Rotorcraft Flight Control Design with Alleviation of
Unsteady Rotor Loads
Joseph F. Horn
Department of Aerospace Engineering
The Pennsylvania State University
University Park, PA 16802
Mark B. Tischler
Aviation Development Directorate
CCDC Aviation & Missile Center
Moffett Field, CA
Abstract—The objective of this paper is to develop helicopter
ﬂight control laws that minimize unsteady rotor loads while
meeting desired handling qualities. These control laws are meant
to act solely through the primary ﬂight controls. First, an
overview on how the harmonic decomposition methodology is
used towards load alleviation control is presented. Next, explicit
model following ﬂight control laws are developed to provide
insight on how the feed-forward and feedback paths can be
used towards load alleviation. Their impact on the handling
qualities is also studied. Finally, the control laws are optimized
with CONDUIT R
The beneﬁts of load alleviation control (LAC) and envelope
cueing have been demonstrated in numerous simulation stud-
ies, Refs. [1-6]. The use of Automatic Flight Control Systems
(AFCS) or active control sticks to alert the pilot to observe
structural constraints can extend the life of critical dynamic
components and reduce operating and support (O&S) costs.
These technologies can also improve handling qualities by
alleviating pilot workload associated with monitoring envelope
limits. Load alleviating controls have been implemented on the
V-22 tilt-rotor aircraft, using cyclic pitch control to reduce in-
plane loads during forward ﬂight maneuvers .
Many of the critical structural limits on rotorcraft are
associated with vibratory loads and fatigue limits. These loads
are strongly inﬂuenced by higher harmonic (greater than
1/rev) dynamics in the rotor systems. These dynamics are not
modelled in the Linear Time Invariant (LTI) dynamic models
normally used for rotorcraft primary ﬂight control design. On
the other hand, Linear Time-Periodic (LTP) models are well-
suited for representing vibratory loads on rotorcraft, including
the dominant Nb/rev vibratory forces and moments at the hub
and associated dynamic components, and they can be derived
directly from the physics-based models. Methods have been
developed for approximating LTP systems using high-order
LTI models , , . The harmonic decomposition method
transforms higher frequency harmonics into states of an LTI
state space model.
The use of harmonic decomposition methods for combined
Higher-Harmonic Control (HHC)/AFCS design has been well-
0Distribution Statement A: Approved for public release.
studied in Refs. , , and has been applied towards
the design of load alleviation control and cueing methods
that act solely through the primarily ﬂight controls (1st har-
monic swashplate control) and AFCS . Recently, harmonic
decomposition models have been combined with redundant
control effectors and rotor state feedback to further improve
load alleviation . Although these studies demonstrated
considerable reduction of vibratory loads in maneuvering
ﬂight, the control action appeared to deteriorate the handling
The objective of this paper is to thoroughly study the effect
of load alleviation on the handling qualities, and to overcome
the shortcomings of the load alleviation control design method-
ology. Speciﬁcally, the Control Designer’s Uniﬁed Interface
) and design methods of Ref.  are used to
optimize controller gains to meet ADS-33E-PRF speciﬁcations
for military rotorcraft while minimizing rotor loads.
The paper is organized as follows. First, an overview
on how the harmonic decomposition methodology is used
towards the design of load alleviation control laws is presented.
Next, explicit model following control laws are developed to
understand how the feed-forward and feedback paths can be
used towards load alleviation. Their impact on the handling
qualities is also studied. The information gathered is used to
optimize the control laws to meet desired handling qualities
while minimizing rotor loads. Finally, conclusions are drawn.
II. DYNA MI CA L MOD EL
A. Nonlinear Models
This investigation uses a FLIGHTLAB R
model of a no-
tional conventional helicopter representative of a UH-60, as
shown in Fig. 1. To accurately model the rotor loads, the
model includes ﬂexible blades with representative in-plane,
out-of-plane, and torsional bending modes, in addition to the
rigid blade ﬂap and lag dynamics. Complete nonlinear aero-
dynamic look-up tables are used for airframe and rotor blade
aerodynamic coefﬁcients. The inﬂow dynamics are described
by a six-state Peters-He inﬂow model. Further details on the
helicopter model are found in .
Fig. 1: UH-60 Black Hawk.
