AilR OLRllSw1_COM_ABCDE_AilR_P

Gn:

6.07

OLRllSw1_NAV_ABCDE_AilR_P

Gn:

6.07

OLRllSw1_COM_ABCDE_AilC_P

Gn:

6.43

OLRllSw1_NAV_ABCDE_AilC_P

Gn:

6.30

Figure 8. Measured and Identified Frequency Responses for Aileron Command to Aileron Response (Blue), Aileron Response to Roll Rate (Red), and Aileron Command to Roll Rate (Green)

GRoll (s) =

Lδa e−τδa s + Lp

(2)

Lp = 30.4 Lδa = 5.1 τδa = 0.0099s The actuator dynamics are among the fastest available for commercial, recreational aircraft. Similarly, the aircraft roll convergence mode is rapid compared to aircraft with different configurations or with higher roll moment of inertia. Even so, the challenge of mitigating disturbances from turbulence is evident in the relative time scale comparison shown in Figure 9. The green, blue, and red lines show the step responses of the identified models for the actuator, aircraft-only, and aircraft with actuator. The green actuator response shows the starting delay typical of second-order systems and a small amount of overshoot due to the low damping ratio. The blue aircraft response shows a 0.01 second delay, followed by a rapid initial rise of the first-order response. The combined system shows a relatively long delay due to the combination of first-order delay and second-order response. The vertical dashed black line on the left of the response show the time required for airflow at the freestream speed of 9 m/s to transit one chord length. The dashed black line to the immediate right shows the airflow transit time from the angle of attack vane. In both cases, the times are small compared to the responses, indicating that even perfect disturbance sensing may not provide a material benefit due to the relative slowness of the dynamics. Rise-time annotations for each set of dynamics show the distance traveled by the aircraft through the air mass during the dynamic response. This indication is equivalent to the required look-ahead distance in 6 of 15 American Institute of Aeronautics and Astronautics

Step Response 1.4

Chord transit time

Aircraft Servo Combined

Vane to aileron transit time 1.2

Amplitude

1

0.8

1.02 m look−ahead 0.81 m look−ahead 0.41 m look−ahead

0.6

0.4

0.2

0

0

0.05

0.1

0.15

0.2

0.25

Time (seconds)

Time (Sec) Figure 9. Step Responses of Actuator (Green), Aircraft (Blue) and Combined Dynamics (Red) With Annotations Indicating Relative Distances

order to achieve a 90% dynamic response. For a notional disturbance, the actuator model would require a measurement 0.41 m in front of the aircraft in order to generate opposing control effort. As the dynamics continue to slow with the aircraft and combined systems, the look-ahead distance increases to 1.02 m. The implications of this look-ahead value are significant. Even for an aircraft flying at a relatively low speed with fast actuator dynamics and highly-damped roll convergence mode, a disturbance must be measured more than a meter ahead of the aircraft to permit full suppression. In this case, the required look-ahead distance is slightly more than two wingspan-lengths and is certainly longer than the distance from the angle of attack vane to the trailing edge control surface on the wings.

IV.

Sensitivity of Disturbance Rejection to Control Architecture

The wind tunnel flight tests used several types of control augmentation, ranging from open-loop to multi-loop, highly-compensated. These modes are described in the following sections. IV.A.

Open-Loop

Open-loop control provides no feedback compensation and the architecture consists only of a scale factor in the feedforward path. Piloted inputs to the roll, pitch, and yaw stick axes are scaled to provide control surface commands to the ailerons, elevator, and rudder, respectively. IV.B.

Angular Rate Tracking

Angular-rate tracking is the minimum level of feedback control. Piloted stick inputs are scaled to provide roll, pitch, and yaw rate commands which are subsequently input to a reference command filter. The filtered angular rate reference commands are input to a PID-FF controller, which then outputs moment efforts to the control allocation matrix. The aircraft uses a simple and conventional allocation strategy in which the roll rate tracking loop generates a roll rate moment effort that results in anti-symmetric aileron deflection. Similarly, the pitch rate and yaw rate tracking loops command the elevator and rudder surfaces, respectively. IV.C.

