AIAA-2000-4205
DESIGN AND TEST OF FLIGHT CONTROL LAWS FOR THE
KAMAN BURRO UNMANNED AERIAL VEHICLE
Chad R. Frost*
NASA
Mark B. Tischler†
U.S. Army Aeroflightdynamics
Directorate (AMRDEC)
Army/NASA Rotorcraft Division
Flight Control and Cockpit Integration Branch
Ames Research Center
Moffett Field, California 94035
ABSTRACT
A flight control system was developed for an
unmanned vehicle based on the Kaman K-MAX
helicopter. The initial design was based on an 8-DOF
linear state-space aircraft model extracted from flight
test data. The aircraft dynamics were combined with
estimated sensor and actuator dynamics, around which
the control law architecture was developed. The
baseline control system gains were tuned using
optimization software to meet a selection of applicable
performance and handling-quality specifications. Realtime evaluation of the control laws was accomplished
on a desktop simulation. Flight test of the resulting
control laws revealed discrepancies between the model
and the aircraft; the model was updated with accurate
sensor and actuator dynamics identified from flight-test
data. After re-tuning the control system gains, the
aircraft performance closely matched prediction.
*
Aerospace Engineer, Member AIAA
Flight Control Technology Group Leader, Senior
Member AIAA
‡
Project Engineer III
§
Systems Specialist
†
Copyright © 2000 by the American Institute of Aeronautics and
Astronautics, Inc. No copyright is asserted in the United States under
Title 17, U.S. Code. The U.S. Government has a royalty-free license
to exercise all rights under the copyright claimed herein for
Governmental Purposes. All other rights are reserved for the
copyright owner.
Mike Bielefield‡
Troy LaMontagne§
Kaman Aerospace Corporation
Bloomfield, Connecticut 06002
INTRODUCTION
BURRO program / mission
Kaman Aerospace is developing an unmanned
version of the K-MAX "aerial truck" (Figure 1.) Under
contract to the Marine Corps Warfighting Lab, an
autonomous K-MAX will demonstrate Broad-area
Unmanned Responsive Re-supply Operations
(BURRO)1 capability for supporting Marines deployed
ashore. With a slung-load payload capacity equal to its
6,000-pound (2720 Kg) weight, the K-MAX BURRO
UAV will be capable of quickly delivering large
amounts of supplies and equipment to troops without
risking a pilot's life.
This paper focuses on the initial development
of a flight control system for the BURRO Phase 1 flight
demonstrations. In Phase 1, a ground operator
commands the aircraft, and a safety pilot is present
aboard; flight is limited to the hover/low-speed flight
regime, without an external load. The work was
performed under a Cooperative Research and
Development Agreement (CRDA) between Kaman
Aerospace and the Army/NASA Rotorcraft Division at
Ames Research Center. Follow-on work is underway to
expand the flight envelope to include hover with a
slung load and forward flight, both with and without a
slung load.
Turning the K-MAX into a UAV presents a
particular challenge – the aircraft has an unstable roll
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mode at 0.63 rad/sec, with a time-to-double of 2.4 sec;
this forms a lower bound on the control system
bandwidth. Combined with a mission profile that
places the aircraft in close proximity to personnel, naval
ships, and terrain, these characteristics dictate a
comparatively high bandwidth control system capable
of accurately maintaining aircraft position and attitude.
•
CIFER® (Comprehensive Identification from
FrEquency Responses)5, used to extract linear
state-space models from flight-test time history
data.
• CONDUIT (the CONtrol Designer's Unified
InTerface)6, which provides a graphical
environment for control system modeling,
evaluation, and optimization.
• RIPTIDE (Real-time Interactive Prototype
Technology Integration / Development
Environment)7, a desktop flight simulation and
control system testing tool.
The COSTAR tools were used extensively in
the K-MAX BURRO program, and their use is
highlighted where applicable.
AIRCRAFT MODELING
Figure 1. Kaman K-MAX helicopter
BURRO development strategy
Because the BURRO demonstrator aircraft
was required to be developed in a very short time span
and for a low cost, Kaman Aerospace used many
existing assets. This approach resulted in the use of an
electromechanical actuator system originally developed
for UH-1 drones, modified for the BURRO application.
Similarly, the sensor package and flight control
computer are the same as those used in the development
of Kaman’s SH-2G(A).
To keep development time to a minimum,
Kaman chose the latest software tools available.
