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A, B, C, D State matrix, input matrix, output matrix, feedthrough matrix
a, b Zero/pole coefficient in compensator
bS Wingspan
CS Cable damping coefficient
e Error state vector
FH, FL, FC State vector functions for helicopter, load and DI controller
FS Cable tension force
h Altitude for the Dryden wind turbulence model
H Forming filter transfer function
K Compensator gain
KS Cable stiffness
l Cable position
L Turbulence scale length
p, q, r Roll, pitch, and yaw rates
pL Load relative position vector
rCH Cargo hook position vector
TEH Earth to helicopter body transformation matrix
xii
TEL Earth to load body transformation matrix
THL Helicopter to load body transformation matrix
u, v, w Inertial velocity components
u Control command vector
V Aircraft airspeed norm
x, y, z Longitudinal, lateral, and vertical position
x State vector
XA, XB, XC , XP Lateral and longitudinal stick, collective, pedals
y Helicopter states output vector used for outer loop DI con-troller
β0, β1S, β1C Main rotor flapping angles
∆l Cable stretch
δ Vector of pilot control commands
λ0, λ1S, λ1C Dynamic inflow components
ν(t) DI controller pseudo-commands vector
νφ, νθ, νVD, νr DI controller pseudo-commands for roll, pitch, aircraft vertical
speed, and roll rate.
σ Turbulence intensity
φ, θ, ψ Roll, pitch, and yaw Euler angles˙( ) Time rate of change
( ) Unit vector
||.|| Vector norm
( )C Relative cable angles
( )cmd Commands
( )f Filtered commands
xiii
( )F Fuselage
( )H Helicopter
( )L Load
( )N,E,D North, east, down
( )rp Relative position
( )R Rotor
( )RMS Root mean square
( )u,v,w Airspeed components
xiv
Acknowledgments
Firstly, I would like to start by thanking Dr. Jacob Enciu and Dr. Joseph Horn for
the great opportunity to conduct this research in the Vertical Lift Research Cen-
ter of Excellence (VLRCOE) as well as for all the recommendations, observations,
guidance, and everything I learnt from them.
I would also like to acknowledge my colleagues from the University of Buenos Aires,
especially to Lic. Susana Gabbanelli, Dr. Leonardo Rey Vega, Dr. Juan Giribet,
and Dr. Daniel Vigo, who were all very patient and helpful with my time at Penn
State University.
This work was also possible thanks to the people working in the BecAr Programme
and the Argentinean Fulbright Foundation. I would like to thank them not only
for the financial support but also for all the help and orientation they gave me.
Of course, nobody has been more important to me in the pursuit of this project
than the members of my family. I would like to thank my mother, whose love
and guidance through my studies made it possible for me to be here, and to my
brother, who makes me realize about the important things.
Finally but not least, I would like to make a special mention to my wife, whose
love has become the main reason for improving myself in everything I do.
This research was partially funded by the Government under Agreement No.
W911W6-17-2-0003. The U.S. Government is authorized to reproduce and dis-
xv
tribute reprints for Government purposes notwithstanding any copyright notation
thereon. The views and conclusions contained in this document are those of the
authors and should not be interpreted as representing the official policies, either
expressed or implied, of the Aviation Development Directorate or the U.S Govern-
ment.
xvi
Dedication
To my family...
xvii
Chapter 1 |Introduction
1.1 Motivation
External load missions are among the most significant tasks that a helicopter can
perform. Carriage of external loads for either civil or military objectives is used
in rescue missions, transport of consumable products to flood zones, fire-fighting,
transport of military equipment to bases close to enemy territories, and other
situations (Figure 1.1). In all of these cases the helicopter flight speed during the
mission has a high impact on the mission safety and efficiency. Nonetheless, the
dynamics of the external load is usually not a part of the helicopter design process.
Therefore, external load carriage can lead to a degradation in the stability and
control of the coupled helicopter and external load system during forward flight.
The factors that generate these instabilities include the load pendulum dynamics,
the load aerodynamics, the rotorcraft dynamics, and the pilot’s compensation [1]-
[3].
1.2 Background
In the past, several techniques for passive and active stabilization of slung loads
were analyzed in various studies [4]-[8]. One approach for the avoidance of slung
1
Figure 1.1. External load mission examples1
load instabilities during flight involved the use of a flight director that provided
pilots with guidance cues for damping the load pendulum modes [9]-[12]. For var-
ious reasons, neither of these technical solutions culminated into an operational
system.
In recent years, studies have been conducted for the use of load state feedback
to the primary control system of the rotorcraft for increasing the load damping or
improving the handling qualities of the coupled systems. In [13], Krishnamurthi
and Horn demonstrated stability in hover and low speed flight by the use of a
primary flight control law based on relative cable angle measurements and lagged
relative cable angle feedback (LCAF). In [14], Ottander et al. simulated and flight
validated slung load station keeping above a moving vehicle using a combination of
input shaping and delayed swing feedback. In [15], Ivler et al. designed a primary
flight control based on rate and angle feedback tested on a UH-60 RASCAL. In the
study presented in [16], a control system based on the classical root locus technique
was used to design a load damping architecture for hover and low speed flight by
using LCAF. In [17], Patterson et al. developed and flight demonstrated a hybrid
solution consisting of an active cargo hook and a flight control load stabilization1Left: http://www.vortexxmag.com, right: http://fightersweep.com/3041/milestone-
monday-ch-47-chinook-54
2
mode in the primary control system using LCAF. Recently, the stabilization of
external loads in forward flight has been demonstrated by a collaborative research
between the Technion University, and the US Army. The stabilization methods
used in this research included passive stabilization using rear mounted fixed fins
[18] and active rotational stabilization using controlled anemometric cups [19].
Both methods were demonstrated in flight and produced an extended carriage
envelope of approximately 120 kt for box-like loads that are currently limited to
60 kt. Although these methods provide stability to the system, their operational
implementation implies a drag penalty, as well as some logistic problems and per-
formance degradations like preparing the loads for flight or reducing the amount
of cargo load due to the hardware weight used to achieve stability.
A research program for the development of stabilization methods of external loads
during high speed flight was more recently initiated by the US ARMY. The re-
search is performed collaboratively by researchers from Penn State University and
the Tel Aviv University and includes the development of active stabilization meth-
ods for external load carriage and their validation by real-time piloted simulations
and hardware in the loop wind tunnel tests.
