A Real-Time Expert Control System For Helicopter Autorotationireal.gatech.edu/wp-content/themes/twentytwelve-child/... · 2015. 12. 29. · JOURNAL OF THE AMERICAN HELICOPTER SOCIETY

JOURNAL OF THE AMERICAN HELICOPTER SOCIETY 60 022008 (2015)

A Real-Time Expert Control System For Helicopter Autorotation

Zachary N Sunberg Nathaniel R Miller Jonathan D Rogerslowast

Graduate Student Assistant ProfessorTexas A amp M University College Station TX Georgia Institute of Technology Atlanta GA

A control algorithm for autonomous helicopter autorotation is proposed and evaluated The algorithm consists of a multi-phase control law with fuzzily defined transitions and provides outputs in the form of collective commands desired forwardspeed and maximum pitch and roll angle limits The algorithm is designed to be used in conjunction with an inner loopvelocity tracking controller A unique feature of the proposed control law is its use of estimated time to ground impact tocompute near-optimal flare trajectories from a wide range of initial conditions The performance of the proposed expertcontrol system is evaluated through six degree-of-freedom simulation of both a full-size helicopter and a small hobby-sizehelicopter and Monte Carlo examples demonstrate robustness to various initial flight conditions Limited flight-test resultsare presented demonstrating suitable performance of the algorithm in realistic disturbance environments

Nomenclature

h altitude above ground level (minusz) ftIR main rotor polar moment of inertia about shaft slug-ft2

[Ic]B moment of inertia matrix about the center of massresolved in the body reference frame slug-ft2

KE kinetic energy (slug-(fts)2)m helicopter mass slugsp q r angular velocity components in body reference frame

radsR main rotor radius ftr radial distance from rotor hub ftu v w mass center velocity components in the body reference

frame ftsx y z mass center position components in a north-east-down

inertial coordinate system ftβ blade flapping angle radβ0 β1c β1s first harmonic blade flapping angle components radη total magnitude of vehicle roll and pitch angles

η equivradic

φ2 + θ2 radηmax maximum limit on total magnitude of roll and pitch

angles radθtr tail rotor collective pitch radθ0 main rotor collective blade pitch radθ1c main rotor lateral cyclic pitch radθ1s main rotor longitudinal cyclic pitch radλi main rotorndashinduced inflow nondimensionalλ0 λc λs component states of induced inflow distribution

nondimensional

lowastCorresponding author email jonathanrogersmegatecheduManuscript received September 2013 accepted August 2014

μsmall membership function defining fuzzy set of small velocitiesφ θ ψ roll pitch and yaw Euler angles radψMR main rotor azimuth angle rad main rotor rotation rate rads

Introduction

When a single engine helicopter encounters engine failure or whenany helicopter suffers a catastrophic transmission or tail rotor failurean autorotative maneuver must be performed to bring the aircraft toa safe landing During autorotation rotor kinetic energy is maintainedby extracting energy from air flowing through the main rotor disk indescending flight The recent rise of autonomous helicopter technologyof various scales has led to new demand for automatic control systems thatcan perform autorotation manuevers autonomously as part of the flightcontrol system Incorporation of an autonomous autorotation controlcapability enhances overall system safety and may improve prospectsfor integration of autonomous helicopters into the National AirspaceSystem on a large scale In manned aircraft an autorotation controllermay be used as part of an avionics system to provide pilot guidancein emergency situations degraded visual environments or in difficultscenarios in which the maneuver is initiated inside the ldquodeadmanrsquos curverdquoregion of the heightndashvelocity (HndashV) diagram (Ref 1)

Autonomous autorotation controllers have been studied by severalinvestigators although few have been fielded in production systems todate An early study of the autorotation problem from an automatic con-trol perspective is provided by Johnson (Ref 2) In this work optimaldescent trajectories and a nonlinear controller using an offline gradientdescent approach are used to minimize the predicted total velocity atimpact but the results are intended to be used for vehicle design ratherthan real-time feedback control Lee et al (Ref 3) improved on thisinitial analysis by adding constraints relating to physical performance