Several UAV and manned aircraft development
programs have shown that the use of such tools can
dramatically reduce the time required to bring a vehicle
from concept to flightworthy aircraft.2,3,4
The
Army/NASA Rotorcraft Division at NASA Ames
Research Center has assembled a set of cooperative
design and evaluation tools under the COntrol and
Simulation Technologies for Autonomous Rotorcraft
(COSTAR) initiative. The COSTAR tools include:
Prior to designing the BURRO flight control
system, an accurate model of the aircraft dynamics was
required. This entailed modeling the basic airframe, the
attitude, attitude rate, altitude and translational rate
sensors, and the control actuators.
First, piloted frequency sweeps were flown
using an unaugmented K-MAX. Colbourne,
Tomashofski and Tischler used the CIFER® software
package to identify an eight degree-of-freedom
linearized state-space model of the helicopter dynamics
from the flight data.1 The model included rotor
dynamic inflow and coning states. Figure 2 (from
Reference 1) compares the CIFER®-identified on-axis
roll response to flight data; the results for the other
responses are similarly good matches.
The identified model was verified in the time
domain by comparing model doublet responses to flight
data. The model matched the aircraft response very
well, as seen in the roll and pitch responses to a roll
control input shown in Figure 3 (also from Reference
1.)
The sensor dynamics were then modeled as
equivalent time delays using second-order Pade
approximations. The delays used were based on the
sensor manufacturers’ specifications. Bench-test
frequency sweeps of the actuators were processed using
CIFER® to obtain second-order transfer function
models of the actuator dynamics.
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-200
-50
-60-40 -20 0 20
Flight results
Math Model
-350
Phase (deg)
Magnitude (dB)
Roll rate to lateral stick
1
Control system architecture
0.6
0.2
Coherence
Command/Altitude
Hold
and
Heading
Command/Heading Hold are used as the basic control
modes. These modes will be used by the autonomous
guidance and navigation software as well as for the
ground operator's direct control of the aircraft. An
Attitude Command/Attitude Hold (ACAH) mode is
available, at least in the demonstration vehicle, for
ground operator use in precision control of the aircraft.
0.1
1
10
20
Frequency (Rad/Sec)
2
0
20 -2
0
20 -20
Math model
Flight data
1
1
0
Control input
Velocity
Translational
Velocity
2
Control input Attitude
-20
Pitch Rate
Response
Roll Rate
Lateral
Response Control Deflection
Figure 2. CIFER-identified roll rate response
The control system architecture was designed
to implement the selected FCS modes. The basic
control system layout consists of outer loops for the
TRC function and inner loops for stability and attitude
control (Figure 4.) A simple control system architecture
was desired to facilitate later manual implementation in
flight-worthy C code. Therefore, proportional-integralderivative (PID) controllers (Figure 5) for each of the
primary axes provide the stabilization and attitude
control functions. For each of the longitudinal and
lateral channels, the TRC controller is implemented
with a P-I scheme (Figure 6), whose output is fed to the
attitude controller. The PID/PI scheme allows classical
control design methods to be used and provides insight
into the function of each of the gains in the system.
0
1
2
3
4
5
Time (Sec)
6
7
Attitude rate
Attitude
Linearized 8DOF
Aircraft dynamics
3
Attitude rate
Figure 3. Time-domain verification of CIFER®
model
All the elements of the aircraft model were
then assembled into a Simulink® block diagram within
the CONDUIT environment. The resulting model
provided a basis from which to design the flight control
system.
PID
Attitude controller
PI
Velocity controller
Figure 4. Control scheme
1
Ki
s
Limited
Integrator
Integrator Gain
1
Attitude command
Kp
1
Control output
Proportional Gain
Tr
2
Rate feedback
Feedback Time Constant
(ratio of attitude and rate feedbacks)
3
Attitude feedback
Figure 5. PID attitude controller
CONTROL LAW DEVELOPMENT
The flight control system (FCS) modes were
selected based on the BURRO system specification
requirements for autonomous guidance and navigation,
combined with ground operator control during the
terminal phases of flight. Earth-referenced Translational
Rate Command (TRC), with Altitude Rate
Ki
Integrator Gain
1
Velocity command
Kp
1
s
Limited
Integrator
1
Attitude command
Proportional Gain
2
Velocity feedback
Figure 6. PI velocity controller
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Preliminary values for the control system gains
were calculated using classical design methods, from
the 8-DOF CIFER-identified state-space model. The
gains were chosen to achieve at least 45 degrees of
phase margin and greater than 6 dB of gain margin. For
the desired stability margins, with the crossover
frequency ωc occurring at the point of maximum phase,
the system’s total equivalent time delay, τSL , can be
used to estimate the maximum achievable crossover
frequency of the control system8 via the formula
ωc =
0.37
.