Attitude Tracking

Attitude tracking provides an outer-loop to the angular rate tracking inner-loops. Piloted stick inputs are scaled to provide roll and pitch angle commands, in addition to yaw rate commands. The attitude loop uses the same PID-FF architecture of the inner-loop, including the first-order reference command filter. The output of the roll and pitch angle controllers are roll rate and pitch rate commands, respectively. The yaw rate loop remains unchanged in this mode.


IV.D.

Direct Force Control

Direct force control uses a multiplexed control allocation strategy which uses the surfaces normally for roll, pitch, and yaw motions, but also uses the ailerons and elevators to provide a direct change lift coefficient by simultaneously changing the camber on the wing and tail, respectively. Direct control of lift permits tracking, regulation, or damping of vertical acceleration in addition to the three moments. Such a strategy can decrease phase delay in responses to plunge disturbances in which the vehicle is required to change overall lift. A conventional loop architecture uses pitch angle or pitch rate tracking as an inner-loop to normal acceleration. When subject to a disturbance, the normal acceleration error generates a pitch command, which then uses the elevators to change the pitch angle and increase the wing angle of attack. The non-minimum phase behavior of this loop architecture generates delay, particularly for aircraft with high moment of inertia about the pitch axis. The direct force approach eliminates the need for pitch changes, but is also limited by the lift effectiveness of the deflected control surfaces. IV.E.

Differential Angle of Attack Damping

Differential angle of attack damping provides additional turbulence disturbance rejection to an attitude tracking loop by augmenting roll moment effort. Miniature angle of attack vanes are mounted to each wingtip and extend nearly one chord-length ahead of the wing leading edge. The vanes are calibrated over a range of +/- 40 degrees and provide a measurement with sub-degree precision. During flight in turbulence, the aircraft may encounter laterally-asymmetric flow which causes a non-uniform span-wise angle of attack variation and a subsequent roll disturbance. The two wingtip angle of attack vanes can measure such disturbances and provide stabilizing control effort that is phase-advanced compared to the inertially-based attitude loop.

V. V.A.

Sensitivity of Disturbance Rejection to Design Parameters

Control Loop Rate

The control loop rate is a fundamental parameter in the design of digital flight control systems. The loop rate defines how frequently the control law is computed and, implicitly, the length of the loop interval in which the controller does not respond to new commands or feedback. Acceptability of a particular loop rate is based largely on the dynamics of the system, which include moments of inertia, control effectiveness, disturbance bandwidth, and subsystem frequency response. An excessively low control loop rate is slow in comparison to the vehicle dynamics and allows the aircraft to incur a significant change of state in between control updates. Conversely, an excessively high control loop rate wastes computational power without providing a material improvement to the control tracking performance. Studying the sensitivity of the control loop rate provides insight into choosing an acceptable loop rate relative to the vehicle dynamics and operating environment. The control loop rate is defined independently of the actuator command rate. For instance, a 100 Hz control loop rate runs the control law and generates a desired actuator command every 10 ms. This desired actuator command is queued and sent to the actuator at the actuator command. For most small UAVs, the actuator command rate is defined by a pulse-width modulated (PWM) frequency generated by the flight controller to command PWM-compatible actuators. An actuator command rate of 50 Hz provides a new command every 20 ms. When a 100 Hz control loop is coupled to a 50 Hz actuator rate, roughly half the loop updates are discarded due to the relative slowness of the actuator. Since the control loop and the actuator update are not necessarily synchronized, changes to the main loop rate can still provide a benefit by decreasing the latency between measurement and control command. Figures 10 and 11 show the sensitivity of the inner-loop performance to variation in the control loop rate for flight in 7% and 12% turbulence intensity, respectively. Error is measured for each of the roll, pitch, and yaw rate loops as root-mean-squared (RMS) tracking error during a fixed-interval of steady flight. The top plot in Figure 10 shows that roll rate error decreases slightly with increasing main loop rate, with the most significant decrease between 40 Hz and 60 Hz loop rates. Similarly, the pitch error shows a sharp initial decrease followed by smaller improvements for higher loop rates. Yaw rate error, shown in the lower plot, appears nearly insensitive to loop rate. Previous experiments have shown that the roll axis is the most sensitive to roll disturbances due the low moment of inertia and little or no static stability.4 The results show that roll tracking improves up to a loop


rate of roughly 150 Hz, while pitch tracking improves only up to 100 Hz.

