Flight Simulation and Control of a Helicopter Undergoing RotorChord Extension Morphing

Jayanth KrishnamurthiGraduate Research Assistant

Rensselaer Polytechnic InstituteTroy, NY 12180

Farhan GandhiRedfern Professor of Aerospace Engineering

Rensselaer Polytechnic InstituteTroy, NY 12180

ABSTRACTThe current study focuses on flight simulation and control of a helicopter undergoing rotor chord morphing.A model-following dynamic inversion controller with inner and outer loop control laws (CLAWS) is imple-mented and chord extension is introduced as an additional feedforward component to the inner loop CLAW.Simulation results based on a chord-morphing variant of the UH-60A Black Hawk helicopter at 20,000 lbsgross weight are presented. From the baseline rotor blade, the chord is increased from 63% to 83% of therotor span by means of a trailing-edge plate (TEP) extension at a deployment angle of 2 degrees. Chordmorphing at sea-level and hot-and-high conditions are considered. The controller is shown to regulate theoperating state of the aircraft well over the nominal morphing duration of 60 seconds and also for reduceddurations down to 15 seconds. Differences between baseline and morphed states are discussed. In addition,the performance of the controller with respect to rate of morphing is evaluated and the effect of asynchronousmorphing is also considered.

NOTATION

A System matrixB Control matrixc Elemental blade chord (ft)C Output matrixCl ,Cd Elemental lift, drag, and moment coefficientsCmdL,dD Elemental lift, drag, and moment (lbs)dMdr Length of blade element (ft)D Direct feedthrough matrixe Error vectorg Gravitational acceleration (ft/s2)KC Collective feedforward gainKD Derivative gainKI Integral gainKP Proportional gainp,q,r Body-frame rotational velocities (rad/s)Qe Engine torque (ft-lbs)u Control vectoru,v,w Body-frame translational velocities (ft/s)U∞ Elemental free-stream velocity (ft/s)VX ,VY Inertial velocities (ft/s)VZx State vectory Output vector

Presented at the AHS 72nd Annual Forum, West PalmBeach, Florida, May 17–19, 2016. Copyright © 2016 bythe American Helicopter Society International, Inc. Allrights reserved.

X ,Y,Z Inertial positions (ft)Xu,Xv Speed stability derivatives (1/s)Yu,Yvβ Rotor flapping angle (rad)δ Control input (%)∆() Change in quantityε Trailing-edge-plate extension (%)ζ Damping ratioη TEP deployment angle (deg)θ Pitch attitude (rad)λ Inflow ratioν Pseudo-commandρ Air density (slugs/ft3)τ Time constant (sec)φ Roll attitude (rad)χ f Engine fuel flow (lbm/s)ψ Yaw attitude (rad)ωn Natural frequency (rad/s)Ω Rotor rotational speed (rad/s)()lat Lateral input/component()1s()long Longitudinal input/component()1c()coll Collective input/component()0()ped Pedal input/component()0T R

()tht Throttle input()d Differential component()1 Primary control inputs/components()2 Morphing control inputs/components

1

()r Reduced-order()cmd Commanded value()re f Reference value()inner Pertaining to the inner loop CLAW()outer Pertaining to the outer loop CLAW

INTRODUCTIONWith the optimum rotor geometry known to vary de-pending on the operating state, a fixed-geometry rotorcan perform optimally in a specific set of conditions withsignificant penalties in other conditions, or alternatively,represent a compromise design with adequate but sub-optimal performance in most conditions. Recently, therehas been significant interest in rotor morphing, or recon-figuration, to enhance performance in diverse operatingconditions, as well as expand the flight envelope and op-erational flexibility of rotary-wing aircraft. Although ro-tor morphing faces substantially greater challenges thanmorphing in fixed-wing aircraft due to a smaller availablearea in which to fit the actuators and morphing mecha-nisms, requirement for these to operate in the presenceof a large centrifugal field, and requirement for powertransfer to the rotating system, the potential pay-off iseven greater. Among the various methods of rotor mor-phing considered in the literature, rotor chord extensionmorphing (Refs. 1–5) is advantageous when the aircraftis operating in stall-dominant conditions. In Ref. 2, itwas shown that for a UH-60A Black Hawk Helicopter,chord extension could reduce rotor power requirementsby as much as 18% at high gross weight and altitude.The study also showed increases of 18 knots in maximumspeed capability, 1500 lbs. in maximum gross-weight ca-pability, and 1800 ft. in maximum altitude, with chordextension. The ability to selectively extend the rotorblade chord in stall-dominant conditions is advantageousover using fixed-geometry, wide-chord rotor blades as thelatter results in undesirable profile drag penalties at mod-erate operating conditions (where the aircraft is not nearthe envelope boundary and susceptible to stall). A num-ber of different rotor chord extension mechanisms havebeen considered in the literature to demonstrate feasi-bility of the concept, as seen, for example, in Refs. 3–5.The studies described on rotor chord morphing have thusfar focused broadly on quantifying potential performancebenefits and possible implementation methods. However,transient behavior and control of the aircraft during thechord morphing process has thus far received no atten-tion. A helicopter undergoing chord morphing will natu-rally tend to leave its trimmed flight condition. In orderfor the aircraft to maintain its current operating condi-tion (speed, altitude, heading etc.), compensatory pri-mary control inputs would be required. Recently, Ref. 6addressed this gap in knowledge for rotor span morph-ing. That study focused on the design and application ofa model-following dynamic inversion controller to main-tain the aircraft’s current operating state during rotor

span morphing. The current study follows Ref. 6 andfocuses on application of the controller for rotor chordmorphing. Simulation results are provided for a UH-60ABlack Hawk helicopter in forward flight to demonstratethe effectiveness of the controller during morphing, andthe differences between the baseline and morphed statesare discussed as well. The controller’s effectiveness is alsoconsidered with respect to rate of morphing and asyn-chronous morphing.