1.3 Goal and Organization of the Thesis
In the work presented in this thesis, we extend the concepts shown in [13] and
[16] from hover to forward flight. The root locus technique is used to design an
airspeed scheduled controller to stabilize the slung load at airspeed ranging from
hover to high speed flight. The studies conducted here are focused on the design
and simulation for a coupled controlled system of a UH-60 Black Hawk utility
helicopter and an external load. The UH-60 helicopter uses a dynamic inversion
(DI) controller to provide stability and trajectory control to the clean aircraft. The
external load model is that of a 2500 lb empty CONEX cargo container fixed with
3
33 degree rear mounted fins that prevent rotation but do not guarantee stability
throughout the flight envelope. This particular load was chosen for this study due
to the availability of a high fidelity dynamic model that was validated in both
dynamic wind tunnel tests and flight tests. The controller achieves its objective by
providing additive control signal to the existing baseline controller in the UH-60
helicopter. Although the control method is applied to a load that includes fins,
the designed method is intended to be applied to any external load that does not
rotate about the cable axis.
The outline of the thesis is as follows: In Chapter 2 the basic dynamic character-
istics and model of the isolated external load, the sling cables, the helicopter, and
the coupled helicopter-external load system are described. Chapter 3 presents the
details of the controller design. In Chapter 4 the results of the simulations are
then presented showing the controller performance for cruise level flight for two
airspeeds in which the system without the relative cable angle feedback controller
is unstable or marginally stable. For this maneuver, the controller is also analyzed
when it is turned on during oscillatory responses. In addition, the controller per-
formance during a complex maneuver is examined. These simulations are then
followed by adding different levels of atmospheric turbulence to the helicopter and
the load models, and rechecking the controller performance. Finally, Chapter 5
presents the conclusions and future works.
4
Chapter 2 |Model Description
2.1 Introduction
A first principles physical model was developed to study the feasibility of using
relative cable angle feedback to stabilize the load and helicopter in high airspeed
(see Appendix A). The positive results from this analysis supported the next phase
of the research. More precise simulation results, need validated models. For the
aircraft, an UH-60 GenHel Black Hawk model was used, and for slung load, an
empty CONEX cargo container model which was validated in test flight and wind
tunnel tests [20] was used. These models, along with the sling cables, integrate to
create a coupled system. This system presents instabilities for airspeeds close to
100 kt and very low damping for the airspeed range between 15 kt and 35 kt.
2.2 External Load Model
The external load model used is that of an 8ft x 6ft x 6ft CONEX cargo container
with two rear mounted stabilization fins. The fins prevent load rotation but do not
guarantee load stability throughout the helicopter flight envelope. This model was
selected due to its extensive use in the studies mentioned previously. The two fins
are inclined in 33 degrees relative to the box side faces, trailing edge out (Figure
5
Figure 2.1. Cargo container with fins inclined in 33 degrees relative to the box (picturefrom [21])
2.1). The model also assumes a total weight of 2489 lb, which represents an empty
container with the four sling cables. For this study, the load center of gravity was
set to be 0.3 ft aft of the CONEX geometric center. This makes the load unstable
at an airspeed of 100 kt, selected as the target airspeed for load stabilization in
the current research.
The dynamic model described above has been thoroughly validated using dedicated
wind tunnel tests and flight tests. The aerodynamic model of the fin stabilized load
uses static aerodynamic forces and moment coefficients measured in a wind tunnel
for the complete load (fins included). These coefficients are augmented by a theo-
retical calculation to include the fins quasi-steady damping effect (due to the arm
between the fins and the load center of gravity). This approach was validated by
dedicated dynamic wind tunnel tests (see [22] for details).
The load’s equations of motion are implemented as a state space model with the
6
state vector being comprised of the load’s inertial velocities, attitude angles, an-
This chapter shows the simulation results obtained with the designed controller.
Different scenarios were designed to verify the effectiveness of the controller. The
first set of simulations is for a trimmed cruise flight, which can be considered a
baseline test. These tests were executed for the low and high airspeed presented
in Chapter 3. The second set of simulations is for a more demanding scenario in
which a complex maneuver combining four segments was used. The third set of
tests was designed to verify the controller performance when it was turned on when
instabilities were developed. Finally, the previously mentioned scenarios, trimmed
cruise flight and complex maneuver, were modified to include wind turbulence with
light, moderate, and severe turbulence levels.
4.2 Trimmed Cruise Flight
For the two airspeeds used as examples for the controller design procedure in Chap-
ter 3, 25 kt for low airspeed and 97 for high airspeed, a simulation for a trimmed
cruise flight was executed.
Once the coupled system was trimmed at the corresponding airspeed, the simula-
35
tion started and a perturbation at t = 3 sec was applied. Such a perturbation was
a combination of a roll doublet and an increase in the load velocity (a “push”).
As previously mentioned in Chapter 2, for an airspeed in the range of 96kt to
105kt and depending on the level of the perturbation, instabilities can be pre-
sented as severe symmetric LCO or milder asymmetric LCO. Simulations to verify
the performance of the controller for these two cases were executed.
4.2.1 Simulation at 25 kt
For this airspeed the simulation showed the presence of LDO, a lightly damped
oscillatory response to the push applied 3 seconds after the simulation started.
The undesired characteristic of these oscillations are related to two factors: its long
duration, which could easily be more than 300 seconds, and its large initial value
(which actually depends on the excitation level) that induces lateral accelerations
in the cockpit, which for a long period of time reduces the pilots ride qualities.
Figure 4.1 presents the relative cable angles for 25 kt constant airspeed cruise
Figure 4.1. Relative cable angles simulation result for 25 kt
36
maneuver where LDO can be observed. The improvements achieved with the
controller are noticeable. The yaw angle time history when the controller is not
active (ψC , red curve in Figure 4.1) presents a time to half of 115.5 seconds (where
the damping ratio obtained from the simulation of the nonlinear model was ζ =
5.4 10−3, which is close to the one obtained from the linear model). With the
controller on, the time to half amplitude is reduced to 14.2 seconds (ζ = 4.7 10−2,
increased by a factor of 10), which is approximately 12.5% of the previous value.