B. Linear Time-Periodic Model
Starting from the nonlinear model, a ﬁrst order LTP system
representative of the periodic rotorcraft dynamics at 120 kts is
obtained, as demonstrated in Ref. :
where ψis the rotor azimuth angle. The state and output
vectors of the LTP system are:
xRB are the rigid-body states,
xRare the higher-order rotor states, and
PLL is the longitudinal load of a reference pitch link.
The rigid-body state vector is given by, in order, the body
velocities u,v,w, the body angular rates p,q,r, and the Euler
angles φ,θ,ψ. The rotor states include inﬂow, rigid ﬂap, lag
and torsion in multi-blade coordinates (MBC), the slowest 11
bending modes also in MBC, and the time derivatives of all
the variables in MBC. The input vector is:
uT= [δlat δlon δped](3)
δlat is the lateral stick,
δlon is the longitudinal sticks, and
δped is the pedal.
The collective stick is omitted as it is not used for the
subsequent control design. The system has a total of 116 states,
14 outputs, and 3 inputs.
C. Harmonic Decomposition Model
The state, input, and output vectors of the LTP system
are decomposed into a ﬁnite number of harmonics via Fourier
xic cos iψ +xis sin iψ (4a)
yic cos iψ +yis sin iψ (4c)
Harmonics up to the 4th are retained for state and the output
(i.e., N=4 in Eqs. 4(a) and 4(c)). However, only the 0th
harmonic of the input vector is retained. This is because the
present study considers solely primary ﬂight control actuation,
thus disregarding any sort of higher harmonic control. In
fact, the desired maximum bandwidth of the control signal
is signiﬁcantly less than the main rotor angular speed. As
demonstrated in Ref. , the LTP model is transformed into
an approximate high-order LTI model:
X=AX +BU (5a)
Y=CX +DU (5b)
1s. . . xT
1s. . . yT
are respectively the augmented state, control, and output vec-
D. Reduced-Order Model
The measurement or estimation of states associated with
the higher-order ﬂap, lead-lag, torsion and inﬂow dynamics
is impractical in real applications. For this reasons, reduced-
order models are derived from the high-order LTI model. The
problem is addressed through residualization, a method based
on singular perturbation theory that accurately models low
frequency dynamics and steady-state, but neglects higher-order
dynamics . The method assumes that the “fast” and stable
states in a system reach steady-state more quickly than the
“slow” states. The state vector is hence divided into fast and
slow components. The slow component comprises the rigid-
body states, whereas the fast component includes the remaining
· · · xT
where RB subscripts denote rigid-body states and Rsubscripts
denote rotor states. The higher-harmonics of the rigid-body
states are truncated from the output because they are impracti-
cal to observe and of negligible amplitude when compared to
their respective 0th harmonic. The output reduces to:
RB0PLL0PLL1cPLL1s· · · PLL4s(8)
Following the derivation in Ref. , a new reduced-order
system is obtained:
The rotor loads are predicted with sufﬁcient accuracy using
the 9-state approximation of the high-order LTI model, as
demonstrated in Ref. . The pitch link load harmonics are
kept in the output to capture the dependence of controls and
rigid-body states on the rotor loads. This model is used in the
control design presented in the next section.
III. CON TRO LL ER DESIGN
A controller is designed to achieve stability and desired
rate-command/attitude-hold (RCAH) response around the roll,
pitch and yaw axes. The controller acts solely through primary
ﬂight controls. This restricts the maximum desired bandwidth
of the input to be considerably less than the main rotor angular
speed. This way, higher-harmonic control is excluded. Note
that the collective stick is left open-loop. The chosen control
strategy is Explicit Model Following. The inverse plant is
based on the inverses of the following set of decoupled 1st
order linear models:
(s) = Lδlat
(s) = Mδlon
(s) = Nδped
where the stability and control derivatives are pulled from the
9-state model. The command ﬁlters are 1st order linear models:
(s) = kδlat
τps+ 1 (11a)
(s) = kδlon
τqs+ 1 (11b)
(s) = kδp ed
τrs+ 1 (11c)
where kδlat ,kδlon , and kδped are the conversion constants from
pilot commands to commanded angular rates, and τp,τq, and
τrare the command ﬁlter time constants. To each command
ﬁlter time constant corresponds a break frequency that is the
inverse of the time constant. This means that ωp= 1/τp,
ωq= 1/τq, and ωr= 1/τr. The commanded responses in
each axis are delayed by τφ,τθ, and τψ, respectively, for
synchronization with the (higher-order) measured responses.