DOI 104050JAHS60022008 Ccopy 2015 The American Helicopter Society022008-1

Z N SUNBERG JOURNAL OF THE AMERICAN HELICOPTER SOCIETY

limits to the optimization problem and evaluating initial conditions wellwithin the heightndashvelocity avoid region This analysis concluded that theflight envelope for safe autorotation can be significantly enlarged usingautomatic control More recently in research focused on autonomous ro-torcraft Hazawa et al (Ref 4) created a traditional proportionalndashintegralcontroller for landing a small helicopter in cases of engine failure Abbeelet al (Ref 5) created a reinforcement learning controller that attempts tomatch trajectories recorded from autorotative descents performed by ahuman pilot Algorithm performance was verified experimentally duringsuccessful autonomous autorotations executed with a small hobby-sizedhelicopter Dalamagkidis et al (Ref 6) developed an autorotation controlsystem based on receding horizon neural network optimization althoughthe controller was limited to vertical autorotations only and was testedin simulation using a simplified one-dimensional dynamic model Thesetests were further restricted in the case of full-scale aircraft to includeonly vehicles modified with a high-energy rotor system (Ref 7) provid-ing a high margin for error in control system performance

Additional research has focused on control automation during specificphases of descent or for vehicle path planning Yomchinda et al (Ref 8)have proposed a path-planning algorithm for the steady-state descentphase whereas Tierney and Langelaan (Ref 9) have presented a methodfor calculating the set of flare entry points from which a helicopter cansafely land Others have developed methods to reduce pilot workloadduring autorotation using simple heuristic criteria that communicate to apilot upon approaching a dangerous state (Ref 10) Recently Bachelderet al (Ref 11) developed an autonomous autorotation controller basedon iterative optimization The control law was implemented in an avion-ics package and was meant to provide pilot cues and guidance duringautorotative descents

Many elements common to previous approaches have limited theirutility in practical systems Reinforcement learning algorithms requireextensive training data that may not be available and since they are tiedto a specific flight platform they are limited in flexibility and scalability toother aircraft Iterative optimization algorithms such as those proposedin Refs 6 8 and 11 require significant computational capability and ingeneral lack convergence guarantees Such iterative algorithms may notbe suitable for certification especially given the time constraints inher-ent in autorotation trajectory generation and the robustness guaranteeslikely to be required Throughout the autorotation control literature ithas been almost universally recognized that computation of a feasibleflare trajectory is one of the most difficult control tasks inherent in themaneuver given the variety of initial flight conditions the presence of ex-ternal disturbances and the high dimensionality of the problem (Ref 9)Especially for low-cost platforms new autorotation control laws areneeded that provide suitable flexibility and robustness while avoidingiterative optimization high-fidelity onboard dynamic models or blackbox reinforcement learning approaches

At the same time significant recent research efforts in the handlingqualities community led by Padfield et al (Refs 12ndash14) have noted theimportance of estimated time to contact with a point or obstacle in a widevariety of pilot maneuvers This value termed optical tau and defined asthe ratio between distance to a certain viewpoint and closing velocityhas been demonstrated to be a critical factor in pilot trajectory trackingevasive maneuvers and pilot-induced oscillation Specifically Jump andPadfield (Ref 15) have shown that during flare maneuvers close to theground pilots adjust the estimated motion tau to ground impact throughcontrol inputs to match a pilot-generated reference value Similarly itis shown here that predicted time to impact with the ground plays animportant role in autorotation control and is the mechanism that providesflexibility in flare trajectory generation and tracking