As mentioned in the previous chapter, this improvement has an impact in the
helicopter dynamics. Figures 4.2 and 4.3 show that the helicopter Euler angles
and the helicopter control commands (simulation time shown was reduced to 60
seconds). In both of these figures, it can be observed that when the controller
was on, the responses presented higher levels of oscillations at the beginning of the
simulation as compared to the case in which the controller was off. This difference
can mostly be observed in the helicopter roll Euler angle (Figure 4.2) and in the
collective and lateral commands (Figure 4.3). However, the oscillations in the
Figure 4.2. Helicopter Euler angles simulation result for 25 kt
37
Figure 4.3. Helicopter controls commands simulation result for 25 kt
helicopter Euler angles were damped in less than 60 seconds, and for the case of
the helicopter commands, the small differences were far from making the helicopter
control commands reach their mechanical limits (which could bring saturation
problems) and they were also quickly damped. It is important to note that the
LDO were mostly impacting the load Euler angles, which present similar results
to those presented for the relative cable angles (Figure 4.1). Nevertheless, these
oscillations (as well as the previously shown) were quickly damped by the stability
improvement granted by the designed controller.
4.2.2 Simulation at 97 kt
For this airspeed, the instabilities were presented as LCO rather than LDO. Similar
to the case of 25 kt, the coupled model was perturbed with a lateral stick dou-
blet and load push applied 3 seconds after the simulation started. As previously
mentioned, the intensity of the perturbation will produce severe symmetric LCO
or milder asymmetric LCO responses. The characteristics of the LCO presented
38
Figure 4.4. Relative cable angles simulation result for 97 kt
at this airspeed were similar to that previously explained for the isolated load at
an airspeed of 100 kt. The instabilities at this airspeed make this case a more
demanding scenario than the 25 kt airspeed. However, the controller allowed the
system to quickly achieve stability no matter the type of LCO.
Figure 4.4 presents the relative cable angle results for an airspeed of 97 kt. In this
figure it can be observed that, for this case, the instabilities were severe symmetric
LCO. By knowing that these results were similar to the load Euler angles, it can
be seen that the severe symmetric oscillation (at least 40 degrees peak-to-peak for
φL) could lead to the load striking the helicopter’s tail boom and, in this way,
endanger the crew and the mission. However, when the controller was used, these
oscillations were quickly damped. Figure 4.5 presents the helicopter controls for
this simulation, in this figure it can be observed that the controller’s higher im-
pact was in the initial 10 seconds. In that interval, the helicopter’s longitudinal,
collective, and pedals controls were slightly increased and then all oscillations were
damped. On the other hand, when the controller was turned off the helicopter com-
39
Figure 4.5. Helicopter controls simulation result for 97 kt
Figure 4.6. Helicopter Euler angles simulation result for 97 kt
mands present oscillations that impacted in the helicopter Euler angles. Figure 4.6
presents the helicopter Euler angles, for the same simulation, showing the level of
40
Figure 4.7. Relative cable angles simulation result for 97 kt, asymmetric LCO
oscillations to which the helicopter and the crew would be subjected if the con-
troller was off. These oscillations lead to significant lateral acceleration levels in
the cockpit that would likely degrade flying qualities and increase the pilot’s work-
load.
The relative cable angles can be observed in Figure 4.7, where asymmetric LCO
were present. Comparing this figure with Figure 4.4, it is easy to observe that the
sustained oscillations in the roll angle present a lower peak-to-peak amplitude of
7.49◦ (compared to the 29.45◦ from the symmetric LCO) and a higher frequency of
1.36 rad/sec (compared to the 0.83 rad/sec for the symmetric LCO). In the case of
the helicopter (Figure 4.8) and load (relative cable angles presents similar results,
Figure 4.7) roll angle, when the controller is off, the oscillation amplitudes were
also less severe and their impact on the flight qualities and safety of the crew/mis-
sion would likely be smaller than in the case of the severe symmetric LCO. It can
also be observed in figures 4.7 and 4.8 that the damped oscillations (controller on)
that started at t = 10 seconds presented a higher initial amplitude. This can be
41
Figure 4.8. Helicopter Euler angles simulation result for 97 kt, asymmetric LCO
Figure 4.9. Helicopter controls simulation result for 97 kt, asymmetric LCO
42
explained by observing the helicopter controls in Figure 4.9. This figure shows
that the initial 20 seconds of the results obtained with the controller on presented
higher amplitude oscillations in the helicopter controls, which increased the ampli-
tude of the oscillations in the helicopter. However, this increase in the amplitude
of the controls was far from making them reach their mechanical limits and it is a
small price to pay in order to subside the LCO in 70 seconds.
4.3 Complex Maneuver
As explained earlier, the design process was repeated for airspeeds from hover to
130 kt in 5 kt steps (or smaller steps where needed) in order to secure stability.
In this way, an airspeed scheduled controller assembled from 56 separate lag and
lead controllers was obtained (Table 3.1). To verify the correct operation of the
scheduled control system in a more demanding scenario, a complex maneuver was
simulated. The maneuver started with the helicopter in hover from where it accel-
erated to 97 kt in 20 seconds and stayed trimmed at that airspeed for 70 seconds
(which, as seen in the previous section, is the necessary time to damp the oscilla-
tions that last longer, the asymmetric LCO). After that time, the helicopter made
a 180 degrees right level turn at 97 kt which took 40 seconds to complete, and
finally, resumed straight and level flight at that airspeed for 40 additional seconds.
It is important to mention that no perturbations were used during the maneuver.
Table 4.1 describes this maneuver.
Figure 4.10 presents the helicopter Euler angles throughout the complex maneu-
ver. In it, the initial variation in the pitch angle is related to the acceleration that
the helicopter is performing at the beginning of the maneuver. When the accel-
eration is terminated, the pitch angle remains at the negative trim value required
for flight at the constant airspeed of 97 kt. After 90 seconds of simulation, the
180◦ right level turn began and the roll and yaw angles changed (lateral dynamic);
43
Time Period[sec] Segment Description
0 - 20 Acceleration from hover to 97 kt20 - 90 Straight and level flight at 97 kt90 - 130 180 degrees right level turn at 97 kt130 - 200 Straight and level flight at 97 kt
Table 4.1. Complex maneuver description
the turn was completed when the yaw angle reached 180 degrees. Then, the he-
licopter continued in a straight and level flight at 97 kt and the helicopter Euler
angles presented the same response than in the previous similar segment (from 20
to 90 seconds). Besides the description of the maneuver that this figure provides,
it is important to note the oscillations that were self-induced (no perturbation was
added to the simulation) during the straight and level flight segments.