SIMULATION MODELA simulation model of the UH-60A Black Hawk has beendeveloped in-house, which is a derivative of Sikorsky’sGenHel model (Ref. 7). The model includes a non-linear,blade element representation of a single main rotor witharticulated blades using airfoil table look-up. The bladesthemselves are approximated to be rigid, undergoing ro-tations about an offset flapping hinge. The lag degree offreedom is neglected. The 3-state Pitt-Peters dynamicinflow model (Ref. 8) is used to represent the inducedvelocity distribution on the rotor disk. The tail rotorforces and torque are based on the closed-form Baileyrotor model (Ref. 9), with the inflow distribution cal-culated using the uniform component of the Pitt-Petersmodel. The rigid fuselage and empennage (horizontaland vertical tail) forces and moments are implementedas look-up tables based on wind tunnel data from theGenHel model. A simple 3-state generic engine modelgiven by Padfield (Ref. 10) is used for the propulsion dy-namics, with the governing time constants approximatedbased on the GenHel engine model.

x = f (

x ,

u ) (1)

y = g(

x ,

u )

where y is a generic output vector. The state vector,

x , is given by

x = [u,v,w, p,q,r,φ ,θ ,ψ,X ,Y,Z, (2)

β0,β1s,β1c,βd , β0, β1s, β1c, βd ,λ0,λ1s,λ1c,λ0T R

Ω,χ f ,Qe]T

The state vector comprises of 12 fuselage states (3 bodyvelocities (u,v,w), 3 rotational rates (p,q,r), 3 attitudes(φ ,θ ,ψ), and 3 inertial positions (X ,Y,Z), 11 rotor states(4 blade flapping states (β0,β1s,β1c,βd) and their deriva-tives in multi-blade coordinates, and 3 rotor inflow states(λ0,λ1s,λ1c)), tail rotor inflow state (λ0T R), and 3 propul-sion states (rotational speed (Ω), engine fuel flow (χ f )and engine torque (Qe). The control input vector is givenby

u =

[δlat ,δlong,δcoll ,δped ,δtht

]T (3)

and is comprised of lateral, longitudinal, and collectivestick inputs to the main rotor, pedal input to the tailrotor, and throttle input to the engine.

2

Baseline Model Validation

The baseline simulation model was validated against atrim sweep of flight test and GenHel data (Ref. 11), for agross weight of 16000 lbs and altitude of 5250 ft. For val-idation purposes alone, elastic twist deformations on theblades, based on an empirical correction in the GenHelmodel (Ref. 7), were incorporated to improve the correla-tion of the simulation model. Figure 1 shows representa-tive results and the baseline simulation model correlateswell with both flight test and GenHel. For the designof control laws, the nonlinear equations of motion werelinearized using numerical perturbation at specific oper-ating conditions. The linearized version of Equation 1can be written as

∆x = A∆

x +B∆

u (4)

∆y =C∆

x +D∆

u

Validation of the linear model with GenHel and flightdata (Ref. 12) is shown in Figure 2 for hover and 80 knotsforward flight, for a gross weight of 15350 lbs at sea level.The model correlates fairly well in the frequency rangeof 0.5-10 rad/s, as shown.

Variable Chord Rotor Blade

The simulation model is now modified to incorporatechord morphing on the blades, based on prior work re-ported in Refs. 2, 13. A schematic of the mechanism isillustrated in Figure 3, taken from Ref.2. As shown inthe figure, chord extension is achieved by means of anextendable trailing-edge plate (TEP), where the lengthof extension, ε, is given as a percent of the nominal airfoilchord and the angle of deflection, η , is measured relativeto the chord line. The chord extension is implemented be-tween 63% and 83% span on the UH-60A blade. Refs. 2and 13 point out that the extension of the TEP alters thesectional aerodynamic coefficients through the increasedchord length and the change in the resulting airfoil pro-file. The sectional aerodynamic coefficients (Cl ,Cd ,Cm)utilized in this study are normalized with respect to theextended chord. Figure 4 shows the lift and moment co-efficients of the baseline SC-1094R8 airfoil and modifiedversions incorporating a TEP extension of ε = 20% anddeflection angles of η = 0, η = 2, and η = 4 degrees forMach 0.4. They are derived using a Navier-Stokes com-putational fluid dynamics (CFD) code and presented inmore detail in Ref. 13. In this study, a deflection angleof η = 2 degrees is used throughout the simulations (seesection on results). The elemental lift, drag, and moment

are then given by

dL =12

ρU2∞(c+ ε)Cldr (5)

dD =12

ρU2∞(c+ ε)Cddr

dM =12

ρU2∞(c+ ε)2Cmdr

where ρ, and U∞ are the density and elemental freestream velocity. With this modified blade, an additionalchord morphing input is specifically introduced into thedynamics given by Equation 1. The equations of motionnow become

x = f

(x ,

u 1,

u 2

)(6)

y = g

(x ,

u 1,

u 2

)where u1 is now the primary input vector given by Equa-tion 3 and u2 is the morphing input vector given by

u 2 = ε (7)

Correspondingly, the linear model for the baseline air-craft given by Equation 4 now becomes

∆x = A∆

x +B1∆

u 1 +B2∆

u 2 (8)

∆y =C∆

x +D1∆

u 1 +D2∆

u 2

where B1 and B2 are the control matrices that correspondto the primary and morphing input vectors, respectively.

CONTROL SYSTEM DESIGN

The design of the control system is based on model fol-lowing linear dynamic inversion (DI) (Ref. 14). Modelfollowing concepts are widely used in modern rotorcraftcontrol systems for their ability to achieve task-tailoredhandling qualities via independently setting feed-forwardand feedback characteristics (Ref. 15). In addition, thedynamic inversion controller typically does not requiregain scheduling since it takes into account the nonlinear-ities of the aircraft (i.e. a model of the aircraft is builtinto the controller). It is thus suitable for a wide rangeof flight conditions (Ref. 14).