These higher-order dynamics include the computational delays,
actuators, rotor ﬂapping lag, and sensors which cannot be
included in the inverse model without causing actuator satura-
tion. The time delays are calculated following the methods of
Ref. . Turn coordination and turn compensation laws are
incorporated in the feed-forward path of the control system
A linear quadratic regulator (LQR) is used for both feed-
back compensation and load alleviation. The control system
block diagram is shown in Fig. 2. The LQR gains are deter-
mined by using the 9-state model previously derived (Eq. 9).
The cost function that is minimized is:
The state weighting matrix Qand control weighting matrix R
are obtained by directly constraining the output through the
TABLE I: Command ﬁlter gains.
Parameter Units Value
kδlat deg/(s-%) 0.90
kδlon deg/(s-%) 0.45
kδped deg/(s-%) 36.9
Rare diagonal matrices. The diagonal elements
Rare formed by the penalties on the outputs and
Q= diag wT
R= diag (wU)(14b)
wRB is the penalty vector on the rigid-body stetes,
wPLL is the penalty vector on the pitch link load harmon-
wUis the penalty vector on the controls.
The method described allows to transfer the constraints
on each harmonic of the pitch link load response to the
rigid-body states, effectively providing a load limiting control
action based on the feedback of the 0th harmonic rigid-body
states. Most notably, the controller minimizes rotor loads
perturbations from their periodic equilibrium. It follows that
this methodology is well suited for alleviating unsteady loads.
However, it does not affect stationary (trim) loads.
IV. PARAMETRIC STUDY
This section analyzes how the feed-forward and feedback
paths of the controller can be used towards load alleviation.
Speciﬁcally, command model tailoring is examined for the
feed-forward path, whereas tailoring of the LQR weights on
the pitch link load harmonics is explored for the feedback path.
The impact of these two strategies on the handling qualities is
First, the LQR weights are optimized with CONDUIT R
meet a comprehensive set of stability, handling qualities, and
performance speciﬁcations without considering load allevia-
tion. Handling qualities speciﬁcations are taken from ADS-33E
while stability margin requirements of SAE-AS94900 are used.
In particular, the weights on the rigid-body states and controls
are optimized whereas the weights on the pitch link load
harmonics are set to zero and frozen during the optimization.
The linear model used as the plant model for the optimization
is the high-order LTI model previously derived. The controller
thus obtained is referred to as the “baseline” controller. The
command ﬁlters properties for the baseline controller are found
in Tables I and II. The stability and control derivatives used
for the inverse plants are found in Table III. The equivalent
delays are shown in Table IV. The state and control penalties
are reported Tables V and VI, respectively.
Next, the closed-loop frequency responses of the pitch link
load to the commanded angular rates are computed, as shown
in Fig. 3. This is done to understand the sensitivity of the rotor
loads to pilot commands. Commanded angular rates are chosen
in favor of pilot stick commands as they share common units
Fig. 2: Control system block diagram.
TABLE II: Command ﬁlters break frequencies.
Parameter Units Value
TABLE III: Stability and control derivatives.
Parameter Units Value
Lδlat rad/(s-%) 0.0976
Mδlon rad/(s-%) 0.0242
Nδped rad/(s-%) -0.1526
TABLE IV: Equivalent delays.
Parameter Units Value
(rad/s). Results are presented to cover the typical frequency
range of operation for pilots (1-60 rad/s). It appears that the
rotor loads are mostly affected by the pitch rate command in
this particular ﬂight condition (dashed blue line in Fig. 3).
Commanded roll rate is shown to impact the rotor loads more
than the commanded yaw rate, especially at frequencies higher
than 10 rad/s. The parametric study that follows will therefore
concentrate on the roll and pitch axes.
A. Command Model Tailoring
Command ﬁlter break frequencies of the baseline controller
are varied separately for the roll and pitch axes. Figure 4 shows
the closed-loop pitch rate and pitch attitude responses to a
longitudinal stick doublet for varying command ﬁlter break
frequencies. Decreasing command ﬁlter break frequencies cor-
respond to decreasing pitch accelerations. Decreasing pitch
accelerations result in decreasing peak-to-peak pitch link loads,
as shown in Fig. 5. A running mean (or median) is obtained
by taking the sum of the maximum and minimum peaks for
each cycle and dividing by two. The curves that are plotted
are the maximum and minimum peaks minus the median.