In Figure 4.11 the relative cable angles obtained from the simulation can be ob-
served. This figure shows that when the controller is off, severe symmetric LCO
can be observed in the straight and level flight segments and milder asymmetric
Figure 4.10. Helicopter Euler angles for a complex maneuver simulation
44
Figure 4.11. Relative cable angles for a complex maneuver simulation
LCO in the right level turn. When the controller was on, the oscillations in these
segments were damped, providing stability in short time.
The perturbations in the load were similar to those in Figure 4.11. When the
controller was off, severe self-induced symmetric LCO (with more than 30 degree
peak-to-peak value) can be observed in the roll angle (φC). These self-induced os-
cillations were observed in the straight and level flight segments along with milder
asymmetric LCO for the 180 degrees right level turn. However, as for the case of
the relative cable angles, these LCO where damped when the lateral and longitu-
dinal controllers were on.
4.4 Delayed Controller Activation
A preliminary study showed sensitivity to the controller activation time due to
the nonlinear nature of the system. For this reason a delayed controller activation
analysis was performed. In addition to being a more challenging scenario, it can
45
potentially occur in practice and therefore needs to be analyzed.
4.4.1 Trimmed Cruise Flight with Time-Triggered Controller
Trimmed cruise flight maneuvers were used for analysis of the system behavior for
delayed controller activation following appearance of oscillations. These simpler
maneuvers allowed easier comparisons of the different results obtained. For both
airspeeds tested (25 kt and 97 kt), the controller was turned on at 20 different
consecutive time points during a single cycle of the oscillatory response.
4.4.1.1 Simulation at 25 kt
For this airspeed the cycle analyzed started at t = 26.25 sec and for a time cycle
of T = 6.21 sec the N = 20 time points where the controller was activated were
separated by ∆t = T/N = 0.31 sec.
As expected for this airspeed, the controller performance was similar to the one
Figure 4.12. Relative cable angles results for 25 kt with controllers turned on att = 29.05 sec
46
presented in section 5.2.1 for the 20 different test cases. As an example of the
results obtained, Figure 4.12 shows the response when the controller was turned
on at the peak of the cycle, at t = 29.05 sec, where the controller effectiveness in
this scenario is verified.
4.4.1.2 Simulation at 97 kt
Due to the proximity of 97 kt to the hysteresis effect zone (101kt) and the fact
that turning on the controller during the LCO introduces a perturbation in the
system, it is expected that the results differ depending on the time frame in which
the controller was turned on. The current analysis allowed to observe if in this
scenario the controller stabilized the system. The analyzed cycle used started at
t = 24.43 sec, where the time period was T = 7.54 sec. With N = 20, the time
interval between the points where the controller was turned on was ∆t = T/N =
0.38 sec.
For all the 20 simulations, the controller was able to achieve stability when it
Figure 4.13. Example of excellent result for 97 kt
47
was switched on in the middle of the oscillation. However, as mentioned before,
different results were obtained. To categorize the results, they were divided in three
different sets according to the oscillatory response obtained when the controller was
activated. For simplicity, the sets were named: excellent results, good results, and
adequate results. For the first case, Figure 4.13 shows an example of excellent
results, it can be observed that after the controller was turned on (25.5 seconds)
the system was stabilized quickly. In Figure 4.14, an example of a good result is
shown. For this case, in the roll and yaw angles (φC and ψC) at t = 40 seconds,
it can be seen that the system stabilized after making an abrupt change in the
relative cable angles. This abrupt change was due to hysteresis effect explained in
Chapter 2 and this set of results is characterized by having one abrupt change.
Finally, in Figure 4.15, an example of an adequate result is presented. This set of
results contain the cases in which the perturbation energy was such that the roll
and yaw angles (φC and ψC) abruptly changed two or more times before finally
stabilizing.
Figure 4.14. Example of good result for 97 kt
48
Figure 4.15. Example of adequate result for 97 kt
Figure 4.16. Time-triggered controller results summary for an airspeed of 97 kt
In Figure 4.16 the results obtained for the 20 different time points in which the
controller was turned on are summarized. In this figure it can be observed that the
effect of the controller activation time presents a lower impact when the controller
49
is turned on in the green round dots. Those are the recommended moment for
which the controller should be turned on in order to obtain the best performance
and avoid large oscillations. The blue square dots present the points in which
the controller was turned on and good results were obtained. Finally, the red
pentagram points present the results where more than one large oscillation was
presented when the controller was turned on.
It should be noted that despite the differences in the times required for oscillations
decay, the controller was able to achieve stability in all the cases tested.
4.5 Turbulent Air Simulations
To further test the controller performance in more demanding conditions, simula-
tions in turbulent air were executed. With this objective in mind, wind turbulence
was generated with the Dryden Wind Turbulence Model and added to the load
and helicopter airspeed during the simulation. As mentioned in Chapter 3, the
wind turbulence was generated for two different altitudes (1000 ft for low altitude
and 4000 ft for medium/high altitude) and three different intensities of turbulence
(light, moderate, and severe intensity). The turbulence model parameters used in
each simulation can be observed in Table 3.1.
4.5.1 Trimmed Cruise Flight
For the trimmed cruise flight, simulations for 97 kt airspeed are presented here
because of the LCO present when the controller was turned off. The simulation
scenario was the same as that presented in the previous sections, with a doublet
and an initial “push” perturbation that was used for exciting the symmetric LCO.
The maneuver duration for the constant airspeeds was increased to 200 seconds in
order to verify that the continued perturbations provided by the turbulence did
not destabilize the coupled system when the controller was on.
50
4.5.1.1 Light Level of Turbulence
In Figure 4.17, the relative cable angle results for a constant airspeed of 97 kt and
a low altitude (σ = 2.5 ft/s) are shown. In this figure, the severe symmetric LCO
can be observed after the initial perturbation when the controller was off. Close
to 140 seconds after the simulation started, the LCO fade due to a lower value
in the load airspeed as a consequence of the continuous perturbation provided by
the turbulence. However, with the controller on, the results did not present LCO
during the entire simulation.
On the other hand, Figure 4.18 presents the relative cable angles results for a
medium/high altitude. In this case, when the controller was off the LCO were
present for around 50 seconds before they were damped. Once again with the
controller on, no LCO were observed during the entire simulation.