Monash Wind Eng. Tunnel, 7% TI, 50 Hz Servo RMS_Tracking_Error (deg/s)^2

75

Roll_Rate_Error

70 65 50

100

150

200

250

Pitch_Rate_Error

50 40 30 50

100

150

200

30

250 Yaw_Rate_Error

28 26 50

100

150

200

250

Main_Loop_Rate (Hz) Figure 10. Inner-loop Tracking Error Versus Main Loop Rate in 7% Turbulence Intensity with 50Hz Actuator Rate

Figure 11 shows the tracking error variation with loop rate in the RMIT industrial wind tunnel, which exhibits higher turbulence intensity and shorter length scale compared to the Monash wind engineering tunnel. The overall tracking error is higher for all axes due and decreases more gradually with increasing loop rate. Roll rate shows a sharp initial decrease in error followed by smaller improvements up to about 200 Hz. Pitch rate tracking improves up to 150 Hz, while yaw rate tracking shows modest improvements up to 150 Hz.

RMS_Tracking_Error (deg/s)^2

RMIT Tunnel, 12% TI, 50 Hz Servo 105 100 95 90 85

Roll_Rate_Error

50

100

150

200

54 52 50 48 46 44 42

250

Pitch_Rate_Error

50

100

150

200

27

250 Yaw_Rate_Error

26 25 24 50

100

150

200

250

Main_Loop_Rate (Hz) Figure 11. Inner-loop Tracking Error Versus Main Loop Rate in 12% Turbulence Intensity with 50Hz Actuator Rate

Figure 12 shows the spectral content versus time of the three angular rate measurements for flights in the RMIT Industrial wind tunnel with 12% turbulence intensity. There is no discernible difference between the performance and disturbance bandwidth for the highest rates. Control loop rates of 80 Hz show increased content in all axes the disturbance increase in energy and bandwidth for decreasing rates of 60 and 40 Hz.


Figure 12. Spectrogram of Roll, Pitch, and Yaw Rate Measurements With Loop Rate Variations from 40 Hz to 260 Hz


V.B.

Actuator Rate

Figure 13 shows the variation of inner-loop tracking performance with actuator update rate in the wind engineering tunnel at Monash University with 7% turbulence intensity. The main control loop rate is fixed at 100 Hz. Tracking performance improves slightly with increasing servo update rate for roll, pitch, and yaw rate loops.

Monash Wind Eng. Tunnel, 7% TI, 100 Hz Loop RMS_Tracking_Error (deg/s)^2

70

Roll_Rate_Error

65 60 50

60

70

80

34 32 30 28 26 24 50

90

100

Pitch_Rate_Error

60

70

80

30

90

100

Yaw_Rate_Error

29 28 27 50

60

70

80

90

100

Servo_PWM_Rate (Hz) Figure 13. Inner-loop Tracking Error Versus Actuator Rate in 7% Turbulence Intensity with 100Hz Main Loop Rate

Figure 14 shows the sensitivity of tracking performance with actuator rate for the industrial wind tunnel at RMIT university with 12% turbulence intensity. The overall error is larger compared with flight at more benign turbulence and the performance improvements continue to higher frequencies.

RMIT Tunnel, 12% TI, 100 Hz Loop RMS_Tracking_Error (deg/s)^2

95

Roll_Rate_Error

90 85 50

60

70

80

46

90

100

Pitch_Rate_Error

44 42 50

60

70

80

27

90

100

Yaw_Rate_Error

26 25 50

60

70

80

90

100

Servo_PWM_Rate (Hz) Figure 14. Inner-loop Tracking Error Versus Actuator Rate in 12% Turbulence Intensity with 100Hz Main Loop Rate

V.C.

Differential Angle of Attack Feedback

Figure 15 shows a 25-second segment of flight data which includes flight in both attitude and differential angleof-attack feedback modes. There is no obvious change in the attitude or angular rate tracking performance


during the mode transition, apart from increased frequency in the aileron command (blue line, lower plot).

Figure 15. Time History of Flight in RMIT Industrial Tunnel with 12% Turbulence Intensity with Attitude Mode (t 223s)

Figure 16 shows a spectrogram of aileron command and position measurement during a flight that included variation in control mode (attitude and differential angle of attack), main loop frequency (100 and 200 Hz), and servo PWM frequency, (50 and 100 Hz). The frequency content of the aileron commands increases markedly during the three transitions from attitude mode to differential angle of attack mode. This increased spectral content is less evident in the spectrogram of the aileron position segment, partly because the commanded frequencies were above the actuator response bandwidth.