It is concluded that command model tailoring effectively
provides load alleviation by limiting the commanded angular
Figure 6 shows the bandwidth and phase delay for varying
command ﬁlter break frequencies. The bandwidth and phase
delay speciﬁcations for forward ﬂight (target acquisition and
tracking) are also reported on the plot . For the roll
axis, decreasing command ﬁlter break frequencies result in
Fig. 3: Closed-loop frequency response of the the pitch link
load to the commanded angular rates.
Fig. 4: Closed-loop pitch rate and pitch attitude responses to
a longitudinal stick doublet for varying command ﬁlter break
decreasing bandwidth. For the pitch axis, decreasing command
ﬁlter break frequencies result in decreasing bandwidth and
increasing phase delay. In general, decreasing command ﬁlter
break frequencies appear to negatively impact the handling
qualities. It is concluded that load alleviation through feed-
forward compensation is effective in providing alleviation of
the rotor loads. However, it comes at the cost of a degradation
in the handling qualities.
B. LQR Weighting Tailoring
Starting from the baseline controller, the LQR weights on
the rigid-body states and controls are frozen while the weights
on the pitch link load harmonics are varied to generate a set of
LQR feedback gain matrices. Figure 7 provides an insight on
Fig. 5: Closed-loop peak-to-peak pitch link load response to
a longitudinal stick doublet for varying command ﬁlter break
Fig. 6: Bandwidth and phase delay speciﬁcations for varying
command ﬁlter break frequencies.
how the weights on the pitch link load harmonics wPLL affect
the rigid-body weights in the state penalty matrix Q. Only
the diagonal terms of the state penalty matrix are shown. It is
evident that constraining the pitch link load harmonics leads to
increased constraints on the roll and pitch rates. The pitch rate
is most affected by the 1st and 2nd cosine harmonics. The roll
rate is most affected by the 1st, 2nd, and 4th sine harmonics. In
general, the pitch rate is affected more severely than the roll
rate. This is expected and is due to the increased sensitivity
of pitch link load to pitch rate, as compared to pitch link load
to roll rate (Fig. 3). Both weights on the body velocities and
the Euler angles are unaffected. Figure 8 provides an insight
on how the weights on the pitch link load harmonics in the
output penalty matrix wPLL affect the weights on the controls
in the controls penalty matrix R. Only the diagonal terms of
the controls penalty matrix are shown. Constraining the pitch
link load harmonics leads to increased penalties mostly on the
longitudinal stick. The 0th and 1st harmonics are the major
Figure 9 provides insight on how the weights on the pitch
Fig. 7: Gradient of the diagonal terms of the states penalty
matrix with respect to the weights on the pitch link load
Fig. 8: Gradient of the diagonal terms of the of the controls
penalty matrix with respect to the weights on the pitch link
link load harmonics in the output penalty matrix wPLL affect
the LQR feedback gains. Only the on-axis gains are shown.
Increasing penalties on the pitch link load harmonics leads to
decreasing LQR on-axis gains. This is particularly evident for
the gains relating the longitudinal stick with pitch attitude and
pitch rate. Although not shown in the plot, the gains relating
the body velocities with the controls are largely unaffected.
These ﬁndings indicate that increasing load alleviation leads
to decreasing pitch axis performance.
Controllers with increasing weights on the pitch link load
harmonics are compared to assess the impact on handling
qualities and controller performance. Figure 10 shows the gain
and phase margins of the broken-loop response for increasing
LQR weights on the pitch link load harmonics. The stability
margin requirements deﬁned in SAE-AS94900 are reproduced
in the plot . Most notably, the roll axis gain and phase
Fig. 9: Gradient of the on-axis LQR gains with respect to the
weights on the pitch link load harmonics.