From these results it can be observed that although the LCO is finally disappearing
when the controller is off, having large oscillations even for low periods of time
Figure 4.17. Cruise flight at low altitude with light turbulence intensity and 97 ktairspeed
51
Figure 4.18. Cruise flight at medium/high altitude with light turbulence intensity and97kt airspeed
creates a ride quality problem and significantly increases pilot’s workload, which is
a safety of flight issue. It can be also be concluded that the controllers stabilized
the system when light intensity turbulence was present. However, the continuous
perturbation introduced by the turbulence produced small oscillations when the
controller was on, which were not seen when the controller was off and the LCO
were damped.
4.5.1.2 Moderate Level of Turbulence
Figures 4.19 and 4.20 presents the relative cable angles obtained when the simula-
tion was executed with moderate turbulence and for low altitude and medium/high
altitude, respectively.
For a low altitude (Figure 4.19) and when the controller was off, LCO were ob-
served from the initial perturbation to 130 seconds, when they faded due to the
effects of the continuous perturbation in the load airspeed. Unlike in the previous
52
Figure 4.19. Cruise flight at low altitude with moderate turbulence intensity and 97kt airspeed
Figure 4.20. Cruise flight at medium/high altitude with moderate turbulence intensityand 97 kt airspeed
53
case, the higher turbulence intensity produced small oscillations that can be ob-
served after the LCO faded. When the controller was on, no LCO were observed.
However, jumps between the asymmetric branches of the isolated load (section 3.2)
where observed during the simulation.
For the case of medium/high altitude (Figure 4.20) and the controller off, the rela-
tive cable angles present LCO during the first 25 seconds of the simulation. For the
rest of the simulation some jumps were seen along some oscillations that took place
in the range between 100 seconds and 150 seconds. However, with the controller
on, the system did not present severe symmetric LCO but the small oscillations
observed with light turbulence become milder asymmetric LCO.
As mentioned in Section 2.6, the cargo load width span was used for the wind
turbulence model. With this, the worst case scenario in which all the turbulence
energy was concentrated in a smaller span was used. By using the rotor span, the
results obtained were slightly different, as can be observed in Figure 4.21 for the
case of medium/high altitude with moderate turbulence intensity at 97 kt airspeed.
Figure 4.21. Cruise flight at medium/high altitude with moderate turbulence intensityand 97 kt airspeed (rotor span)
54
Figure 4.22. Cruise flight at medium/high altitude with moderate turbulence intensityand 97 kt airspeed (40 minutes simulation)
Longer duration simulations were executed in order to verify the behavior of the
controller when LCO appeared during the simulation as a product of the continu-
ous perturbation provided by the turbulence. Figure 4.22 present the relative cable
angles for a simulation of 2400 seconds (40 minutes). In this figure, short duration
LCO in three different time frames can be observed. The first from 0 seconds to
30 seconds, the second from 340 seconds to 380 second, and the last from 1320
seconds to 1390 seconds. Figures 4.23-4.25 present the relative roll cable angle
and the load airspeed for each one of these time frames. In these figures, it can
be observed that the LCO were originated by an abrupt increase and reduction
(doublet) of the load airspeed when it was higher than 99 kt (hysteresis zone). On
the other hand, when the airspeed falls below 96 kt (where the coupled system is
stable) the LCO faded. These figures also showed no presence of LCO when the
controller was on, just a large transitory oscillations as for the case in Figure 4.24.
55
Figure 4.23. Relative roll Euler angle and load airspeed for the first LCO observed in40 minutes simulation
Figure 4.24. Relative roll Euler angle and load airspeed for the second LCO observedin 40 minutes simulation
56
Figure 4.25. Relative roll Euler angle and load airspeed for the third LCO observed in40 minutes simulation
4.5.1.3 Severe Level of Turbulence
In Figures 4.26 and 4.27 the relative cable angles for the severe level of turbulence
at low altitude and medium/high altitude, respectively, can be observed. In both
cases, when the controller was off, no LCO were observed due to the high level
of turbulence, only transitory oscillations were detected. When the controller was
on no LCO were detected, however the transitory oscillations were also seen in
this case. It is important to note that the controller was not designed to provide
suppression of transient oscillations. All in all, for this particular case of turbulence,
the impact of the controller is small.
4.5.2 Complex Maneuver
Of all the test scenarios presented previously, the complex maneuver was the most
demanding scenario and was therefore even more challenging when wind turbulence
57
Figure 4.26. Cruise flight at low altitude with severe turbulence intensity and 97 ktairspeed
Figure 4.27. Cruise flight at medium/high altitude with severe turbulence intensityand 97 kt airspeed
58
was included. For the following simulation results the scenario used is the one
described in section 4.3, where no perturbation other than the wind turbulence
was applied.
4.5.2.1 Light Level of Turbulence
For this level of turbulence, Figure 4.28 presents the relative cable angles for the
low altitude case. Like in the case in which no turbulence was present, with the
controller off, self-induced LCO were present in the first segment of cruise level
flight (between 21 seconds and 90 seconds). However, the turbulence level at the
end of the simulation damped the LCO for the second segment of cruise level flight
(from 130 seconds to 200 seconds). For the 180◦ level turn segment (90 seconds
to 130 seconds) milder asymmetric oscillations were observed. On the other hand,
when the controller was on, the LCO in the cruise level flight and in the 180◦
level turn were damped. Nevertheless, when the second cruise level flight segment
started, large symmetric oscillation were observed (at 130 seconds) but they were
Figure 4.28. Complex maneuver at low altitude with light turbulence intensity
59
Figure 4.29. Complex maneuver at medium/high altitude and light turbulence intensity
damped by the controller, achieving stability at the end of the simulation.
In Figure 4.29, the results for the medium/high altitude can be observed. In this
case, when the controller was off, the severe symmetric LCO were only observed
in the first cruise level flight segment but they were damped by the intensity of
the turbulence before this segment concluded. As in the previous case, milder
asymmetric LCO were observed in the level turn segment, however, for this case
the oscillations amplitude were higher. Contrarily, when the controller was on, no
symmetric or asymmetric LCO were observed. However, as in the previous case,
when the 180◦ level turn segment was finished a large transient oscillation was
observed, but it was damped faster than in the low altitude case.