This paper presents a novel multiphase expert control system forhelicopter autorotation The controller is composed of multiple phases

which are executed sequentially as the autorotation maneuver progressesPhase changes are fuzzily defined and are initiated through altitude andpredicted time-to-impact criteria A novel aspect of the control design isits use of time-to-impact predictions during the flare maneuver and its useof a desired time-to-impact reference value conditioned on the vehiclersquoshorizontal velocity vertical velocity and rotor kinetic energy A set oftuning parameters allows the controller to be applied to a wide set ofhelicopter platforms with minimal structural changes Furthermore thesimplicity of the controller design minimizes computational burden andimproves its prospects for flight certification First the control systemis described in detail followed by a brief description of the simulationmodel used to evaluate controller performance Monte Carlo simulationresults are presented for both the Bell AH-1G helicopter as well as fora small remote-controlled (RC) sized helicopter Finally results from alimited set of flight experiments are provided to demonstrate controllerperformance in a realistic environment

Control Law Formulation

The control law is designed based on several requirements and de-sign principles First it must be applicable to forward flight scenarios andshould not be restricted to vertical autorotation only Second the con-trol law must not rely on a high-fidelity dynamic model of the aircraftwhich may not be available or may be too computationally expensiveThird the controller should be portable to various classes of helicoptersboth manned and unmanned Finally the controller should avoid itera-tive optimization and exhibit minimal computational burden This finaldesign constraint is meant to allow the autorotation controller to functionon many low-cost autopilot systems which are becoming increasinglypopular in the small unmanned aerial vehicle (UAV) community

These design principles led to formulation of the autorotation con-troller as an expert system The term ldquoexpert systemrdquo has been usedto describe a wide range of control systems and other computationalstructures Essentially two characteristics define expert system controlarchitectures First such controllers generally imitate control methodolo-gies applied by expert human operators Second these control systemsusually have ldquoexpertrdquo knowledge already available to them at runtime inthe form of a deterministic low-order dynamic model that is there is noiterative learning high-fidelity model prediction or optimization at run-time An example of an expert control law applied to a similar problem isthe controller derived by Livchitz et al (Ref 16) for autonomous landingof a small fixed-wing aircraft Unlike the controller described in Ref 16which relies mainly on a fuzzy logic structure the controller proposedhere uses a combination of several reasoning approaches including crisplogic fuzzy logic and proportional-integral-derivative control

The control structure considered in this paper consists of a standardinner-outer loop control architecture in which an inner-loop controller isresponsible for tracking velocity commands generated by an outer loopcontroller A block diagram of this control architecture is shown in Fig 1During nominal powered operating scenarios a waypoint following con-troller may send velocity commands to the inner loop controller (labeledas a ldquovelocity-tracking controllerrdquo) which is responsible for achievinga suitable vehicle orientation to track these commands The inner-loopcontroller therefore generates main rotor cyclic and collective commandsas well as tail rotor collective commands given desired velocity values Inthe case of autorotation the outer loop waypoint following controller isreplaced by the autorotation controller described here The autorotationcontroller therefore provides forward velocity commands (udes) maxi-mum pitch and roll orientation limits (ηmax) and main rotor collectivecommands (θ0) as shown in Fig 1 The velocity commands and orienta-tion constraints are sent directly to the inner-loop controller for trackingThus the autorotation control system is designed for straightforward

022008-2

A REAL-TIME EXPERT CONTROL SYSTEM FOR HELICOPTER AUTOROTATION 2015

Fig 1 Control system block diagram The autorotation control law determines main rotor collective desired forward speed and maximumpitch and roll limits for tracking by an inner-loop velocity tracking controller

integration with an existing inner loop autopilot controller Note thatan autorotation path planning scheme such as that developed in Ref 8for landing site selection may also be incorporated as an additionalouter loop that feeds desired waypoint data to the autorotation control(although such extensions are not explored here) Further note that thecontroller outputs a maximum orientation angle limit η equiv

radicφ2 + θ2

which is the total magnitude of the vehicle pitch and roll angles to sim-plify the controller structure While this does not limit the generality ofthe control design for many applications it may be desired to specifyseparate maximum roll and maximum pitch limits This can certainly beaccomplished within the proposed architecture by adding an additionaloutput to the controller in each phase