Fig. 10: Stability margins for varying LQR weights on the
pitch link load harmonics.
margins appear nearly unaffected; however, the pitch axis
gain margin increases with increasing weights. This is better
explained by looking at the crossover frequency, shown in
Fig. 11. The pitch axis crossover frequency rapidly decreases
with increasing weights. Although this leads to a higher gain
margin, it effectively results in an unsatisfactory minimum
crossover frequency . The high sensitivity of the crossover
frequency to increasing LQR weights on the pitch link load
harmonics constitutes a severe limitation in the achievable load
Next, bandwidth and phase delay for increasing weights
on the pitch link load harmonics are shown in Fig. 12. The
bandwidth and phase delay speciﬁcations for forward ﬂight
(target acquisition and tracking) are also reported on the plot
. The roll axis bandwidth and phase delay do not appear to
be particularly affected. However, the pitch axis phase delay
decreases with increasing weights.
Figure 13 show the disturbance rejection bandwidth (DRB)
and peak (DRP) for increasing LQR weights on the pitch
link load harmonics. Similarly to the trend seen for crossover
frequency, the DRB and DRP speciﬁcations are taken from
 and reproduced on the plot. The DRB appears to decreases
Fig. 11: Crossover frequencies for varying LQR weights on
the pitch link load harmonics.
Fig. 12: Bandwidth and phase delay speciﬁcations for
varying LQR weights on the pitch link load harmonics.
with increasing weights on both roll and pitch axes. This leads
to a degradation of handling qualities in the pitch axis for low
weights. This poses another possible limitation in achievable
The observations made for the handling qualities speciﬁ-
cations in the frequency domain are reﬂected in time-domain
simulations. The closed-loop response to a longitudinal stick
Fig. 13: Disturbance rejection bandwidth (DRB) and peak
(DRP) for varying LQR weights on the pitch link load
Fig. 14: Closed-loop angular response to a longitudinal stick
Fig. 15: Closed-loop peak-to-peak pitch link load response to
a longitudinal stick doublet.
doublet input is obtained for the different controllers, as shown
in Fig. 14. It is apparent that increasing LQR weights on the
pitch link harmonics effectively limits the pitch rate response,
which substantiates the ﬁndings in . Figure 15 shows
the resulting load alleviation in terms of peak-to-peak pitch
link load. Since satisfactory minimum crossover frequency
and DRB for the pitch axis are obtained for minimum LQR
weights on the pitch link load harmonics (ωPLL = 1e−4), the
maximum achievable load alleviation for the utility helicopter
conﬁguration is very modest, at least for the baseline controller
that was derived.
This ﬁnding is further substantiated by the frequency
response from a disturbance in the pitch rate to the pitch
link load, as shown in Fig. 16. This particular response is
chosen because, as opposed to the response from longitudinal
stick to pitch link load, it is more representative of the
Fig. 16: Response from angular rates disturbances to pitch
feedback action only of the controller. Since pilots operate in a
frequency range of about 1-60 rad/s, considerations are made
based on that window. Indeed, the magnitude of the response
decreases for increasing LQR weights on the pitch link load
harmonics. However, weights of ωPLL = 1e−4lead to a very
modest reduction. Considering the frequency response from a
disturbance in roll rate to the pitch link load, it is also observed
that increasing LQR weights on the pitch link load harmonics
do not result in any load alleviation.
In conclusion, it appears that load alleviation through
feedback compensation comes at the cost of a degradation in
the handling qualities, particularly in the pitch axis. In order
to achieve signiﬁcant load alleviation while still meeting the
handling qualities requirements, a design margin optimization
of the pitch axis DRB and minimum crossover frequency
should be run on the baseline controller.
V. OPTIMIZATION RE SU LTS
An overall optimization of both the feed-forward and feed-
back paths is run in CONDUIT R
. The optimization is done in
a two-step process. First, a design margin optimization of the
pitch axis DRB and minimum crossover frequency is run on
the baseline controller. In this phase, the LQR weights on the
pitch link load harmonics are set to zero and frozen. Next, the
LQR weights on the pitch link load harmonics are optimized to
meet ADS-33E-PRF speciﬁcations while minimizing the area
under the PLL/qdist frequency response. In this second phase,
the new weights on the rigid body states and controls are frozen
and the LQR weights on the pitch link load harmonics are set
as separate optimization variables.
Figure 17 shows how the area under the PLL/qdist response
is minimized for the optimized LAC controller. This directly
translates to an alleviation in rotor loads, as shown for a pitch
rate doublet in Fig. 18. The handling qualities are all met
for the optimization controller, as shown in Fig. 19. Model
following requirements in the pitch aixs are not Level 1 as the
response of the rotorcraft is actually best modelled by a 2nd
order model in high-speed forward ﬂight. The controller design
Fig. 17: Minimization of the angular rates disturbances to
pitch link load response.