τ SL
(1)
If the closed-loop bandwidth ωBW is defined as
the lowest frequency at which the augmented vehicle
exhibits 45 degrees of phase margin or 6 dB of gain
margin, then ωBW ≈ ωc. An equivalent time delay of τSL
= 0.095 sec was found, based on the Simulink® models
of the aircraft, actuator and sensor dynamics. This
value of τSL predicts an achievable bandwidth of ωBW =
3.9 rad/sec, which is within the 2 – 4 rad/sec ωBW range
suggested for light rotorcraft with ACAH response
characteristics.9
Because translational rate response equivalent
rise time (where Tx˙ eq occurs when x˙ = 0.632 x˙ ss ) faster
than 2.5 sec produces an objectionably abrupt attitude
response,10 the outer-loop gains were selected to place
crossover at around 0.4 rad/sec.
Only the roll-to-pedal response exhibits a large
amount of coupling, due to the K-MAX’s synchropter
rotor configuration. A simple crossfeed gain provided
satisfactory decoupling at frequencies above the control
system bandwidth. The required gain corresponds to
the ratio of the control derivatives, Kcf = -Lδ pedal/Lδ lat. stick
= -0.48.
Tuning in CONDUIT
The CONtrol Designer's Unified Interface
(CONDUIT) provides a single, graphical, interactive
environment for the development, evaluation and
automated tuning of flight control systems. CONDUIT
makes use of aircraft/control system models built in
either the MATLAB / Simulink® or MatrixX /
SystemBuild® graphical block-diagram tools. Key to
the optimization function of CONDUIT is the graphical
representation of specifications. A broad selection of
time- and frequency-domain specifications
encompassing performance and handling-quality
requirements are included with the CONDUIT
software, and users are provided with tools for
constructing and modifying specifications to their own
needs. A set of specifications is selected to constrain an
aircraft/control system model; the control system
engineer chooses control system gains to use as variable
design parameters. The CONDUIT optimization engine
then attempts to tune the design parameters to satisfy
the set of specifications. If the basic requirements of all
specifications can be achieved, CONDUIT proceeds to
tune the design parameters to minimize a designated
subset of the specifications.
The Simulink® aircraft model was updated for
use in CONDUIT by adding nonlinear effects such as
rate and saturation limits to the actuators, and output
limits to the control system integrators. CONDUITspecific switches were added to allow broken-loop
stability analysis. Finally, the PID controller gains in
the Simulink® model were designated to be tunable
CONDUIT design parameters. A higher-level view of
the lateral controller model, shown in Figure 7,
illustrates the complexity of the system.
Selection of Specifications
To evaluate and tune the performance of the
K-MAX BURRO, a set of handling-quality,
performance, and stability specifications were selected
from the built-in CONDUIT libraries. While the KMAX BURRO is nominally an unmanned vehicle, a
safety pilot will be on board the aircraft throughout the
demonstration program. Also, the aircraft is not a
purpose-built UAV – the dynamic components and
airframe were designed from the beginning to operate
within the usual bounds imposed upon a manned
vehicle. Finally, it is anticipated that a ground operator
will be in command of the aircraft during near-earth
operations. Thus, handling qualities consistent with
manned VTOL vehicles were selected to avoid
situations wherein the control system's commands
might be contrary to those expected by the safety pilot,
or might exceed the normal operating parameters of the
vehicle.
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6
Command_Mode
[ 1= Velocity 2 = Attitude ]
1
FCC_State
FCC_State
.05
4
Trim_Right
trim sensitivity (right)
Trim +
Total Control
1
1/57.3
Trim -
stick sensitivity
deg per stu
.05
3
Direct
Trim_Left
trim sensitivity (left)
Control Mixer
2
Stick Input
[stu]
deg > rad
discrete latch
Holds input value
when FCC_State = Active (1)
(Attitude hold)
Attitude
Command
Mode
trigger
in
out
Velocity
Command
Mode
Integrator
limited windup
(50%)
Attitude limit
+/ .523 rad
(30 deg)
dpp_aKi
m
Integrator gain
Proportional gain
stu/rad
Roll angle
5
1
s
dpp_aKp
1
Lateral_Servo_Command [stu]
dpp_aTp
Roll rate
sensors
Feedback time constant
rad/(rad/sec)
Vd
1
stick sensitivity
ft/sec per stu
discrete latch
Holds input value
when FCC_State = Active (1)
(Velocity hold)
Integrator
limited windup
.523 rad
(30 deg)
trigger
in
out
1
dpp_aKi_v
s
dpp_aKp_v
Integrator gain
Proportional gain
rad/(ft/sec)
Figure 7. Simulink® model of lateral controller
Within CONDUIT, specifications are
presented graphically, as shown in the example of
Figure 8. Aircraft time and frequency responses are
processed to extract information pertinent to the
specification, which is then plotted on the graphical
figure. Three levels of performance are shown as
bounded regions. The Level 1 region represents
satisfactory performance, while Level 2 results are
considered to be in need of improvement. Level 3
results are deemed so deficient that improvement is
mandatory. A brief description of each specification
and the rationale for its selection follows.
