Evaluation of a Precision Hover Task
Using Time-Varying Cutoff Frequency
Amanda K. Lampton, Ph.D.
David H. Klyde
Daniel J. Alvarez
P. Chase Schulze
Peter M. Thompson, Ph.D.
Chi-Ying Liang, Ph.D.
Systems Technology, Inc.
Hawthorne, CA
Presented to
67th Annual Forum of the American Helicopter Society
Virginia Beach, VA
May 4 2011
ACKNOWLEDGEMENTS
•
NASA Research Announcement under Topic A.3.6, “Rotorcraft
Flight Dynamics and Control”
•
NASA: William Decker (COTR) and VMS Team
•
HOH AERONAUTICS: Dave Mitchell (PI) and Tom Nicoll
•
AMRDEC: Jeff Lusardi
•
ADVANCED ROTORCRAFT TECHNOLOGIES
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PRESENTATION OUTLINE
•
•
•
•
•
•
Introduction
Baseline & Added Dynamics
Time-varying Cutoff & Power Frequency
Piloted Simulation Description
Precision Hover Task Analysis
Conclusions
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INTRODUCTION
• The objective of this research program was to
investigate pilot thresholds of detection as higher-order
dynamics were introduced to a baseline rotorcraft model
• The investigation took the form of a piloted simulation
that was conducted in February 2009 using the NASA
Ames Research Center Vertical Motion Simulator (VMS)
• The focus of this paper is to assess the utility of timevarying cutoff and power frequency as a means of
differentiating run-to-run and pilot-to-pilot differences in
pilot-vehicle system behavior
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BASELINE ROTORCRAFT
DYNAMICS
• The baseline helicopter model used was a modified OH-6A
with the cross coupling and higher order terms of the model
removed.
• Removing the cross coupling terms helped to insure that any
changes seen in the dynamics of the helicopter by the pilot
were due to the added dynamics only and not from potential
cross-coupling.
• The baseline rotorcraft dynamics represented uncoupled pitch
and roll dynamics resulting in first order pitch and roll rate
command systems.
• The pitch and roll damping derivatives were set to provide one
high and one low bandwidth configuration in each axis.
• The simplified model was valid only for low speed and hover.
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ROTORCRAFT ADDED
DYNAMICS
• The added dynamics took the form of a second order
lead/lag or lag/lead transfer function filter.
• The filter was cascaded with the baseline rotorcraft
dynamic model.
• The gain, pole frequency, and zero frequency could all
be varied individually.
• The pole and numerator damping were set to the same
initial value and were then varied together.
• The added dynamics had the following form:
 z , n 
z
K 
 p , n p 