A schematic of the overall control system is shownin Figure 5. The control system is effectively split intoinner and outer loop control laws (CLAWS). In design-ing the CLAWS, the full 26-state linear model given byEquation 8 was reduced to an 8-state quasi-steady model.Firstly, the rotor RPM degree of freedom (Ω) is assumedto be regulated via the throttle input determined by theRPM Governor, with the remaining propulsion states (χ fand Qe) coupling only with Ω. Therefore, the propulsionstates and throttle input are truncated from the linear

3

model. Secondly, since the rotor dynamics are consider-ably faster than the fuselage dynamics, they can essen-tially be considered as quasi-steady states and folded intothe fuselage dynamics (Ref. 10), which reduces compu-tational cost. The resulting system is an effective 8-statequasi-steady model whose state and control vectors aregiven by

∆x r = [∆u,∆v,∆w,∆p∆q,∆r,∆φ ,∆θ ]T (9)

∆u 1r =

[∆(δlat) ,∆

(δlong

),∆(δcoll) ,∆

(δped

)]T

∆u 2 = [∆ε]T

In this reduced-order model, the output vector is setup such that it contains only the states themselves or con-tains quantities which are a function of only the states.Therefore, the matrices D1 and D2 given in Equation 8are eliminated from the model structure. In addition,note that while the controller uses a reduced-order linearmodel, its performance was ultimately tested with thefull nonlinear model given by Equation 6.

Inner Loop CLAW

A diagram of the inner loop CLAW is shown in Figure 6.In the inner loop, the response type to pilot input is de-signed for Attitude Command Attitude Hold (ACAH) inthe roll and pitch axis, where pilot input commands achange in roll and pitch attitudes (∆φcmd and ∆θcmd) andreturns to the trim values when input is zero. The heaveaxis response type is designed for Rate Command HeightHold (RCHH), where pilot input commands a change inrate-of-climb and holds current height when the rate-of-climb is zero. The yaw axis response type is designedfor Rate Command Direction Hold (RCDH), where pilotinput commands a change in yaw rate and holds cur-rent heading when yaw rate is zero. These are based onADS-33E specifications for hover and low-speed forwardflight (V ≤ 45 knots) (Ref. 16).

The commanded values (shown in Figure 6) are givenby

∆y inner,cmd =

∆φcmd∆θcmd∆VZcmd∆rcmd

(10)

They are subsequently passed through command filters,which generate the reference trajectories (∆

y re f ) and

their derivatives (∆y re f ) (see Figure 6). The parame-

ters of the command filter were selected to meet Level1 handling qualities specifications (bandwidth and phasedelay) given by ADS-33E for small amplitude responsein hover and low-speed forward flight (Ref. 16). Ta-ble 1 shows the parameters used in the command filtersin the inner loop CLAW, where the roll and pitch axes

use second-order filters and the heave and yaw axes usefirst-order filters.

Table 1: Inner Loop Command Filter Parameters

Command Filter ωn (rad/sec) ζ τ (sec)Roll 2.5 0.8 -Pitch 2.5 0.8 -Heave - - 2Yaw - - 0.4

In dynamic inversion, the technique of input-outputfeedback linearization is used, where the output equation(∆

y inner in Equation 11) is differentiated until the input

appears explicitly in the derivative (Refs. 14, 17). Theinversion model implemented in the controller uses the8-state vector given by Equation 9. Writing the reduced-order linear model in state space form, we have

∆x r = Ar∆

x r +B1r∆

u 1r +B2r∆

u 2 (11)

∆y inner =Cr∆

x r

where the Ar matrix is 8x8, B1r is 8x4, B2r is 8x1, Crmatrix is 4x8, and the output vector ∆

y inner is 4x1.

Applying dynamic inversion on Equation 11 results inthe following control law

∆u 1r =

[CrAk−1

r B1r

]−1(

ν −[CrAk

r

]∆x r

−[CrAk−1

r B2r

]∆u 2

)(12)

where k = 2 for the roll and pitch axes, and k = 1 forthe heave and yaw axes. The term

[CrAk−1

r B2r]

∆u 2 is an

additional feedforward component due to the morphinginput. The process of feeding the morphing control intothe inversion is similar to applications of DI for aircraftwith redundant controls (Refs. 19,20).

The term ν is known as the ”pseudo-command” vec-tor or an auxiliary input vector, shown in Figure 6. Thepsuedo-command vector is a sum of feedforward and feed-back components. It is defined as

ν =

νφ

νθ

νVZ

νr

= ∆y re f +[KP KD KI ]

ee∫e dt

(13)

where the error vector, denoted as e (see Figure 6) isgiven by

e = ∆y re f −∆

y inner (14)

The variables KP,KD, and KI indicate the proportional,derivative, and integral gains in a PID compensator.

4

Note that the application of dynamic inversion inEquation 11 is carried out in the body reference frame.In Equation 13, the pseudo-commands νφ , νθ , and νr areprescribed in the body frame, while νVZ is in the iner-tial frame. Therefore, a transformation was introducedto change the heave axis pseudo-command to the bodyframe (Ref. 18) prior to inversion, and is given by

νw =νVZ +uθ cosθ

cosθ cosφ(15)

If the reduced-order model given by Equation 11 werea perfect representation of the flight dynamics, the re-sulting system after inversion would behave like a set ofintegrators and the pseudo-command vector would notrequire any feedback compensation. In practice, however,errors between reference and measured values arise dueto higher-order vehicle dynamics and/or external distur-bances and therefore require feedback to ensure stability.