0.3
Level 2
Region
L1
-0.5
L3
0
0.5
Real Axis
1
This specification constrains all
eigenvalues of the system to lie in the
left half of the s-plane, thereby
ensuring stability of the aircraft. The
real component of the right-most
eigenvalue is evaluated.
Stability Margins per MIL-F-9490
The stability margin specification
80
requires 45 deg of phase margin
60
and 6 dB of gain margin, within
L1
L2
40
the rigid-body frequency range of
L3
20
0.1 to 40 rad/sec. The
0
specification is based on the
0
5
10
15
20
Gain Margin [db]
broken-loop response and is
therefore imposed upon each control channel.
Level 1
Region
Result
(Phase delay of 0.15 sec,
Bandwidth of 3 rad/sec)
0
0
EigLcG1:
Eigenvalues (All)
StbMgG1: Gain/Phase Margins
(rigid-body freq. range)
0.2
0.1
Eigenvalue Location
Phase Margin [deg]
Phase delay [sec]
Level 3
Region
•
•
Roll Bandwidth
0.4
Two types of specification were used to ensure
a stable aircraft:
1
2
3
4
Bandwidth [rad/sec]
5
Figure 8. Example of CONDUIT specification
Several specifications were chosen to drive the
choice of gains towards values that would produce good
handling qualities. For initial concept demonstration,
the ground operator will not be exposed to adverse or
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•
Damping Ratio per ADS-33D
OvsPiH1: Damping Ratio
Attitude Hold
A damping ratio of at least 0.35
must be maintained, as calculated
from the time response to a step
control input.
1
Damping Ratio (Zeta)
distracting conditions. Therefore, the specifications
(taken primarily from Aeronautical Design Standard
33D, “Handling Qualities Requirements for Military
Rotorcraft”)11 were selected to represent non-aggressive
tasks with operator attention fully directed to control of
the aircraft.
0.8
L1
0.6
0.4
0.2
The chosen handling-qualities specifications
L2
0
L3
were:
FrqHeH1: Heave Response
Hover/LowSpeed
time delay, tau_hdot, sec
0.5
L3
0.4
0.3
L2
0.2
L1
0.1
0
0
0.5
1
heave mode, invThdot, [rad/sec]
The vertical rate response to
collective stick inputs is fit to a
first-order low-order equivalent
system, from which the
characteristic parameters (the
1
inverse time constant
and
Tḣ
the equivalent time delay τ ḣ ) are found. The
specification requires that the heave response meet the
ADS-33D handling quality levels.
•
Bandwidth and Phase Delay per ADS-33D
BnwRoH2: BW & T.D. (roll)
Other MTEs; UCE=1; Fully Att
0.4
Phase delay [sec]
L3
0.3
L2
L1
0.2
0.1
0
0
1
2
3
4
Bandwidth [rad/sec]
The closed-loop attitude response
is required to meet the ADS-33D
limits. The ADS-33D criteria for
fully-attended operations were
used.
5
Translational Rate Rise Time per ADS-33D
The rise time of the translational
6
rate response to a step control
L2
5
input must be greater than 2.5 sec
4
L1
3
and less than 5 sec.
This
L2
2
requirement
is
intended
to
avoid
L3
1
objectionably fast attitude
changes, while keeping attitude-command-like shortterm response of the aircraft.
RisTrH1: Translatl rate rise time
7
L3
Two specifications were selected to evaluate
performance of the system. These specifications were
applied to each of the four control channels. They were:
•
Actuator Saturation
SatAcG1:
Actuator Saturation
0.8
The attitude response to a
disturbance (injected into the
0.5
L2
control system just downstream
0
L1
of the actuators) must fall within
L2
-0.5
the specified envelope. The
L3
-1
0
5
10
15
20
specification ensures that the
Time (sec)
control system retains good
disturbance-rejection qualities, even as the system gains
are reduced.
1
L3
L3
0.6
0.4
L2
0.2
Normalized Attitude Hold per ADS-33D
HldNmH1: Normalized Attitude Hold
Position and rate of the control
actuators are not allowed to
saturate for more than 30% of the
duration of a response to an
aggressive control input.
