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Rotorcraft Flight Control Design with Alleviation of

Unsteady Rotor Loads

Umberto Saetti

PhD Candidate

Joseph F. Horn

Professor

Department of Aerospace Engineering

The Pennsylvania State University

University Park, PA 16802

Tom Berger

Aerospace Engineer

Mark B. Tischler

Senior Technologist

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

.

I. INTRODUCTION

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 [7].

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 [8], [9], [10]. 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. [9], [10], 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 [11]. Recently, harmonic

decomposition models have been combined with redundant

control effectors and rotor state feedback to further improve

load alleviation [12]. Although these studies demonstrated

considerable reduction of vibratory loads in maneuvering

ﬂight, the control action appeared to deteriorate the handling

qualities.

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

(CONDUIT R

) and design methods of Ref. [13] 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 [1].

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. [11]:

˙x =F(ψ)x+G(ψ)u(1a)

y=P(ψ)x+R(ψ)u(1b)

where ψis the rotor azimuth angle. The state and output

vectors of the LTP system are:

xT=xT

RB xT

R(2a)

yT=xT

RB PLL(2b)

where:

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)

where:

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

analysis:

x=x0+

N

X

i=1

xic cos iψ +xis sin iψ (4a)

u=u0(4b)

y=y0+

L

X

i=1

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. [9], the LTP model is transformed into

an approximate high-order LTI model:

X=AX +BU (5a)

Y=CX +DU (5b)

where:

XT=xT

0xT

1cxT

1s. . . xT

Nc xT

Ns (6a)

U=u0(6b)

YT=yT

0yT

1cyT

1s. . . yT

LcyT

Ls(6c)

are respectively the augmented state, control, and output vec-

tors.

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 [14]. 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

states:

XT

s=xT

RB0(7a)

XT

f=xT

R0xT

RB1cxT

R1c

· · · xT

RB4sxT

R4s(7b)

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:

YT

s=xT

RB0PLL0PLL1cPLL1s· · · PLL4s(8)

Following the derivation in Ref. [11], a new reduced-order

system is obtained:

˙

Xs=ˆ

AXs+ˆ

BU (9a)

Ys=ˆ

CXs+ˆ

DU (9b)

The rotor loads are predicted with sufﬁcient accuracy using

the 9-state approximation of the high-order LTI model, as

demonstrated in Ref. [11]. 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:

pcmd

δlatff

(s) = Lδlat

s−Lp

(10a)

qcmd

δlonff

(s) = Mδlon

s−Mq

(10b)

rcmd

δpedff

(s) = Nδped

s−Nr

(10c)

where the stability and control derivatives are pulled from the

9-state model. The command ﬁlters are 1st order linear models:

pcmd

δlat

(s) = kδlat

τps+ 1 (11a)

qcmd

δlon

(s) = kδlon

τqs+ 1 (11b)

rcmd

δped

(s) = kδp ed

τrs+ 1 (11c)

(11d)

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. [13]. Turn coordination and turn compensation laws are

incorporated in the feed-forward path of the control system

[15].

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:

J=Zt

0XT

sQXs+UTRUdτ (12)

The state weighting matrix Qand control weighting matrix R

are obtained by directly constraining the output through the

following relations:

Q=ˆ

CTˆ

Qˆ

C(13a)

R=ˆ

R+ˆ

DTˆ

Qˆ

D(13b)

TABLE I: Command ﬁlter gains.

Parameter Units Value

kδlat deg/(s-%) 0.90

kδlon deg/(s-%) 0.45

kδped deg/(s-%) 36.9

where ˆ

Qand ˆ

Rare diagonal matrices. The diagonal elements

of ˆ

Qand ˆ

Rare formed by the penalties on the outputs and

inputs, respectively:

ˆ

Q= diag wT

RB wT

PLL(14a)

ˆ

R= diag (wU)(14b)

where:

wRB is the penalty vector on the rigid-body stetes,

wPLL is the penalty vector on the pitch link load harmon-

ics, and

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

also studied.

First, the LQR weights are optimized with CONDUIT R

to

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

ωprad/s 3

ωqrad/s 4.5

ωrrad/s 2

TABLE III: Stability and control derivatives.

Parameter Units Value

Lp1/s -2.9560

Mq1/s -1.3061

Nr1/s -0.3855

Lδlat rad/(s-%) 0.0976

Mδlon rad/(s-%) 0.0242

Nδped rad/(s-%) -0.1526

TABLE IV: Equivalent delays.

Parameter Units Value

τφs 0.055

τθs 0.136

τψs 0.025

(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

acceleration.

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 [16]. 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

frequencies.

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

frequencies.

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

contributors.

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

harmonics.

Fig. 8: Gradient of the diagonal terms of the of the controls

penalty matrix with respect to the weights on the pitch link

load harmonics.

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 [17]. 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 [13]. 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

alleviation.

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

[16]. 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

[18] 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

load alleviation.

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

harmonics.

Fig. 14: Closed-loop angular response to a longitudinal stick

doublet.

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 [12]. 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

link load.

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.

VI. CONCLUSION

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

Q.

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

R.

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

commands.

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

handling qualities.

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.

VII. ACKNOWLEDGMENTS

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

thereon.

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

Aviation Development Directorate or the U.S Government.

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LOAD ALLEVIATING CONTROL, M.S. Thesis, The Pennsylvania State

University, December 2014.

[2] Geiger, B. R., Flight Control Optimization on a Fully Compounded Heli-

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