The autorotation maneuver is divided into several fuzzily definedphases based on altitude h and the estimated time to ground impactassuming constant velocity TTIh=0 equiv minushh A specific control law isdefined for each phase and phase transitions are initiated by predeter-mined criteria on altitude and time to ground impact defined for a specificaircraft The five maneuver phases selected for the controller are termedthe steady-state descent preflare flare landing and touchdown phases(although other phases may be selected this set of five phases was shownto provide suitable flexibility and robustness through extensive simula-tion and limited flight experiments) Boundaries between each phase aredefined in the altitude and time-to-impact domains through a strict fuzzypartition using trapezoidal membership functions Figure 2 shows thedefinition of the phases using example transition values chosen for theBell AH-1G Cobra Note that there is an ldquoORrdquo relationship between thealtitude and time to impact phase definitions such that the controller willadvance to the next phase if either or both of the altitude and time toimpact criteria are met As the autorotation maneuver progresses for-ward phase transitions are initiated sequentially and backward transitions(ie preflare to steady-state descent) are not allowed even if altitude in-creases This prohibition on backward progression through the phasesmeans that there is not necessarily a unique mapping from the physicalstate of the helicopter at a given time to a control output Instead the con-trol output also depends on the internal controller state or equivalentlythe time history of the helicopter physical state

Control system phases are defined in a fuzzy manner meaning thattransitions between phases are not ldquocrisprdquo like a switching control butrather happen over a finite time period (hence the blurred lines in Fig 2)Use of a fuzzy transition helps to avoid control transients caused byabruptly switching to a different phase control law A phase controlauthority value for each phase is defined between 0 and 1 representingthe extent to which that phase is active For instance when transitioning

Time to impact at constant velocity (s)

Alti

tude

AG

L (f

t minus lo

g sc

ale)

SS Descent

Preflare

Flare

Landing

Touchdown

0 2 4 6 8 1010

0

101

102

103

Fig 2 Example autorotation controller phase diagram Dashed linesdenote the beginning and end of transitions The regions that con-tain text are flat regions of the contour except for the region la-beled ldquotouchdownrdquo because the touchdown membership functiononly reaches saturation at ground level

from landing to touchdown the phase control authority value for landingwill start at 1 and transition continuously to zero Likewise the phasecontrol authority value for touchdown will start at zero and transitioncontinuously to 1 When two phases are partially active control outputsfrom each phase are blended together linearly using the phase controlauthority values as weights An extensive description of fuzzy controland its advantages is provided in Ref 17

A detailed discussion of each of the phase control laws follows Notethat throughout this section controller tuning parameters are indicatedby use of a fixed-width teletype font with underscores eg U_AUTO

Steady-state descent

In the steady-state descent phase the controller attempts to managerotor rotational energy in descending flight while the vehicle maneuversto a suitable landing site During the descent a pilot or a path-planningalgorithm (such as that developed in Ref 8) may provide speed and ori-entation commands and thus the autorotation controller simply passesthese commands to the velocity-tracking controller while managing

022008-3


collective directly Since integration of a path planner is beyond thescope of this study a constant forward speed U_AUTO is commandedand no limits are placed on helicopter orientation outside of those usedin the velocity-tracking controller Therefore the following equationsdescribe control outputs for this phase

udes = U_AUTO (1)

ηmax = limited only by velocity-tracking controller (2)