1
0
•
Normalized attitude response
•
Eq. Rise Time (Txdo t, Tydo t) [sec]
Heave Response per ADS-33D
Actuator Position Saturation
•
•
L1
0
0.5
Actuator Rate Saturation
1
_Attitude Rise Time
RisPiV1: Pitch Attitude
Change in 1 sec
L3
0
L2
1
2
3
d_theta [deg]
To ensure that control authority is
maintained, the attitude change
produced within one second of a
step control input is required to be
above a certain value.
L1
4
After meeting the Level 1 requirements of all
specifications, CONDUIT proceeds to minimize any
that are defined as "objectives".
Two such
specifications were included for each of the four control
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Crossover Frequency
CrsLnG1: Crossover Freq.
(linear scale)
L1
L2
L3
0
5
10
15
20
Crossover Frequency [rad/sec]
performance,
requirements.
•
_
PM = 46.8 deg. (ωc = 3.75 rad/sec)
GM = 9.7 dB, (ω180 = 11.23 rad/sec)
20
The broken-loop crossover frequency
of the system is minimized by
CONDUIT's optimization engine
after all other constraints have been
satisfied. This keeps the activity of
the control system at the minimum
level required to meet the
stability and handling-quality
0
-20
-40
0
Phase (deg)
•
_
design parameters to meet the Level 1 requirements of
all specifications. Further tuning was able to minimize
the Actuator Position RMS and Crossover Frequency
specifications.
Gain (dB)
channels. These specifications were also grouped to
form a single "summed objective", such that
minimization would be performed on the sum of the
component objectives. This ensures that the best
possible performance will be extracted from each
component of the grouped objectives, rather than
attempting to minimize the single worst objective. The
objective specifications are:
-100
-200
-300
-400
1
10
Frequency (rad/sec)
Actuator Position RMS
Figure 9. Baseline lateral stability margins
RmsAcG1: Actuator RMS
The RMS position of the actuators,
normalized by the maximum position
L2
of the stick and the actuators' full
L1
L3
travel, is minimized by the
CONDUIT optimization engine after
0
0.5
1
satisfaction of all other requirements.
Actuator RMS
Minimizing the RMS position
effectively reduces saturation and actuator sizing
requirements as much as possible; an additional benefit
is the reduction of component fatigue.12
Evaluation and Tuning
First, CONDUIT was used to evaluate the
performance of the aircraft with the classically-derived
preliminary gain values. The aircraft was stabilized,
with adequate stability margins; as seen in Figure 9 for
the lateral channel, the crossover frequency was
approximately at the value predicted using Equation 1.
However, at this crossover frequency the actuator
activity and saturation were excessive.
Next, the control system gains were tuned
using CONDUIT. CONDUIT was able to tune the
RIPTIDE evaluation
Prior to flight testing the CONDUIT-tuned
control laws, the Simulink® aircraft model was tested in
the RIPTIDE desktop simulation environment (Figure
10.) Evaluation of the control laws in RIPTIDE
provides a quick piloted assessment of the behavior of
the aircraft. It is especially useful for identifying
problems arising from nonlinear effects, such as those
due to control mode switching. Testing of the K-MAX
BURRO allowed tuning of trim rates and control
authority, and uncovered an error in mode-switching
logic. Without RIPTIDE, these changes would have
required significant test time in the aircraft.
FLIGHT TEST
Testing of the aircraft with the CONDUITtuned control laws commenced in January 2000. Initial
flights demonstrated a considerable deviation in the
aircraft behavior from that predicted by the CONDUIT
model and RIPTIDE simulation, exhibiting unstable
roll oscillations. An example is shown in Figure 11.
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considerably below the delays encountered in flight
test. Finally, the initial FCS design assumed that the
sensor data would not require any filtering, while
during flight test it was found that considerable lowpass filtering of the attitude rate was required. Using
the updated value of τSL = 0.290 sec in Equation 1, the
predicted achievable control system bandwidth was
reduced to 1.27 rad/sec. This value is well below the
recommended range and would be considered Level 2
in a piloted aircraft.