4.5.2.2 Moderate Level of Turbulence
For the case of low altitude with a moderate level of turbulence, the results are
presented in Figure 4.30. Here, it can be observed that the intensity level of turbu-
lence was such that no severe symmetric LCO were observed when the controller
60
Figure 4.30. Complex maneuver at low altitude and moderate turbulence intensity
Figure 4.31. Load airspeed at low altitude for moderate turbulence intensity
was off; only the milder asymmetric oscillation during the level turn segment were
present. However, when the controller was on it presented transient oscillations
during the cruise level flight segments, but it was able to subside the asymmetric
61
LCO during the 180◦ level turn.
In order to understand the oscillations observed, Figure 4.31 shows the load air-
speed as a function of time for this simulation. It can be seen that at t =
140 seconds the load airspeed was less than 95 kt and in less than ten seconds
the load was moving at 101 kt, entering the hysteresis zone. This change in the
airspeed was the cause of the large oscillation that started at t = 140 seconds.
It can also be observed that the significant variations in airspeed kept the load
within the hysteresis zone for an important part of the segment, generating the
large oscillations presented in Figure 4.30.
For the case of medium/high altitude, the relative cable angle results can be ob-
served in Figure 4.32. The results when the controller was off present no severe
symmetric LCO, only transient oscillations in the level turn segment. When the
controller was on, no LCO was observed in the cruise level flight and the transient
oscillations in the level turn segment were subsided. However, small oscillations
were observed in the cruise level flight along with large transient oscillations at
the beginning and the end of the turn level flight segment. Figure 4.33 presents
the load airspeed for the case of medium/high altitude. In this figure, the large
oscillations that can be observed in Figure 4.32 around 100 seconds correspond to
portion in which the load airspeed is equal or greater than 100 kt, which is the
hysteresis zone. The same conclusions can be arrived for the oscillations observed
around 140 seconds. However, besides all these oscillations presented for this level
of turbulence, the controller managed to avoid the presence of severe symmetric
LCO for low and medium/high altitude.
62
Figure 4.32. Complex maneuver with moderate turbulence intensity at medium/highaltitude
Figure 4.33. Load airspeed at medium/high altitude for moderate turbulence intensity
63
4.5.2.3 Severe Level of Turbulence
Figures 4.34 and 4.35 presents the relative cables angles for low altitude and medi-
um/high altitude, respectively. From these figures, it can be observed that no
improvement was provided by the controllers in any of these cases. However, as in
the previous cases, no severe symmetric LCO were observed when the controller
was on.
Figure 4.34. Complex maneuver at low altitude with severe turbulence intensity
64
Figure 4.35. Complex maneuver at medium/ high altitude with severe turbulenceintensity
65
Chapter 5 |Conclusions and Future Works
5.1 Conclusions
Stabilization of a test slung load at high airspeeds was achieved by using a relative
cable angle feedback to the primary flight control system. The airspeed scheduled
control systems was evaluated under different maneuvers and turbulence level from
which the following conclusions can be drawn:
1. The lead/lag relative cable angle feedback strategy can be used for load
stabilization in forward flight.
2. The scheduled controller approach by linearization of the nonlinear model
proved to be a feasible way to improve stability for low speeds, and provide
stability for high airspeeds.
3. For the ideal case where no turbulence was present, the controller was able
to stabilize the system for the conditions in which LCO were persistent. For
lower airspeeds, it was able to improve the stability of the coupled system
by increasing the damping ratio of the load pendulum modes.
4. The effectiveness of the controller usually depends on the time in which it
was turned on. However, the use of relative cable angles feedback always pro-
66
vided stabilization when the controller was turned on during the oscillatory
response.
5. The controller was able to respond well for light and moderate turbulence
levels by quickly damp the LCO; however, transient oscillations were ob-
served.
6. In the vicinity of the hysteresis zone, persistent excitation provided by at-
mospheric turbulence is able to generate/fade LCO by changing the load
airspeed.
7. In general, the controller is effective in providing load stability a complex
maneuver. In ideal conditions (no turbulence) the airspeed scheduled con-
troller presented significant improvements by quickly damping LCO. For the
case of light/moderate turbulence, LCO at the beginning of the simulation
were damped by the controller but after that the improvements due to the
controller were not significant.
8. For the severe turbulence case, the controller did not present significant im-
provements for straight and level flight and for the complex maneuver. Fur-
ther, as the turbulence omits the appearance of sustained instabilities, the
stability of the system is generally sufficient without the controller. Still,
these are considered extreme test conditions that can possibly be avoided by
changing the flight level.
9. In any of the simulations with wind turbulence the controller prevented the
development of sustained LCO.
5.2 Future Work
Future work can be conducted to improve the stability of the system for airspeeds
in the hysteresis zone (between 99kt and 102 kt). For this objective, combining
67
relative cable angle feedback with a different active stabilization technique (such as
an active cargo hook) can be studied. It is also advisable, using the advantage of
having validated models, use nonlinear controllers methods like model predictive
control (MPC).
On the other hand, future research can also be aligned with the next generation
of helicopters which are able to flight at velocities exceeding 200 kt. By using
models for compound helicopters as the Piasecki X-49 or for tilt rotor aircrafts as
the V-22 Osprey, new control systems can be designed for larger loads moved at
higher speeds.
Load stabilization feasibility can also be check for using relative cable angles feed-
back in a dual point carriage configuration.
68
Appendix A|First Principles Physical Model
A.1 Introduction
A first principles physical model was designed to analyze the feasibility of the
research objectives. The model is a reduced lateral dynamic model of a UH-60
Black Hawk GenHel model and a CONEX cargo container with stabilizing fins
at 33 degrees with respect to the side box faces (both described in Chapter 2),
which Dr. Enciu provided for this research. This appendix explains the helicopter
model reduction, its stability augmentation system, and the roll relative cable angle
feedback designed to increase the stabilization of the helicopter and load system.