θ0 = K_D_SS + K_P_SS( minus RPM_AUTO) (3)

where RPM_AUTO is the desired rotor rotational rate in steady-state de-scent and K_D_SS gt 0 K_P_SS gt 0 are user-defined gains Notethat the commands provided in Eqs (1) and (2) may be replaced bythose generated by a human pilot or path-planning algorithm In the ab-sence of a path-planning algorithm or pilot guidance U_AUTO may beset to the forward flight speed which minimizes total power requiredtherefore minimizing the steady-state descent rate The RPM_AUTO set-point value is typically 80ndash120 of the nominal operating rotor rotationrate (Ref 1) As shown in Eq (3) the derivative of collective pitch θ0

is governed by a simple proportional derivative (PD) controller whichdrives collective toward a value corresponding to trimmed autorotationThe gains K_D_SS and K_P_SS can be chosen to yield a reasonableresponse using simplified or high-fidelity dynamic flight simulation Ingeneral if gains are chosen appropriately this control law will be stablein the normal operating region where the steady-state rotor rotation ratewill decrease if θ0 increases that is partSSpartθ0 lt 0 The only foreseeablecase where this condition might be violated is when a large negativecollective (only available on small hobby-sized aerobatic helicopters) iscommanded which forces the helicopter to accelerate downward and therotor rotation to slow This can be avoided by placing a positive lowerbound on the collective during autorotation if needed

The steady-state control law is designed to maintain an appropriaterotor rotational rate regardless of the forward speed of the helicopter ormaneuvers used to reach a safe landing site This makes it suitable foruse in piloted flight (where the pilot controls cyclic commands) or withhigher level path-planning algorithms Simulation tests have shown thatthe controller is able to adjust θ0 to suit a range of steady-state forwardspeeds

Preflare

During the preflare phase the controller attempts to bring the heli-copter state into the subspace that will likely result in a successful flaremaneuver The preflare controller is identical to the steady-state descentcontroller except that it places limits on the total vehicle orientation an-gle η to avoid aggressive maneuvers when entering the flare phase Thefollowing equations define control outputs for this phase

udes = U_AUTO (4)

ηmax = PRE_FLARE_MAX_ANGLE (5)


Once again appropriate velocity commands may be substituted forU_AUTO given pilot guidance or a path-planning algorithm

Flare

The flare maneuver is the most critical aspect of the autorotationand proper timing is vital The goal of the flare phase is to reducethe vertical and horizontal velocities to values suitable for safe entryinto the landing phase To that end the desired horizontal velocity isset to a small reference value U_TOUCHDOWN and η is not limited to

Table 1 Time to Impact Variables and parameters usedin the flare control law

Variable TTI h=0 (horizontal axis in Fig 2)Physical meaning Estimated T ime-To-Impact assuming speed

remains constantSource Calculated as minushhUse Determining controller phase

Variable TTI_LPhysical meaning Desired T ime-To-Impact during the Landing phaseSource Tunable control law parameterUse Landing phase control law and determining TTI F

Variable TTLEPhysical meaning Desired T ime-To-Landing phase EntrySource Determined by algorithm in Eq (13)Use Determines TTI F

Variable TTI FPhysical meaning Desired T ime-To-Impact during the F lare phaseSource TTI F equiv TTI_L+ TTLEUse Flare phase closed-loop control law

Example values for each parameter are shown in the Simulation Results section

provide the velocity-tracking controller enough flexibility to achieveU_TOUCHDOWN as quickly as possible Thus the desired velocity andorientation limits in the flare phase are given by

udes = U_TOUCHDOWN (7)


The remaining task for the autorotation controller is to determine andtrack a vertical trajectory that will cause the helicopter to enter the landingphase at the same time that the aircraft velocity reaches U_TOUCHDOWNDetermining a feasible flare trajectory is noted as a challenge in the litera-ture (Ref 5) Instead of attempting to directly specify a feasible trajectoryin the helicopterrsquos physical state space the problem is transformed intoa new time-to-impact domain that lends itself to a heuristic reasoningapproach for trajectory generation Four important variables in the time-to-impact domain are used by the controller given by (1) TTIh=0 theestimated time to ground impact assuming constant vertical speed (2)TTI_L the desired time to ground impact during the landing phase (3)TTLE the desired time to landing phase entry and (4) TTIF the desiredtime to ground impact during the flare phase These four variables sum-marized in Table 1 allow the flare trajectory to be generated in a robustand flexible manner based on state feedback Note that TTIh=0 TTLEand TTIF are computed directly from feedback values whereas TTI_Lis a constant controller tuning parameter