Table 1. Comparison of estimated and actual delay
Figure 10. Control law evaluation using RIPTIDE
40
Actuators
Sensors
Computer
Filters
TOTAL
Roll attitude command
30
Roll Attitude (degrees)
20
Component
Roll attitude
10
Estimated
Delay (ms)
50
25
20
0
95
Actual Delay
(ms)
107
53
40
90
290
0
Model updated
-10
-20
A decided advantage to using COSTAR's
CIFER and CONDUIT tools lies in their capability to
rapidly re-tune the control system gains as components
of the aircraft and control system are changed or whose
properties become better known. The new sensor, filter
and actuator dynamics were incorporated into the
Simulink® block diagram, and the model was evaluated
in CONDUIT. With the updated components, the
model predictions matched the flight test data; the
model response was oscillatory at the same 0.4 Hz
frequency seen in the aircraft (Figure 12.)
®
-30
-40
0
5
10
15
20
25
30
35
40
45
Time (sec)
Figure 11. Oscillatory roll response during initial
flight testing
To identify the source of the instability,
longitudinal and lateral doublets were flown, and
CIFER® was used to extract frequency responses at
various points in the control system. This process
allowed accurate identification of the sensor and
actuator dynamics, as installed in the aircraft.
Significantly, the equivalent time delay of these
components was over 200% greater than originally
modeled – a comparison of the component
contributions is shown in Table 1. The increased
actuator delay was due to a difference in performance
as installed in the vehicle, versus the bench-test; the
manufacturer’s estimates for sensor delay were
optimistic. The delay attributed to the computer, which
runs at 50 Hz, was initially based on 1/2 frame for zeroorder hold plus an additional 1/2 frame of
computational delay. These estimates proved to be
Gains re-tuned using CONDUIT
Next, the gains were re-tuned to accommodate
the updated dynamics. With the added time delay, the
system becomes very highly constrained in pitch and
roll – as compared to the lateral broken-loop responses
of the XV-15 tiltrotor and the SH-2F Sea Sprite
helicopter in Figure 13, the aircraft is conditionally
stable over a very narrow frequency range. At low
frequency, this is due to unstable rigid-body dynamic
modes. At higher frequency, the large amounts of
delay cause a rapid phase roll-off. While conditional
stability (e.g. both a gain increase margin and a gain
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5
4
Roll attitude command
0
Phase (degrees)
Roll (degrees)
3
2
Roll attitude
1
-100
XV-15 Tilt Rotor
SH-2F
-200
-300
0
Narrow range of stability
K-MAX BURRO
-400
0
1
2
3
4
5
6
7
8
9
1
Frequency (rad/sec)
10
10
Time (sec)
Figure 13. Comparison of lateral broken-loop phase
responses
Figure 12. CONDUIT model roll response
1
Attitude Commands
Attitude limit
+/ .523 rad
(30 deg)
Integrator
limited windup
(50%)
2
Attitude feedback
dpp_aKfp/dpp_aKfz
3
Rate feedback
dpp_aTp
filter gain
s+dpp_aKfz
s+dpp_aKfp
Lead filter
dpp_aKp
dpp_aKi
Proportional gain
stu/rad
Integrator gain
1
s
1
Servo Command [stu]
Feedback time constant
rad/(rad/sec)
Figure 14. Roll attitude controller with added lead filter
reduction margin) is typical for hovering aircraft, the
K-MAX BURRO has an unusually narrow frequency
range over which it is stable. Above 6 rad/sec, or
below 0.8 rad/sec, the aircraft is laterally unstable.
To maintain reasonable phase margin, the crossover
frequency should be greater than 1.4 rad/sec
(approximately twice the minimum stable frequency.)
The aircraft also has a lightly-damped mode at 6
rad/sec that is not captured by the 8-DOF model;
adequate suppression of this mode requires that
crossover be a factor of three lower, i.e. below 2.0
rad/sec. The characteristics of the pitch axis are
similar. Note that the 1.27 rad/sec crossover based
on the high-frequency dynamics using Equation 1 is
below the crossover frequency desired to stabilize the
0.63 rad/sec mode. To allow some increase in the
crossover frequency, lead filters were added to the
pitch and roll attitude control architecture, as shown
in Figure 14. This allows an increase in ω C by
to allow CONDUIT to trade off gain margin for
increased phase margin in the region of crossover.
As seen in the broken-loop roll response of
Figure 15, CONDUIT successfully tuned the control
system gains to optimize the stability of the aircraft.