The PID compensator gains are selected to ensurethat the tracking error dynamics due to disturbances ormodeling error are well regulated. A typical choice forthe gains is that the error dynamics be on the same orderas that of the command filter (ideal) model for each axis.Table 2 shows the compensator gain values used in eachaxis.

Table 2: Inner Loop Error Compensator Gains

KP KD KI

Roll 10 (1/sec2) 5.75 (1/sec) 4.6875 (1/sec2)Pitch 10 (1/sec2) 5.75 (1/sec) 4.6875 (1/sec2)Heave 1 (1/sec) 0 0.25 (1/sec)Yaw 1 (1/sec) 0 6.25 (1/sec)

Finally, the vector ∆u 1r from Equation 12 is added

to the trim values of u 1r before being passed into the

control mixing unit of the aircraft.

Outer Loop CLAW

In order to maintain trimmed forward flight, an outerloop autopilot is designed to regulate lateral (VY ) andlongitudinal (VX ) ground speed while the aircraft is mor-phing. A schematic of the outer loop CLAW is shown inFigure 7. Note that the overall structure is similar to theinner loop. The response type for the outer loop is trans-lational rate command, position hold (TRC/PH), wherepilot inputs command a change in ground speed and holdcurrent inertial position when inputs are zero. With theimplementation of the outer loop, the pilot input does notdirectly command ∆φcmd and ∆θcmd as in the inner loopCLAW. Rather, they are indirectly commanded throughthe desired ground speeds (see Figure 5).

The commanded values in the outer loop (shown in

Figure 7) are given by

∆y outer,cmd =

[∆VXcmd∆VYcmd

](16)

and passed through first-order command filters. Similarto the inner loop, the parameters of the command filterare selected based on ADS-33E specifications in hoverand low-speed forward flight (Ref. 16).

Table 3: Outer Loop Command Filter Parameters

Command Filter τ (sec)Longitudinal (VX ) 2.5

Lateral (VY ) 2.5

In the outer loop, to achieve the desired groundspeeds, the required pitch and roll attitude commandinput to the inner loop (Equation 10) is determinedthrough model inversion (Ref. 19). A simplified linearmodel of the lateral and longitudinal dynamics is ex-tracted from Equation 11 and is given by

∆x r,outer = AT RC∆

x r,outer +BT RC

[∆φcmd∆θcmd

](17)

∆y outer =

[∆VX∆VY

]=CT RC∆

x r,outer

with AT RC, BT RC, and ∆x r,outer defined as

AT RC =

[Xu XvYu Yv

](18)

BT RC =

[0 −gg 0

]∆x r,outer =

[∆u∆v

]where u and v are body-axis velocities, Xu,Xv,Yu, and Yvare stability derivatives and g is the gravitational acceler-ation. Applying dynamic inversion on this model resultsin the following control law[

∆φcmd∆θcmd

]=

(CT RCBT RC)−1

(ν −CT RCAT RC∆

x r,outer

)(19)

The pseudo-command vector, ν =

[νVX

νVY

], is defined simi-

larly to Equation 13, with the error dynamics also definedin a manner similar to that of the inner loop. The PIDcompensator gains for the outer loop are given in Table 4.

Table 4: Outer Loop Error Compensator Gains

KP (1/sec) KD KI (1/sec)Lateral (VY ) 0.8 0 0.16

Longitudinal (VX ) 0.8 0 0.16

5

RPM Governor

Rotor morphing is certainly expected to impact the rota-tional degree of freedom (Ω). On the UH-60A and in theGenHel model, the rotor RPM is regulated by a complex,nonlinear engine Electrical Control Unit (ECU) (Ref. 7).Since a simplified modeling of the propulsion dynamicsis used in this study, a simple PI controller, with col-lective input feed-forward from the inner loop CLAW, isimplemented to regulate the rotor RPM via the throt-tle input, which is mapped to the fuel flow state (χ f ).The controller is similar in structure to the one given byKim (Ref. 21). A schematic of the RPM Governor isshown in Figure 8. In Figure 8, the gains KP and KI wereempirically selected. The collective feed-forward gain,KC, was approximated using a mapping between throt-tle and collective input, based on trim sweep results ofthe baseline model. Table 5 shows the gains used in thegovernor.

Table 5: RPM Governor Gains

KP (%/(rad/sec)) KI (%/(rad/sec)) KC (nd)Ω 6 1.5 1.2

RESULTS

Sea Level - 40 and 120 knots

The aircraft was trimmed at speeds of 40 and 120 knotswith a gross weight of 20,000 lbs at sea-level. The chordbetween 63% and 83% of the blade span was increased by20% at a deployment angle of η = 2 degrees over 60 sec-onds. Figures 9 to 12 show simulation results at 40 knots.The aircraft steady thrust and main rotor torque (Fig-ure 9(c)) associated with the chord extension. The thrust(Figure 9(b)) is observed to be regulated well and mainrotor torque (Figure 9(c)) increases slightly over the du-ration of morphing, primarily due to higher profile dragon the blade sections with the extended TEP. Figure 10shows the variation in primary controls and aircraft rolland pitch attitude and Figure 11 shows the variation inrotor flapping, over the duration of the morphing. Adecrease of 0.4 degrees in rotor collective pitch (Figure10(c)) is observed because of the chord extension. Thetail rotor pitch (Figure10(d)) increases slightly becauseof the higher rotor torque. The larger lateral force dueto increase in tail rotor thrust and increased roll momentit generates due to its location above the CG affect thelateral force and roll moment equilibrium. Consequently,there is a slight increase in lateral flapping (Figure 11(b))and lateral cyclic pitch (Figure 10(a)), while the roll at-titude remains relatively unchanged (Figure 10(e)). Dueto the tail rotor cant angle on the UH-60A (Ref. 7), theincrease in tail rotor thrust also increases the nose-downpitching moment on the aircraft. Consequently, the for-ward tilt of the tip path plane (Figure 11(c)) reduces

slightly to compensate, with the pitch attitude remain-ing relatively unchanged (Figure 10(f)). Figure 12 showstime histories of the aircraft velocities, which are well reg-ulated by the controller. Recall that the ground speedsVX and VY are regulated by the outer loop and verticalspeed VZ by the inner loop.