With the introduction of the time-to-impact domain the tasks of theflare phase controller are to prescribe a suitable target value for TTLE

using a heuristic rule set and to apply control inputs that will put the he-licopter on a trajectory to enter the landing phase approximately TTLE

seconds in the future Further clarity regarding the meaning and com-putation of these time-to-impact parameters is provided in the followingdiscussion

Prescription of TTLE The desired time to landing entry is conditionedon the amount of kinetic energy available to the helicopter to performmaneuvers Given sufficient rotor rotational kinetic energy or suffi-cient forward flight speed the descent can be more gradual and TTLE

may be larger Conversely if little kinetic energy is available the he-licopter must flare more abruptly and thus TTLE should be smaller to

022008-4


enter the landing phase sooner Thus TTLE is scaled between 0 andTTI_F_MAX minus TTI_L using a scale factor derived from the total ki-netic energy available for maneuver Define total kinetic energy as thesum of the kinetic energy due to vehicle forward velocity and that due torotor rotational kinetic energy according to

KEavailable equiv 1

2mu2 + 1

2IR2 (9)

Furthermore define the target kinetic energy at flare entry and exit as

KEflare entry equiv 1

2m(U_AUTO)2 + 1

2IR(RPM_AUTO)2 (10)

KEflare exit equiv 1

2m(U_TOUCHDOWN)2 + 1

2IR(RPM_AUTO)2 (11)

Thus a scale factor may be defined relating the current kinetic energy tothe desired values at flare entry and exit according to

α equiv KEavailable minus KEflare exit

KEflare entry minus KEflare exit(12)

Finally time to landing phase entry TTLE is calculated as

TTLE = TTLEmax times min (1 max (0 α)) (13)

where TTLEmax equiv TTI_F_MAXminusTTI_L Note that in cases of very lowtotal kinetic energy when KEavailable is less than KEflare exit TTLE = 0and thus an immediate transition to the landing phase is initiated Ifkinetic energy is very high (greater than KEflare entry) the time to landingphase entry is given by the tuning parameter TTI_F_MAX minus TTI_Lproviding a longer and more gradual flare trajectory The computed TTLE

is used to prescribe the desired time to impact for the flare phase TTIF according to the following formula

TTIF = TTLE + TTI_L (14)

Note that values for TTLE and TTIF are continually calculated at ahigh rate during the flare maneuver using feedback measurement dataallowing rapid adjustment of the flare trajectory and compensating fordisturbances such as winds which may significantly alter kinetic energyavailable

Flare trajectory tracking Once the desired time to impact required forvertical deceleration TTIF has been calculated as described above avertical trajectory to the ground is generated During flare trajectorygeneration the vertical flight path is parameterized using a constant ac-celeration model Although a desired constant acceleration is computedit is updated at a high rate based on feedback measurements and thus atime-varying acceleration profile results Let the vehicle altitude aboveground at time t be given as h(t) and vertical velocity as h(t) Withconstant vertical acceleration h(t) the altitude at time t + TTIF is givenby

h(t + TT IF ) = h(t) + h(t) TTIF + 1

2h(t) TTI 2

F (15)

Setting h(t + TTIF ) = 0 yields a desired constant acceleration value of

hdes = minus 2

TTI 2F

h minus 2

TTIF

h (16)

Equation (16) essentially guarantees that t + TTIF will be a root ofEq (15) but does not guarantee that another root does not exist at a timebefore t + TTIF This additional root exists in a trajectory that crossesthe ground plane in the downward direction before t + TTIF and then

crosses the ground plane in the upward direction again at t + TTIF (withh(t +TTIF ) gt 0) The condition on TTIF which guarantees that the firstintersection of the trajectory with the ground plane occurs at t + TTIF