The predicted roll attitude time response is shown in
Figure 16. All of the resulting specifications are
shown in Figure 17. While the collective, pedal, and
TRC margins were solidly Level 1, the best attainable
lateral and longitudinal ACAH stability margins were
Level 2. To achieve even Level 2 stability margins
with the updated dynamics, CONDUIT allowed some
of the other specifications to degrade – control
system bandwidth, pitch attitude damping, and pitch
and roll attitude response time all dropped into the
Level 2 region; yaw attitude response time
deteriorated to Level 3.
sacrificing gain margin relative to the design rules of
Equation 1. The lead filter pole and zero were
designated as CONDUIT-tunable design parameters,
The K-MAX BURRO flight control
software was updated with the new CONDUIT-tuned
gains. The roll response in ACAH mode, shown in
Figure 18, is smooth and stable, although the
Flight test with updated gains
9
American Institute of Aeronautics and Astronautics
acceptable range of
crossover frequency
CONDUIT-tuned result
20
Gain (dB)
0
-20
-40
-60
CIFER identification of the loaded aircraft are
complete,1 and CONDUIT tuning of the control
system is currently in progress. Similar work is
being conducted for forward flight conditions. Turn
coordination, automatic ascent and descent profiles,
and waypoint navigation functions are in
development at Kaman Aerospace.
Phase (degrees)
0
-100
CONCLUSIONS
-200
Extensive use of advanced control system
design tools allowed the Kaman/Ames team to build
a successful system in a six-month period. Several
key points emerged from this project:
-300
-400
1
Frequency (rad/sec)
10
Figure 15. CONDUIT-tuned broken-loop lateral
response
•
60
Roll Attitude (degrees)
50
40
•
Roll attitude command
30
20
Roll attitude
10
•
0
0
5
10
15
20
25
Time (sec)
30
35
40
45
Figure 16. Improved CONDUIT model roll
response
response is somewhat sluggish as indicated by the
low bandwidth, and the unmodeled 1-Hz mode is not
completely suppressed. The flight test response
agrees well with the CONDUIT model prediction of
Figure 16. Responses in other control axes are
similar. Ground operator experience commanding
the aircraft in ACAH mode demonstrated that the low
ACAH margins resulted in high operator workload,
while TRC operation proved easier, but afforded less
precision.
•
•
Application of the COSTAR design and
evaluation tools significantly reduces
development time. The tools facilitated rapid
aircraft and component model identification,
FCS design, gain tuning and desktop simulation.
The design space for the K-MAX BURRO UAV
is very limited. CONDUIT was able to extract
additional performance within the limitations of
the design, tuning 23 design parameters against
33 specification requirements.
A key driver of the control system performance
was accurate knowledge and modeling of highfrequency component dynamics.
CIFER®
proved useful for identification of unknown or
inaccurate elements of the system.
Equivalent time delay provides an accurate
prediction of achievable system performance,
and should be used early in the development
cycle to assess the feasibility of achieving
mission goals with proposed hardware.
Increased phase margin would improve
performance; this could be accomplished by
reducing the total delay in the system, or by
providing phase lead through an architecture
change. Both avenues are being investigated.
CURRENT ACTIVITY
Following a successful demonstration of the
Build 1 K-MAX BURRO to the Marine Corps
Warfighting Lab, work is proceeding on control law
design for hovering flight with an external slung load.
Development of the 10-DOF equations of motion and
10
American Institute of Aeronautics and Astronautics
Gain/Phase Margins
(rigid-body freq. range)
Eigenvalue Location
Gain/Phase Margins
(rigid-body freq. range)
80
Gain/Phase Margins
(rigid-body freq. range)
80
80
40
20
0
0.5
Real Axis
0
1
Gain/Phase Margins
(rigid-body freq. range)
time delay, tau_hdot, sec
40
20
MIL-F-9490D
0
5
15
0
20
0.1
ADS-33D
0
1
2
3
4
Bandwidth [rad/sec]
5
0.1
ADS-33D
5
10
GM [db]
15
0.1
ADS-33D
1
2
3
4
Bandwidth [rad/sec]
5
COL, LON
0.6
0.4
0.2
10
GM [db]
15
20
Ames Research Center
0
0.5
Actuator Rate Saturation
1
0.8
LAT, PED
0.6
0.4
0.2
0
Ames Research Center
0
0.5
Actuator Rate Saturation
1