Figures 13-14 show simulation results at a high speedof 120 knots, with chord extension over 60 seconds (Fig-ure 13(a)). Figures 13(b) and 13(c) show variation inaircraft steady thrust and torque. Again, thrust is regu-lated well and torque increases over the duration of mor-phing due to higher profile drag with extended chord.Figure 14 shows the variation in primary controls andattitudes. The rotor collective pitch (Figure 14(c)) de-creases again by about 0.4 degrees and trends in the re-maining controls are dictated by the change in requiredtail rotor pitch, as they were at 40 knots. It was verifiedthat the flapping response followed similar trends and in-ertial velocities were regulated well (results not shown inpaper).

6K, 95 °F - 40 knots

The aircraft was trimmed at a speed of 40 knots with agross weight of 20,000 lbs at an altitude of 6000 ft anda temperature of 95 °F (hot and high condition). Thechord was again increased by 20% over 60 seconds (Fig-ure 15(a)). Figures 15(b) and 15(c) show the variation inaircraft steady thrust and main rotor torque associatedwith the chord extension. Thrust is regulated well andthe main rotor torque decreases slightly because of reduc-tions in profile drag associated with the aircraft gettingfurther away from stall. Figure 16 shows the variationin controls and attitudes of the aircraft. The rotor col-lective pitch decreases about 0.6 degrees (Figure 16(c))due to the chord extension. There is a slight reductionin the tail rotor pitch because of the torque decrease,which again affects lateral force and roll moment equi-librium. The lower tail rotor pitch reduces the right lat-eral force and right roll moment, which is counteractedby the slightly reduced roll left attitude (Figure 16(e)),while the lateral flap remains relatively unchanged (Fig-ure 17(b)). Similarly, a lower tail rotor thrust reducesthe nose-down pitching moment, which is counteractedby the slight increase in longitudinal tilt of the tip pathplane (Figure 17(c)), while the pitch attitude remainsrelatively unchanged (Figure 16(f)). The inertial veloci-ties were verified to be regulated well over the durationof morphing (results not shown).

Rate of Morphing and Asynchronous Deployment

The previous sections considered chord extension atdifferent flight conditions. In this section, questions ad-dressed are: (1) the impact of reducing the morphingduration across all four blades and (2) the effect of asyn-chronous morphing across the blades.

6

Figures 18(b)-18(d) show plots of main rotor torqueand cyclic controls for morphing durations of 60, 30, and15 seconds (Figure 18(a)) at 40 knots, sea-level condi-tions. While the transients are slightly sharper for lowermorphing durations, the controller is robust to morph-ing rates and does not require changes to gains or modelupdates.

In Figure 18 (and all preceding simulations) the mor-phing input was applied identically over all four blades.Due to actuator or control system problems, three spe-cific cases of interest are identified where this may notbe so: (1) the chord extension on one of the blades maydeploy to a different magnitude from the others, (2) thechord extension on one of the blades may deploy to thecorrect magnitude but over a longer duration of time,and (3) the chord extension on one of the blades deploysto the correct magnitude and over the correct durationof time but is temporally offset (for example, delayed rel-ative to the other blades). While case 1 is expected toresult in persistent 1/rev vibratory loads associated withan unbalanced rotor, cases 2 and 3 would be expected toresult in some transient loads and due to unbalance dur-ing the morphing process, which eventually die out whenall the blades have eventually reached the commandedsteady state chord extension amplitudes.

Case 3 is examined here and Figure 19(a) shows thedeployment of the TEP delayed by 15 seconds for oneof the blades and Figures 19(b)-19(d) show the air-craft thrust and cyclic swashplate controls. The con-troller commands a small 1/rev input in addition to thesteady component to the swashplate. In the simula-tion model, the outputs from the control mixing blockgo through actuator servos (shown in Figure 5). Theseare second-order low-pass filters, based on the GenHelmodel (Ref. 11), with a bandwidth of approximately 11.3Hz. While this high bandwidth allows the 1/rev inputs inthe fixed-frame to pass through without much attenua-tion, such inputs may not be desirable due to prohibitivepower requirements to actuate the swashplate.

CONCLUSIONSThe present study focused on the flight simulation andcontrol of a helicopter undergoing rotor chord morph-ing. A model-following dynamic inversion controller isimplemented with inner and outer loop control laws(CLAWS) and chord morphing is introduced as an addi-tional feed-forward input to the inner loop CLAW. Simu-lation results are presented for a chord-morphing variantof a UH-60A Black Hawk helicopter at a gross weightof 20,000 lbs. Starting with the baseline rotor blade,the chord is increased from 63% to 83% by means of atrailing-edge plate (TEP) extension at a deployment an-gle of η = 2 degrees. From the results presented, thefollowing conclusions can be drawn:

1. The dynamic inversion (DI) controller regulates theoperating state of the aircraft well over the nominal

60 second duration of chord morphing and maintainsits effectiveness even when the duration is reducedto 15 seconds.

2. Chord morphing at sea-level conditions resulted inslightly increased torque requirements due to addi-tional profile drag on the blade sections with the ex-tended chord. In the hot-and-high condition, chordmorphing slightly reduces torque due to lower pro-file drag as the rotor’s operating state moves furtheraway from stall.

3. The required rotor collective pitch reduces by about0.4 degrees in sea-level conditions and by about 0.6degrees at hot-and-high conditions. The trends inthe cyclic pitch controls and flapping response aregoverned by changes in the tail rotor thrust, whichaffects the lateral and longitudinal equilibrium of theaircraft.