A.2 Helicopter and Load Reduced Lateral Models
The reduced lateral model was obtained by taking into account the forces and
moments applied in the system that can be observed in Figure A.1. The model
was obtained by using lagrangian mechanics, linearize the equation of motion for
an airspeed of u0 = 100 kt (168.8 ft/s), and then express the model in a state-space
form as can be observed in equation (A.1):
x = Ax +Bu (A.1)
69
Figure A.1. Force and moments for the reduced lateral dynamic model
where:
A =
Yv Yp 0 g −µg Fr − u0
Lv Lp 0 0 0 LrYv−FLv
l− Lv Yv − Lp FLv 0 − g
l(1+µ) 0
0 1 0 0 0 0
0 0 1 0 0 0
Nv Np 0 0 0 Nr
(A.2)
B =
Yδa Yδr
Lδa Lδr
−Lδa −Lδr
0 0
0 0
Nδa Nδr
(A.3)
70
and µ = mL/mH . The velocity of the system was defined as u0 = 168.8 ft/s, l is
the length of the cable, g = 32.174 ft/s2 is the gravity acceleration, the parameter
Y is the aerodynamic force applied to the helicopter in the yh direction, L and N
are the aerodynamic moments about the xh and the zh axes (Figure A.1, where
xh is defined by the right hand rule), respectively, and finally, the parameter FL is
the aerodynamic force acting on the load in the yh direction. For the parameters
Y, L, N, and FL, the subindex indicates the variable to which the parameter was
differentiated (Yv = ∂Y/∂v). Finally, the state vector was:
x = [vy, pH , pL, φH , φL, rH ]T (A.4)
and the control variables:
u =
δlatδdir
(A.5)
A.2.1 Model for Slow State Variables
To obtain the parameters for the model in equation (A.1) an UH-60 Black Hawk
GenHel non-linear model was used. The state variables from this model are pre-
sented in equation A.6:
X = [u, v, w, p, q, r, φ, θ, ψ, XN , YE, ZD,
β0, βls, βlc, β0, βls, βlc, λ0, λls, λlc]T
(A.6)
The state vector was divided to state variables related to fast and slow dynamics.
The fast dynamics are associated with the rotor state variables (from β0 to λlc)
and the slow dynamics are related to the first 12 state variables (from u to ZD).
71
In this way, equation (A.1) can be expressed as:
xsxf
=
Ass Asf
Afs Aff
xsxf
+
Bs
Bf
u (A.7)
By taking into account that the variables with fast dynamics will be stabilized
faster than the state variables from slow dynamics then, for steady-state, it is
reasonable to assumed that xf = 0, and from equation (A.7):
xf = 0 = Afsxs + Affxf +Bfu (A.8)
xf = −(A−1ff )Afsxs − Asf (A−1
ff )Bfu (A.9)
With this result, the slow state variables will be:
xs = Assxs + Asfxf +Bsu (A.10)
xs = Assxs − Asf (A−1ff )Afsxs − Asf (A−1
ff )Bfu+Bsu (A.11)
xs =[Ass − Asf (A−1
ff )Afs]
xs +[Bs − Asf (A−1
ff )Bf
]u = Asxs +Bsu (A.12)
Finally, equation (A.12) was used as the linearized state variable model for this
analysis, where the slow state variables expressed as xs are:
xs = [v, p, r, φ]T (A.13)
And the control variables:
u =
δlatδdir
(A.14)
By proceeding in the same way with the wind tunnel validated model of a load
(which is explained in Chapter 2), the parameters for the equations (A.2) and
72
(A.3) were obtained.
A.3 Helicopter Stability Augmentation System
In order to obtain a stable helicopter system a stability augmentation system
(SAS) was needed. By using the isolated helicopter model for the slow dynamics
from equation (A.12), where its parameters were obtained from a UH-60 Black
Hawk GenHel model, the matrices As and Bs of the model were obtained for the
lateral dynamics with the state variables in equation (A.13). The obtained model
corresponded to a MIMO model with two inputs given by δlat and δdir (see equation
(A.14)). By using the root locus technique two proportional feedback loops were
designed for the SAS. The first one between the input δdir and the yaw rate (r)
and the second between the input δlat and roll Euler angle (φ).
Figure A.2 presents the root locus when the loop between δdir and the yaw rate
was closed. In it, it can be observed that the stabilization design was oriented to
improving the stability of the Dutch roll modes by increasing the damping ratio
Figure A.2. SAS design: Root locus for yaw rate feedback
73
from ζ = 0.157 to ζ = 0.954 by using a gain of Kr = −39.2. However, the increase
of the damping ratio of these poles moved the unstable spiral mode even more
to the right, making this mode more unstable. In order to fix this, the next loop
closed was between δlat and the roll Euler angle, designed to move this pole as much
as possible into the left half plane. Figure A.3, present the root locus diagram for
this case, where the new pole constellation was obtained with a gain of Kφ = 5.9,
and making the system stable. With this SAS, the inputs to the helicopter were
redefined as can be seen in Figure A.4, where:
δp = δdir −Krr δa = δlat −Kφφ (A.15)
In Figure A.5, the displacement of the poles with the different controllers that
integrate the SAS can be observed with thicker blue crosses. These crosses mark
the original location of the helicopter poles, before the relative cable angle feedback
was applied.
Figure A.3. SAS design: Root locus for roll angle feedback
74
Figure A.4. Helicopter block diagram with SAS
A.4 Control System for Helicopter-Load System
The current model configuration obtained in the previous section is one of a reduced
lateral dynamics for a helicopter UH-60 Black Hawk with a designed SAS. In this
section, a control system based on the relative roll cable angles (RCA) for the
helicopter and load system is designed to ensure the stability of this system. For
Figure A.5. Root locus diagram for the helicopter and load system
75
this model the relative roll cable angles were defined as follow:
φC = φL − φH (A.16)
Figure A.5 shows the root locus diagram for the helicopter and load system, where
the transfer function in equation (A.17) was used to displace the poles and improve
the stability:
TRCA(s) = −7.813 [0.81 s+ 1] (A.17)
It can be noticed in Figure A.5 that for the original configuration the system was
stable with a damping ratio of ζ = 0.218. With the compensator added, this
damping ratio was increased to ζ = 0.837, an increase of 384% in damping ratio.
Finally, Figure A.6 presents the final block diagram for the helicopter and load
system with the relative roll cable angle feedback.
Figure A.6. Helicopter and load system with relative roll cable angle feedback
[1] Ronen, T., Bryson, A. E., and Hindson, W. S., “Dynamics of a Helicopter witha Sling Load,” AIAA Atmospheric Flight Mechanics Conference, Williams-burg, VA, August 18-20, 1986.
[2] Lusardi, J. A., Blanken, C. L., Braddom, S. R., Cicolani, L. S., and Tobias, E.L., “Development of External Load Handling Qualities Criteria,” AmericanHelicopter Society 66th Annual Forum Proceedings, Phoenix, AZ, May 11-132010.