Normalized Attitude Hold
(Disturbance Rejection)
1
0.3
0.5
0.2
0
0.1
-0.5
0
5
SatAcG1:
Actuator Saturation
Bandwidth & Time Delay (yaw)
Other MTEs
0.2
ADS-33D
0
Pitch Attitude
Change in 1 Second [deg]
Damping Ratio
Attitude Hold
MIL-F-9490D
0
1
0.4
0
LAT (ACAH)
40
0
20
0.8
0
0
0.5
1
heave mode, invThdot, [rad/sec]
0.3
0
LAT (TRC)
Actuator Saturation
Bandwidth & Time Delay (roll)
Other MTEs;UCE=1;Fully Att
Phase delay [sec]
0.2
0
1
0.4
0.3
60
20
MIL-F-9490D
Heave Response
Hover/LowSpeed
0.2
Bandwidth & Time Delay (pitch)
Other MTEs;UCE=1;Fully Att
Phase delay [sec]
15
0.3
20
0.4
0
10
GM [db]
0.4
0
10
GM [db]
5
Phase delay [sec]
PM [deg]
PED
60
0
0
0.5
80
LON (ACAH)
40
Actuator Position Saturation
0.5
LON (TRC)
20
MIL-F-9490D
Actuator Position Saturation
Ames Research Center
1
60
PM [deg]
60
PM [deg]
PM [deg]
COL
1
2
3
4
Bandwidth [rad/sec]
5
PITCH,
ROLL
YAW
-1 ADS-33D
0
5
10
15
Time (sec)
Roll Attitude
Change in 1 Second [deg]
20
Yaw Attitude
Change in 1 Second [deg]
Damping Ratio (Zeta)
1
ROLL
0.8
0.6
0.4
PITCH
0.2
0
Ames Research Center
ADS-33D
Eq. Rise Time (T
x-dot
,T
y-dot
) [sec]
0
7
Translational Rate Rise Time
4
Ames Research Center
2
3
d_theta [deg]
4
LAT
3
2
LON
LAT
LAT
0.5
Actuator RMS
Ames Research Center
8
PED
Ames Research Center
0
4
6
d_phi [deg]
LON
PED
1 ADS-33D
2
COL
COL
LON
0
Crossover Freq.
(linear scale)
Actuator RMS
6
5
1
Ames Research Center
1
0
5
10
15
20
Crossover Frequency [rad/sec]
Figure 17. Specifications showing CONDUIT-tuned results
11
American Institute of Aeronautics and Astronautics
0
1
2
3
d_psi [deg]
4
5
60
Roll attitude command
Roll Attitude (degress)
40
20
Roll attitude
0
-20
-40
-60
0
5
10
15
20
25
30
35
40
45
Time (sec)
Figure 18. Improved flight-test roll response
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Tomashofski, C. A., LaMontagne, T., “System
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American Helicopter Society 56th Annual Forum,
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2
Mettler, B., Tischler, M. B., and Kanade, T.,
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Helicopter Society 55th Annual Forum, Montreal,
Canada, May 1999.
3
Colbourne, J. D., Frost, C. R., Tischler, M. B.,
Cheung, K. K., Hiranaka, D. K., Biezad, D. J.,
“Control Law Optimization for Rotorcraft Handling
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4
Tomashofski, C. A., Tischler, M. B., “Flight Test
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Digital Flight Control System Development,”
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5
Tischler, M. B. and Cauffman, M. G., "FrequencyResponse Method for Rotorcraft System
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6
Tischler, M. B., Colbourne, J. D., Morel, M. R.,
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Environment For Flight Control Development,"
1
Proceedings of the AIAA Guidance, Navigation, and
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7
Mansur, M. H. Frye, M., Mettler, B., Montegut, M.,
“Rapid Prototyping and Evaluation of Control
System Designs for Manned and Unmanned
Applications,” Proceedings of the American
Helicopter Society 56 th Annual Forum, Virginia
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8
Tischler, M. B., “Digital Control of Highly
Augmented Combat Rotorcraft”, NASA Technical
Memorandum 88346, May 1987.
9
Hoh, R. H., Mitchell, D. G., Ashkenas, I. L.,
Aponso, B. L., Ferguson, S. W., Rosenthal, T. J.,
Key, D. L., “Background Information and User’s
Guide for Proposed Handling Qualities Requirements
for Military Rotorcraft,” Systems Technology Inc.,
TR-1194-3, Hawthorne, CA, December 1985.
10
Hoh, R. H., Mitchell, D. G., Aponso, B. L., Key,
D. L., Blanken, C. L., “Background Information and
User’s Guide for Handling Qualities Requirements
for Military Rotorcraft,” USAAVSCOM Technical
Report 89-A-008, December 1989.
11
Anon., “ADS-33D-PRF, Aeronautical Design
Standard, Handling Qualities Requirements for
Military Rotorcraft,” United States Army Aviation
and Troop Command, St. Louis, MO, May 1996.
12
Rozak, J. N. and Ray, A., "Robust Multivariable
Control of Rotorcraft in Forward Flight: Impact of
Bandwidth on Fatigue Life," Journal of the American
Helicopter Society, Vol. 43, No. 3, 1998, pp. 195 201.
12
American Institute of Aeronautics and Astronautics