4. Asynchronous morphing on the blades resulted insmall 1/rev inputs to the swashplate from the con-troller. Despite the small amplitude, such inputsmay not be desirable due to power limitations.

Author contact:Jayanth Krishnamurthi, krishj@rpi.eduFarhan Gandhi, gandhf@rpi.edu

REFERENCES1Leon, O., Hayden, E., and Gandhi, F., “Rotorcraft

Operating Envelope Expansion Using Extendable ChordSections,” , Proceedings of the 65th AHS InternationalForum and Technology Display, Grapevine, TX, May 27-29, 2009.

2Khoshlahjeh, M., and Gandhi, F., “Extendable ChordRotors for Helicopter Envelope Expansion and Perfor-mance Improvement,” Journal of the American Heli-copter Society, Vol. 59, (1), January 2014.doi: 10.4050/JAHS.59.012007

3Barbarino, S., Gandhi, F., and Webster, S., “Designof Extendable Chord Sections for Morphing HelicopterRotor Blades,” Journal of Intelligent Material Systemsand Structures, Vol. 22, (9), June 2011, pp. 891–905.doi: 10.1177/1045389X11414077

4Gandhi, F., and Hayden, E., “Design, Development,and Hover Testing of a Helicopter Rotor Blade Chord Ex-tension Morphing System,” Smart Materials and Struc-tures, Vol. 24, (3), 2015.doi: 10.1088/09645-1726/24/3/035024

5Moser, P., Barbarino, S., and Gandhi, F., “HelicopterRotor-Blade Chord Extension Morphing Using a Cen-trifugally Actuated Von Mises Truss,” Journal of Air-craft, Vol. 5, (5), 51, pp. 1422–1431.doi: 10.2514/1.C032299

7

6Krishnamurthi, J., and Gandhi, F., “Flight Simula-tion and Control of a Helicopter Undergoing Rotor SpanMorphing,” , Proceedings of the 41st European Rotor-craft Forum, Munich, Germany, Sept. 1-4, 2015.

7Howlett, J.J., “UH-60A Black Hawk Engineering Sim-ulation Program: Volume I - Mathematical Model,”NASA CR-166309, 1981.

8Peters, D.A., and HaQuang, N., “Dynamic Inflow forPractical Applications,” Journal of the American Heli-copter Society, Vol. 33, (4), October 1988, pp. 64–66.

9Bailey, F.J., “A Simplified Theoretical Method of De-termining the Characteristics of a Lifting Rotor in For-ward Flight,” NACA Report 716, 1941.

10Padfield, G.D., Helicopter Flight Dynamics: The The-ory and Application of Flying Qualities and SimulationModeling, Blackwell Publishing, second edition, 2007.

11Ballin, M.G., “Validation of a Real-Time Engi-neering Simulation of the UH-60A Helicopter,” NASATM-88360, 1987.

12Fletcher J.W., “A Model Structure for Identificationof Linear Models of the UH-60 Helicopter in Hover andForward Flight,” NASA TM-110362, NASA, 1995.

13Bae, E.-S., and Gandhi, F., “CFD Analysis of High-Lift Devices on the SC-1094R8 Airfoil,” , American Heli-copter Society 67th Annual Forum Proceedings, VirginiaBeach, VA, May 3-5, 2011.

14Stevens, B.L. and Lewis, F.L., Aircraft Control andSimulation, John Wiley & Sons, second edition, 2003.

15Tischler, M.B. and Remple, R.K., Aircraft and Ro-torcraft System Identification: Engineering Methods withFlight Test Examples, AIAA, second edition, 2012.

16Anonymous, “Aeronautical Design Standard Perfor-mance Specification, Handling Qualities Requirementsfor Military Rotorcraft,” , ADS-33E-PRF, USAAM-COM, 2000.

17Slotine, J.E. and Li, W., Applied Nonlinear Control,Prentice-Hall Inc., 1991.

18Horn, J.F., and Guo, W., “Flight Control Design forRotorcraft with Variable Rotor Speed,” , Proceedingsof the American Helicopter Society, 64th Annual Forum,Montreal, Canada, April 29-May 1, 2008.

19Ozdemir, G.T., and Horn, J.F., “Simulation Analy-sis of a Flight Control Law with In-Flight PerformanceOptimization,” Proceedings of the American HelicopterSociety 68th Annual Forum, Fort Worth, TX, May 1-3,2012.

20Thorsen, A.T., Horn, J.F., and Ozdemir, G.T., “Use ofRedundant Controls to Enhance Transient Response andHandling Qualities of a Compound Rotorcraft,” Proceed-ings of American Helicopter Society 70th Annual Forum,Montreal, Quebec, May 20-22, 2014.

21Kim, F.D., “Analysis of Propulsion System Dynamicsin the Validation of a High-Order State Space Model ofthe UH-60,” , AIAA/AHS Flight Simulation Technolo-gies Conference, Hilton Head, S.C., August 24-26, 1992.