Figure 16. Spectrogram of Actuator Command (Top) and Measured (Bottom) During Flight in 12% Turbulence Intensity in Attitude Mode and With Differential Angle of Attack Feedback With Various Main Loop Rates and Servo PWM Rates

Figure 17 shows a comparison of roll rate tracking performance for attitude and differential angle of attack modes with four combinations of main loop frequency and servo update frequency. The solid lines corresponding to the differential angle of attack mode are generally lower than the dashed lines of the attitude tracking mode. For all configurations other than 100 Hz on both the main and servo rates, roll rate tracking error has a lower amplitude in the low frequency range, particularly for the two peaks at 1 Hz and 3 Hz. The apparently-worse performance of the case shown with a green line is likely caused by irregularities or excessive pilot maneuvering during the data segment. The data for all flight segments shown in the plot are from flights in the RMIT Industrial Wind Tunnel with 12% turbulence intensity and small length scales. Figure 18 shows a power spectral density plot for several parameters during flight in 1.5% turbulence in the Monash Automotive Wind Tunnel. The spectral content for all parameters is concentrated at low 12 of 15 American Institute of Aeronautics and Astronautics

Frequency Content of Roll Rate Tracking T56.3 − Fm=100Hz − Fs=50Hz − Att T56.5 − Fm=200Hz − Fs=50Hz − Att T56.1 − Fm=100Hz − Fs=100Hz − Att T54.1 − Fm=200Hz − Fs=100Hz − Att T56.4 − Fm=100Hz − Fs=50Hz − dA0A T56.6 − Fm=200Hz − Fs=50Hz − dAoA T56.2 − Fm=100Hz − Fs=100Hz − dAoA T54.2 − Fm=200Hz − Fs=100Hz − dAoA

3

Power Spectral Density

10

2

10

1

2

3

4

5

6

7

8

9

10

Frequency (Hz)

Figure 17. Power Spectral Density of Roll Rate Tracking For Attitude and Differential Angle of Attack Modes

frequencies with a peak between 0 Hz and 2 Hz. 3

10

AlphaR AlphaL

2

10

P AilCmd AilMeas

Magnitude

1

10

0

10

−1

10

−2

10

−3

10

0

5

10

15

20

25

Frequency (Hz) Figure 18. Power Spectral Density of Angle of Attack Vanes, Roll Rate, and Aileron Command/Response in 1.5% Turbulence

Flight in the Monash Wind Engineering Tunnel with 7% turbulence intensity with relatively long length scales shows spectral content without the aggressive roll off (Figure 19, note the magnitude scale) compared to flight at 1.5% turbulence. The peak in the roll rate response is broader and both the angle of attack measurements and the aileron command show that energy content remains high up to 17 Hz. Measured aileron position rolls off as the actuator dynamics are unable to comply with the high frequency content. At the highest turbulence intensity of 12%, the low-frequency responses are similar, but the energy content remains nearly constant for the angle of attack sensors up to 14 Hz. Roll rate shows disturbances to high frequencies, even though the response is attenuated due to aircraft dynamics. Both aileron command and aileron response show peaks at 1 Hz and 3 Hz, then roll off at higher frequencies.

VI.

Summary

The current research describes some of the results from a series of flight trials of a small UAV in replicated atmospheric turbulence in several wind tunnels. Statistical properties of the turbulence, namely length scale


AlphaR

3

10

AlphaL P AilCmd

2

AilMeas

Magnitude

10

1

10

0

10

−1

10

0

5

10

15

20

25

Frequency (Hz) Figure 19. Power Spectral Density of Angle of Attack Vanes, Roll Rate, and Aileron Command/Response in 7% Turbulence