Fig. 18: Closed-loop peak-to-peak pitch link load response to
a longitudinal stick doublet.
has to be modiﬁed accordingly. The penalties on the pitch link
load harmonics for the optimized controller are reported in
Table V. It is concluded that constraining the the rotor load
harmonics in LQR design successfully leads to load alleviation
while still meeting desired handling qualities.
An overview on how the harmonic decomposition method-
ology is used towards load alleviation control was presented.
Next, explicit model following ﬂight control laws were devel-
oped to provide insight on how the feed-forward and feedback
paths can be used towards load alleviation. Their impact on
the handling qualities was also studied. Finally, the control
laws were optimized to minimize unsteady rotor loads while
meeting desired handling qualities. Based on this work, the
following conclusions are drawn.
Fig. 19: Handling qualities for optimized LAC controller.
TABLE V: Weights on the diagonal elements of ˆ
Parameter Units Baseline LAC
uft/s 0 0
vft/s 0 0
wft/s 0 0
prad/s 1.0828e+2 1.0828e+2
qrad/s 3.8252e+2 3.8252e+2
rrad/s 2.0207e+1 2.0207e+1
φrad 6.2138e+2 6.2138e+2
θrad 1.9255e+2 1.9255e+2
ψrad 2.9349e+2 2.9349e+2
PLL0lbs 0 1.1040e−3
PLL1clbs 0 2.6080e−3
PLL1slbs 0 2.3360e−3
PLL2clbs 0 2.2328e−3
PLL2clbs 0 2.6670e−3
PLL3clbs 0 1.7931e−2
PLL3slbs 0 7.0606e−2
PLL4clbs 0 2.3700e−4
PLL4slbs 0 6.5220e−3
TABLE VI: Weights on the diagonal elements of ˆ
Parameter Units Baseline LAC
δlat %7.6736e−2 7.6736e−2
δlon %3.7561e−2 3.7561e−2
δped %3.0299e−1 3.0299e−1
1) Rotor loads in high-speed forward ﬂight are partic-
ularly sensitive to pitch rate commands. Roll rate
commands also affect the rotor loads, but in a minor
way. Rotor loads are relatively insensitive to yaw rate
2) Load alleviation through feed-forward compensation
(command model tailoring) is effective in providing
alleviation of the rotor loads. However, it comes at the
cost of a degradation in bandwidth and phase delay.
3) Load alleviation through feedback compensation
comes at the cost of a degradation in the handling
qualities, particularly in the pitch axis. The pitch
axis disturbance rejection bandwidth (DRB) and min-
imum crossover frequency pose potential limitations
in achievable load alleviation.
4) Optimization of load alleviation ﬂight control laws
with this methodology should be conducted in a
two-step process. First, a design margin optimization
should be run to maximize the pitch axis DRB and
minimum crossover frequency. Next, the LQR penal-
ties on the rotor loads harmonics can be optimized to
maximize load alleviation while meeting the desired
5) The optimized load alleviation controller provided
load alleviation while still meeting the handling qual-
ities requirements. Constraining the higher-harmonics
of the rotor loads within an LQR architecture proved
to be an effective load alleviation strategy.
This research was partially funded by the Government
under Agreement No. W911W6-17-2-0003. The U.S. Gov-
ernment is authorized to reproduce and distribute reprints for
Government purposes notwithstanding any copyright notation
The views and conclusions contained in this document are
those of the authors and should not be interpreted as repre-
senting the ofﬁcial policies, either expressed or implied, of the
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dling Qualities Requirements for Military Rotorcraft, ADS-33-PRF, US-
 SAE, Aerospace - Flight Control Systems - Design, Installation and Test
of Piloted Military Aircraft, General Speciﬁcations for, SAE-AS94900,
 Berger, T., Ivler, C., M., Berrios, M. G., Tischler, M. B., Miller, D. G.,
Disturbance Rejection Handling-Qualities Criteria for Rotorcraft, 72nd
Annual National Forum of the American Helicopter Society, West Palm
Beach, FL, May 16-19, 2016.