8

FIGURES

Velocity (knots)

0 50 100 150 200

La

tera

l S

tic

k (

%)

0

20

40

60

80

100

Current Simulation

GenHel (Ref. 11)

Flight Test (Ref. 11)

(a) Lateral StickVelocity (knots)

0 50 100 150 200

Lo

ng

itu

din

al

Sti

ck

(%

)

0

20

40

60

80

100

Current Simulation

GenHel (Ref.11)

Flight Test (Ref. 11)

(b) Longitudinal Stick

Velocity (knots)

0 50 100 150 200

Pit

ch

Att

itu

de

(d

eg

)

-10

-5

0

5

10

Current Simulation

GenHel (Ref.11)

Flight Test (Ref. 11)

(c) Pitch AttitudeVelocity (knots)

0 50 100 150 200

Ma

in R

oto

r P

ow

er

(hp

)

0

500

1000

1500

2000

2500

Current Simulation

GenHel (Ref.11)

Flight Test (Ref. 11)

(d) Main Rotor Power

Fig. 1: Baseline UH-60A Trim Sweep Validation

9

Frequency (rad/s)

Ma

gn

itu

de

(d

B)

-100

-50

0

10-1 100 101

Ph

as

e (

de

g)

-180

-90

0

90

180

270

Current Linear Model

GenHel

Flight Test (Ref. 12)

(a) Hover - ∆p/∆δlat

Frequency (rad/s)

Mag

nit

ud

e (

dB

)

-50

-40

-30

-20

-10

0

10-1 100 101

Ph

ase (

deg

)

-180

-135

-90

-45

0

Current Linear Model

GenHel

Flight Test (Ref. 12)

(b) Hover - ∆q/∆δlong

Frequency (rad/s)

Mag

nit

ud

e (

dB

)

-30

-20

-10

10-1 100 101

Ph

ase (

deg

)

-180

-135

-90

-45

0

45

90

Current Linear Model

GenHel

Flight Test (Ref. 12)

(c) 80 knots - ∆p/∆δlat

Frequency (rad/s)

Mag

nit

ud

e (

dB

)

-40

-30

-20

-10

0

10-1 100 101

Ph

ase (

deg

)

-180

-90

0

90

180

Current Linear Model

GenHel

Flight Test (Ref. 12)

(d) 80 knots - ∆q/∆δlong

Fig. 2: Baseline UH-60A Frequency Response Validation

(a) TEP Extension - Airfoil (b) TEP Extension - Blade

Fig. 3: Chord Extension Mechanism, Ref. 2

10

Angle of Attack (deg)

-10 -5 0 5 10 15 20

Cl

-1

-0.5

0

0.5

1

1.5

SC-1094R8 Baseline (CFD)

ǫ = 20%, η = 0 deg (CFD)

ǫ = 20%, η = 2 deg (CFD)

ǫ = 20 %, η = 4 deg (CFD)

(a) Lift CoefficientAngle of Attack (deg)

-10 -5 0 5 10 15 20

Cd

0

0.05

0.1

0.15

0.2

0.25

SC-1094R8 Baseline (CFD)

ǫ = 20%, η = 0 deg (CFD)

ǫ = 20%, η = 2 deg (CFD)

ǫ = 20 %, η = 4 deg (CFD)

(b) Drag Coefficient

Angle of Attack (deg)

-10 -5 0 5 10 15 20

Cm

-0.2

-0.1

0

0.1

0.2

SC-1094R8 Baseline (CFD)

ǫ = 20%, η = 0 deg (CFD)

ǫ = 20%, η = 2 deg (CFD)

ǫ = 20 %, η = 4 deg (CFD)

(c) Moment Coefficient

Fig. 4: SC-1094R8 - Aerodynamic coefficients for baseline and extendable TEP for Mach 0.4, Ref. 13

Fig. 5: Overview of the Control System

11

Fig. 6: Inner Loop CLAW

Fig. 7: Outer Loop CLAW

Fig. 8: RPM Governor

12

Time (sec)

0 30 60 90 120

ǫ (

% c

ho

rd)

0

5

10

15

20

(a) TEP ExtensionTime (sec)

0 30 60 90 120

Th

rust

(lb

s)

×104

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

(b) Aircraft Thrust

Time (sec)

0 30 60 90 120

Main

Ro

tor

To

rqu

e (

ft-l

bs)

×104

2.6

2.7

2.8

2.9

3

3.1

3.2

(c) Main Rotor Torque

Fig. 9: Chord Extension at 40 knots, Sea-level - TEP Extension, Thrust, and Torque

13

Time (sec)

0 30 60 90 120

θ1

c (

deg

)

2.1

2.15

2.2

2.25

2.3

2.35

2.4

(a) Lateral Cyclic PitchTime (sec)

0 30 60 90 120

θ1

s (

deg

)

-3

-2.9

-2.8

-2.7

-2.6

-2.5

-2.4

(b) Longitudinal Cyclic Pitch

Time (sec)

0 30 60 90 120

θ0 (

deg

)

15

15.5

16

16.5

17

(c) Collective PitchTime (sec)

0 30 60 90 120

θ0

TR

(d

eg

)

15.5

16

16.5

17

(d) Tail Rotor Pitch

Time (sec)

0 30 60 90 120

φ (

deg

)

-1

-0.9

-0.8

-0.7

-0.6

-0.5

Commanded

Actual

(e) Roll AttitudeTime (sec)

0 30 60 90 120

θ (

deg

)

2.2

2.3

2.4

2.5

2.6

2.7

Commanded

Actual

(f) Pitch Attitude

Fig. 10: Chord Extension at 40 knots, Sea-level - Controls and Attitudes (φ is positive roll right, θ is positive noseup)

14

Time (sec)

0 30 60 90 120

β0 (

deg

)

3

3.5

4

4.5

5

(a) ConingTime (sec)

0 30 60 90 120

β1

s (

deg

)

-0.2

-0.1

0

0.1

0.2

(b) Lateral Flapping

Time (sec)

0 30 60 90 120

β1

c (

deg

)

0.5

0.6

0.7

0.8

0.9

(c) Longitudinal Flapping

Fig. 11: Chord Extension at 40 knots, Sea-level - Flapping

15

Time (sec)

0 30 60 90 120

Vx (

kn

ots

)

35

37.5

40

42.5

45

(a) Longitudinal Ground SpeedTime (sec)

0 30 60 90 120

Vy (

kn

ots

)

-5

-2.5

0

2.5

5

Commanded

Actual

(b) Lateral Ground Speed

Time (sec)

0 30 60 90 120

Vz (

kn

ots

)