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NASA AMES VERTICAL MOTION
SIMULATOR (VMS) FACILITY
•
•
The VMS features significant vertical and
horizontal motion that makes the facility
ideal for conducting low speed rotorcraft
evaluation tasks.
The simulator cab was configured with
standard rotorcraft controls (center cyclic,
collective, and pedals) and displays for
forward, side, and chin bubble windows
NASA Photo & Illustration
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PRECISION HOVER TASK
• The evaluation task used was the precision hover task as
specified in ADS-33E-PRF.
• The objective of the task is to evaluate the ability of the rotorcraft
to transition from translating flight to a stable hover over a
designated point, accurately and with adequate aggressiveness.
NASA Photo
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EVALUATION PROCEDURES
• The pilots were familiarized with the evaluation task
using the baseline (no added dynamics) configuration.
• Some adjusting of the lateral and longitudinal cyclic
gains was made, if necessary, to ensure that the pilot
felt comfortable with the baseline configuration such that
the task performance was considered “good.”
• The baseline configuration was often repeated to
recalibrate the pilot to known “good” dynamics.
• For an individual evaluation case, the pilot was given a
unique zero/pole combination with a shared damping
ratio.
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POST RUN PILOT QUESTIONS
• At the conclusion of the task, the pilot was given the
following three questions:
–
–
–
Did you notice the added dynamics?
If you noticed the added dynamics, did they affect the task?
If the added dynamics affected the task, did they improve or degrade task performance?
• The damping ratio would then be changed based on
the responses of the pilot to the above questions.
• This process would be repeated until a more or less
complete set of responses were achieved for that
unique zero/pole pair.
• A new zero/pole pair would then be introduced and
the process would begin again, usually with the
baseline configuration.
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PILOTED SIMULATION SUMMARY
• The piloted simulation was conducted over a three week
period in February 2009.
• Five rotorcraft test pilots participated in the program
resulting in over 1100 evaluation runs.
• These runs consisted of many combinations of added
dynamics in the pitch and roll axes with the added
dynamics being introduced as both time-invariant and
time-varying cases.
• While the majority of runs were conducted with full VMS
motion, a number of runs were conducted with no
motion.
• The full motion of the VMS was required, particularly for
the higher frequency added dynamics cases.
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CLASSIC CUTOFF FREQUENCY
• A spectral analysis method for determining the pilot
operating frequency for pilot-in-the-loop flying tasks
• An alternative measure when it is not possible to
determine pilot-vehicle crossover frequency directly
• A quantitative measure of pilot stick activity derived
by examining controller input power versus
frequency
• Defined as the frequency at which the integral of the
power spectral density (PSD) is half its total value
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TIME-VARYING CUTOFF
FREQUENCY
• Wavelets provide a means of calculating the timevarying power or auto spectrum, called a scalogram
• Rather than using the auto spectrum averaged over the
entire run, the time-varying cutoff frequency is calculated
by numerically integrating the power over the frequency
range for each time increment of the scalogram
1  t 
1
2
 total  t 
2


2

1 t
0
1

2

0
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G  t  d 
G  t  d 
 0.5
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POWER FREQUENCY
• A limitation of the time-varying cutoff frequency is the
lack of a relationship to the magnitude of the power
spectrum
• This can result in a range of behavior that does not fully
correlate to the time-varying behavior seen in the
associated scalogram
• The power frequency metric marries the two by
multiplying the cutoff frequency by the peak magnitude
at each time slice
G  t  
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cutoff  t  max G  t 

1000
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ANALYSIS: SELECTED
ADDED DYNAMICS CASES
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Pilot
Configuration
Added Dynamics
Damping
A
Gain (0.56)
Lead (1.5 r/s)/Lag (2 r/s)
0.5 → 0
C
Lead (4 r/s)/Lag (4.5 r/s)
0.3 → 0
D
Gain (1 → 0.79)
Lead (4 r/s)/Lag (4.5 r/s)
0.4 → 0.01
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ANALYSIS:
Pilot A Time
Histories
 = TV
Lateral
Cyclic
Lateral
Cyclic
Baseline
Roll Rate
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Roll Rate
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ANALYSIS: Pilot A Baseline
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS: Pilot A Time-Varying
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS:
Pilot C Time
Histories
 = TV
Lateral
Cyclic
Lateral
Cyclic
Baseline
Roll Rate
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Roll Rate
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ANALYSIS: Pilot C Baseline
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS: Pilot C Time-Varying
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS:
Pilot D Time
Histories
 = TV
Lateral
Cyclic
Lateral
Cyclic
Baseline
Roll Rate
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Roll Rate
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ANALYSIS: Pilot D Baseline
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS: Pilot D Time-Varying
Cutoff Frequency
Scalogram
Power Frequency
Lateral
Cyclic
Roll Rate
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ANALYSIS SUMMARY
Cutoff Frequency
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Power Frequency
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CONCLUSIONS
• Time-varying power frequency provides a promising new
means to differentiate run-to-run and pilot-to-pilot
characteristics in pilot-vehicle system behavior for closed-loop
tasks.
• The dependence of the time-varying power frequency on the
time, magnitude of the power spectra density, and the
distribution of the power over the frequency range clearly
show the effects of the change in dynamics and the
transitions between phases of the task.
• Time-varying cutoff frequency is a less clear measure of pilot
effort. Without the dependence on the magnitude of the power
in the scalograms, it is difficult to judge pilot effort and to
extract clear differences between runs and pilots.
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