[3] Gera, J., and Farmer, S.W., “A Method of Automatically Stabilizing Heli-copter Sling Loads,” NASA TN D-7593, 1974
[4] Watkins, T. C., Sinacori, J. B., and Kesler, D. F., “Stabilization of Exter-nally Slung Helicopter Loads [Final Report, 1 Jul. 1972 - 31 Oct. 1973],”USAAMRDL-TR-74-42, August 1974.
[6] Asseo, S. J., and Whitbeck, R. F., “Control Requirements for Sling-Load Sta-bilization in Heavy Lift Helicopters,” Journal of the American Helicopter So-ciety, Vol. 18, (3), July 1973, pp. 23-31.
[7] Micale, E. C., and Poli, C., “Dynamics of Slung Bodies Utilizing a RotatingWheel for Stability,” Journal of Aircraft, Vol. 10, (12), 1973, pp. 760-763.
[8] Feaster, L. L., “Dynamics of a Slung Load,” PhD Thesis, Department of Me-chanical and Aerospace Engineering, Massachusetts University, Amherst, June1975.
[9] Hamers, M., and Bouwer, G., “Flight Director For Helicopter with SlungLoad,” 30th European Rotorcraft Forum, Marseilles, France, September 14-16,2004.
98
[10] Hamers, M., and Bouwer, G., “Helicopter Slung Load Stabilization Using aFlight Director,” American Helicopter Society International 60th Annual Fo-rum, Grapevine, TX, June 1-3, 2005.
[11] Hamers, M., “Flight Director for Handling of Helicopter Sling Loads,” 31stEuropean Rotorcraft Forum, Florence, Italy, September 13-15, 2005.
[12] Hamers, M., Von Hinuber, E., and Richter, A., “Flight Director for Slung LoadHandling - First Experiences on CH53,” 33rd European Rotorcraft Forum,Kazan, Russia, September 11-13, 2007.
[13] Krishnamurthi, J. and Horn, J.F., “Helicopter Slung Load Control UsingLagged Cable Angle Feedback,” Journal of the American Helicopter Society,vol. 60, no. 2, 2015.
[14] Ottander, J. A., and Johnson, E. N., “Precision Slung Cargo Delivery onto aMoving Platform,” AIAA Modeling and Simulation Technologies Conference,AIAA Paper 2010-8090, 2010. doi:10.2514/6.2010-8090
[15] Ivler, C.M., Powell, J.D., Tischler, M.B., Fletcher, J.W., Ott, C, “Design andFlight Test of a Cable Angle Feedback Flight Control System for the RASCALJUH-60 Helicopter,” Journal of the American Helicopter Society, vol. 59, no.4, 2014.
[16] Patterson, B., Ivler, C.M., Hayes, P., “External Load Stabilization ControlLaws for an H-6 Helicopter Testbed,” Proceedings of the American HelicopterSociety 70th Annual Forum, Montreal, Canada, May 2014.
[17] Patterson, B., Enns, R., King, C., Kashawlic, B., Mohammed, S., Lukes, G.,and The Boeing Company, “Design and Flight Test of a Hybrid ExternalLoad Stabilization System for an H-6 Helicopter Testbed,” Presented at theAmerican Helicopter Society, 71st Annual Forum, Virginia Beach, Virginia,May 5-7, 2015.
[18] Raz, R., Rosen, A., Carmeli, A., Lusardi, J., Cicolani, L. S., and Robinson,D., “Wind Tunnel and Flight Evaluation of Passive Stabilization of a CargoContainer Slung Load,” Journal of the American Helicopter Society, Vol. 55,(3), July 2010, pp. 0320011- 03200118.
[19] Cicolani, L., Ivler, C., Ott, C., Raz, R., and Rosen, A., “Rotational Stabiliza-tion of Cargo Container Slung Loads,” American Helicopter Society Interna-tional 69th Annual Forum, Alexandria, VA, May 21-23, 2013.
[20] Enciu, K., and Rosen, A., “Nonlinear Dynamical Characteristics of Fin-Stabilized Underslung Loads,” AIAA Journal, Vol. 53, (3), March 2015, pp.723-738.
99
[21] Enciu, J., Singh, A, and Horn, J. F., âĂIJStabilization of External Loads inHigh Speed Flight Using an Active Cargo Hook,âĂİ 43rd European RotorcraftForum, Milan, Italy, September 12-15, 2017
[22] Enciu, K., and Rosen, A., “Aerodynamic Modeling of Fin Stabilized Under-slung Loads,” Aeronautical Journal, Vol. 119, (1219), September 2015, pp.1073-1103.
[23] Nayfeh, A. H., and Balachandran, B., “Applied Nonlinear Dynamics: Analyt-ical, Computational, and Experimental Methods,” Wiley-VCH Verlag GmbHand Co. KGaA, Weinheim, 1995.
[24] Strogatz, S. H., “Nonlinear Dynamics and Chaos”, Perseus Books, Reading,1994.
[25] Wiggins, S. (2003) Introduction to Applied Nonlinear Dynamical Systems andChaos, Springer, New York.
[26] “Dynamical Systems Toolbox,” Coetzee, E., 2011,https://www.mathworks.com/matlabcentral/fileexchange/32210-dynamical-systems-toolbox [retrieved 1 March, 2012].
[27] “AUTO-07P, Software Package,” Computational Mathematicsand Visualization Laboratory, C. U., Montreal, Canada, 2007,http://indy.cs.concordia.ca/auto/ [retrieved March 1, 2012].
[28] Howlett, J. J., “UH-60A Black Hawk Engineering Simulation Program: Vol-ume I - Mathematical Model,” SER 70452 (NASA Contractor Report 166309),December 1981.
[29] Padfield, G. D. (1966) Helicopter Flight Dynamics: The Theory and Applica-tions of Flying Qualities and Simulation Modelling, AIAA Inc., WashingtonDC.
[30] Stevens, B. L., Lewis, F. L., Johnson, E. N., “Aircraft Control and Simulation:Dynamics, Controls Design, and Autonomous Systems,” third edition, Wiley-Blackwell, 2015.
[31] Pitt, D. M., and Peters, D. A., “Theoretical Prediction of Dynamic InflowDerivatives,” Vertica, Vol. 5, (1), pp. 21-34.