-5

-2.5

0

2.5

5

Commanded

Actual

(c) Vertical Speed

Fig. 12: Chord Extension at 40 knots, Sea-level - Inertial Velocities

16

Time (sec)

0 30 60 90 120

ǫ (

%)

0

5

10

15

20

(a) TEP ExtensionTime (sec)

0 30 60 90 120

Th

rust

(lb

s)

×104

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

(b) Aircraft Thrust

Time (sec)

0 30 60 90 120

Main

Ro

tor

To

rqu

e (

ft-l

bs)

×104

2.6

2.8

3

3.2

3.4

3.6

3.8

(c) Main Rotor Torque

Fig. 13: Chord Extension at 120 knots, Sea-level - TEP Extension, Thrust, and Torque

17

Time (sec)

0 30 60 90 120

θ1

c (

deg

)

-0.5

0

0.5

1

1.5

(a) Lateral Cyclic PitchTime (sec)

0 30 60 90 120

θ1

s (

deg

)

-8.5

-8

-7.5

-7

-6.5

-6

(b) Longitudinal Cyclic Pitch

Time (sec)

0 30 60 90 120

θ0 (

deg

)

15.5

16

16.5

17

17.5

18

(c) Collective PitchTime (sec)

0 30 60 90 120

θ0

TR

(d

eg

)

12.5

13

13.5

14

14.5

(d) Tail Rotor Pitch

Time (sec)

0 30 60 90 120

φ (

deg

)

0

0.5

1

1.5

2

Commanded

Actual

(e) Roll AttitudeTime (sec)

0 30 60 90 120

θ (

deg

)

-0.5

0

0.5

1

1.5

Commanded

Actual

(f) Pitch Attitude

Fig. 14: Chord Extension at 120 knots, Sea-level - Controls and Attitudes (φ is positive roll right, θ is positive noseup)

18

Time (sec)

0 30 60 90 120 150

ǫ (

% c

ho

rd)

0

5

10

15

20

(a) TEP ExtensionTime (sec)

0 30 60 90 120 150

Th

rust

(lb

s)

×104

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

(b) Aircraft Thrust

Time (sec)

0 30 60 90 120

Main

Ro

tor

To

rqu

e (

ft-l

bs)

×104

3.2

3.25

3.3

3.35

3.4

(c) Main Rotor Torque

Fig. 15: Chord Extension at 40 knots, 6000 ft, 95 °F. - TEP Extension, Thrust, and Torque

19

Time (sec)

0 30 60 90 120

θ1

c (

deg

)

2.5

2.55

2.6

2.65

2.7

2.75

2.8

(a) Lateral Cyclic PitchTime (sec)

0 30 60 90 120

θ1

s (

deg

)

-4.5

-4.25

-4

-3.75

-3.5

(b) Longitudinal Cyclic Pitch

Time (sec)

0 30 60 90 120

θ0 (

deg

)

18

18.2

18.4

18.6

18.8

19

(c) Collective PitchTime (sec)

0 30 60 90 120

θ0

TR

(d

eg

)

19

19.5

20

20.5

21

(d) Tail Rotor Pitch

Time (sec)

0 30 60 90 120

φ (

deg

)

-1

-0.9

-0.8

-0.7

-0.6

Commanded

Actual

(e) Roll AttitudeTime (sec)

0 30 60 90 120

θ (

deg

)

3.4

3.5

3.6

3.7

3.8

Commanded

Actual

(f) Pitch Attitude

Fig. 16: Chord Extension at 40 knots, 6000 ft, 95 °F. - Controls and Attitudes

20

Time (sec)

0 30 60 90 120

β0 (

deg

)

3

3.5

4

4.5

5

(a) ConingTime (sec)

0 30 60 90 120

β1

s (

deg

)

0

0.1

0.2

0.3

0.4

(b) Lateral Flapping

Time (sec)

0 30 60 90 120

β1

c (

deg

)

1.2

1.25

1.3

1.35

1.4

(c) Longitudinal Flapping

Fig. 17: Chord Extension at 40 knots, 6000 ft, 95 °F. - Flapping

21

Time (sec)

0 30 60 90 120 150

ǫ (

% c

ho

rd)

0

5

10

15

20

60 sec

30 sec

15 sec

(a) TEP ExtensionTime (sec)

0 30 60 90 120 150

Main

Ro

tor

To

rqu

e (

ft-l

bs)

×104

2.7

2.75

2.8

2.85

2.9

2.95

3

60 sec

30 sec

15 sec

(b) Main Rotor Torque

Time (sec)

0 30 60 90 120 150

θ1

c (

deg

)

2.1

2.15

2.2

2.25

2.3

2.35

2.4

60 sec

30 sec

15 sec

(c) Lateral Cyclic PitchTime (sec)

0 30 60 90 120 150

θ1

s (

deg

)

-3

-2.9

-2.8

-2.7

-2.6

-2.5

-2.4

(d) Longitudinal Cyclic Pitch

Fig. 18: Variation in rate of chord morphing - 40 knots, sea-level

22

Time (sec)

0 30 60 90 120 150

ǫ (

% c

ho

rd)

0

5

10

15

20

Blade 1

Blade 2

Blade 3

Blade 4

(a) TEP ExtensionTime (sec)

0 30 60 90 120

Th

rust

(lb

s)

×104

1.8

1.85

1.9

1.95

2

2.05

2.1

2.15

2.2

(b) Aircraft Thrust

Time (sec)

0 30 60 90 120 150

θ1

c (

deg

)

2.1

2.15

2.2

2.25

2.3

2.35

2.4

(c) Lateral Cyclic PitchTime (sec)

0 30 60 90 120 150

θ1

s (

deg

)

-3

-2.9

-2.8

-2.7

-2.6

-2.5

-2.4

(d) Longitudinal Cyclic Pitch

Fig. 19: Asynchronous chord morphing - 40 knots, sea-level

23