AlphaR AlphaL

3

10

P AilCmd AilMeas

Magnitude

2

10

1

10

0

10

−1

10

5

10

15

20

25

Frequency (Hz) Figure 20. Power Spectral Density of Angle of Attack Vanes, Roll Rate, and Aileron Command/Response in 12% Turbulence

and intensity, are modified by changing the configuration of the tunnel upstream of the test section. The resulting well-mixed turbulence provides an environment in which the disturbance-rejection performance of an aircraft control system can be studied in detail. The experiments encompassed methodical variations to the control loop interval, actuator command interval, inner-loop gain margins, control architecture, and sensing methods. These variations were tested over a range of turbulence intensities and length scales. The control loop rate variation shows a trade-off between computational requirement and tracking performance. The optimal loop rate is sensitive to aircraft axes, where roll angle tracking improves up to 150 Hz, pitch angle track shows no discernible improvement for rates beyond 100 Hz for moderate turbulence intensities. For turbulence of higher-intensity, performs improvements are evident for control loop rates up to 200 Hz and 150 Hz, respectively. Attitude tracking provided sufficient disturbance rejection and control authority to fly in all tested turbulence intensities, although pilot workload remained high while providing attitude commands to recover from


flight path and position disturbances. Although tracking performance improved with differential angle of attack feedback, the improvements were modest considering the short distance between the angle of attack vane locations and the wing. A much longer look-ahead distance, over one meter, would be required to completely reject the disturbances using the current aircraft and actuator dynamics.

VII.

Future Work

Wind tunnel flight experiments can be extended to consider the design of more conventional UAVs, including the effects of increasing dynamic coupling and under-actuated control authority. The prevalence of rudder-elevator-only designs in the commercial UAV market results in a large percentage of UAVs having very poor disturbance rejection capability, particularly in the roll axis. Early experiments with such aircraft in open-loop flight led to the unsurprising conclusion that flights in extreme turbulence were usually of quite short duration. These experiments did not consider the role of an autopilot or stability augmentation in the response, although the authors suspect that the slow open-loop dynamics will result in modest improvements compared to open-loop results. The sensitivity of the disturbance rejection response to both phase-advanced sensing and to dynamic response motivates a set of further experiments to study the role of both factors. LIDAR sensors which measure air data ahead of the aircraft can provide the required look-ahead to fully reject disturbances from turbulence. For small aircraft where such sensors are impractical, the authors propose wind tunnel experiments in which aircraft flown downstream of air data probes fixed to the wind tunnel can use disturbance measurements as feedforward elements in the control law. Lateral dynamic response can be improved by designing an airframe with low moment of inertia and fast roll convergence, perhaps actuated with a high-bandwidth macro-fiber composite to reduce actuator response time. Finally, free-flight experiments with fixed-wing aircraft in wind tunnels would benefit with the use of motion tracking systems which would significantly improve data quality and could enable automatic guidance of aircraft in the tunnel. Improved control of aircraft position in the tunnel could motivate formation flying studies with multiple flying aircraft to study optimal formation and wake interactions.

Acknowledgments The authors would like to acknowledge the contributions of faculty and staff at Monash University for facilitating testing at the Monash wind tunnel. Additionally, the authors would like to thank the staff at MEL Consultants for access to the wind engineering tunnel at their facility.

References 1 D.P. Reymer, Aircraft Design: A Conceptual Approach, Fourth Edition, American Institute of Aeronautics and Astronautics, 2006. 2 Abdulrahim, Mujahid, Simon Watkins, Reuven Segal, Matthew Marino, and John Sheridan. ”Dynamic sensitivity to atmospheric turbulence of unmanned air vehicles with varying configuration.” Journal of aircraft 47, no. 6 (2010): 1873-1883. 3 Mohamed, A., M. Abdulrahim, S. Watkins, and R. Clothier. “Development and flight testing of a turbulence mitigation system for micro air vehicles.” Journal of Field Robotics (2015). 4 S. Watkins, J. Milbank, B. Loxton, and W. Melbourne, “Atmospheric Winds and Their Implications for Micro air Vehicles”, AIAA Journal 2006, vol. 44, no. 11, pp. 2591-2600. 5 R.C. Nelson, Flight Stability and Automatic Control, Second Edition McGraw Hill, 1998. 6 Bernard Etkin, Dynamics of Atmospheric Flight, Dover Publications, New York, 2005. 7 J. Lusardi, C. Blanken, and M. Tischler, “Piloted Evaluation of a UH-60 Mixer Equivalent Turbulence Simulation Model”, American Helicopter Society 59th Annual Forum, Phoenix, AX, May 6-8, 2003.