(ie the desired behavior) is given by

TTIF le minus2h

h(17)

If Eq (17) is not satisfied no constant acceleration command will yielda root of Eq (15) with h(t + TTIF ) lt 0 These two possibilities givenby satisfaction and violation of the inequality in Eq (17) are treatedseparately in the flare phase control law

Assuming that Eq (17) is satisfied collective commands must begenerated to achieve hdes computed from Eq (16) The complexity ofrotor aerodynamics in general prohibits a simple mapping between col-lective pitch and corresponding thrust values due to numerous effectssuch as blade stall tip and root losses inflow dynamics and spatial vari-ation ground effect and other aerodynamic phenomena For this reasonthe controller uses acceleration feedback measurements to dynamicallyadjust the collective to attain the proper vertical acceleration A simplemodel to guide this adjustment may be created by assuming low diskloading linear aerodynamics uniform inflow constant chord bladesand zero twist Using these simplifications an expression for the thrustcoefficient may be generated as (Ref 1)

CT = σclα

(θ0

6minus λ

4

)(18)

where CT is thrust coefficient σ is rotor solidity clα is blade sectionlift curve slope and λ is nondimensional inflow Dimensionalizing thisexpression adding gravitational effects and neglecting horizontal com-ponents of rotor thrust yields a linear relationship between collective andvertical acceleration given by

h = ρR32Nc

(θ0

6mminus w

4mR

)+ g (19)

Here ρ is atmospheric density N is number of main rotor blades c

is blade chord w is rotor inflow and g is gravitational accelerationWhile there is significant uncertainty in this relationship introduced bythe various assumptions outlined in Ref 1 it establishes the general trendthat an increase in collective pitch generates a proportional increase invertical acceleration where the constant of proportionality is unknownand varies according to flight condition and other factors ReferencingEq (19) let θD

0 be the (unknown) collective command that achieves hdes

given the current inflow state and let θC0 be the collective command

at time t yielding h(t) Then a simple proportional control law maybe established that drives the collective pitch toward the desired valueaccording to

θ = kθ0

(θD

0 minus θC0

) = K_COL

TAU(hdes minus h) (20)

where kθ0 is a positive constant and K_COL gt 0 and TAU gt 0 are user-defined tuning parameters Thus using the right-hand side of Eq (20)collective is adjusted in the direction of the desired value until the desiredvertical acceleration is achieved Clearly K_COL and TAU are redundantparameters and may be combined into a single value However giventhe linear relationship in Eq (19) K_COL may be tuned according to theapproximation

K_COL asymp 6m

ρR32Nc(21)

which are all known parameters of the helicopter geometry and operatingenvironment TAU may then be adjusted to influence the speed of thecontrol response

022008-5


If the condition in Eq (17) is not met it is not possible to computea constant acceleration which leads to ground impact at time t + TTIF In such a flight regime use of the acceleration expression in Eq (16)yields a root of Eq (15) that occurs at a time before t + TTIF meaningthat the helicopter will impact the ground too soon To prevent this if thecondition in Eq (17) is violated the flare phase controller commands alarge upward adjustment of the collective pitch (given by the controllerparameter FAST_COL_INCREASE) This is analogous to a human pilotsensing that the magnitude of the vertical velocity is too large and inresponse rapidly increasing the collective pitch until the velocity hasreached a suitable value for satisfaction of Eq (17)

Equation (22) summarizes the implementation of the collective por-tion of the flare phase control law This equation combined with Eqs (7)(13) and (14) creates a complete description of the flare phase controllaw

θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF

FAST_COL_INCREASE for minus 2h

hlt TTIF

(22)

Landing

In the landing phase the controller seeks to approach the groundgently with nearly level attitude The control law is similar to the flarephase control law (derived from Eqs (16) and (20)) except that thedesired time to impact remains at a constant value given by the controllerparameter TTI_L An example value of TTI_L = 20 s was found tobe suitable for the AH-1G through simulation experiments Thus thelanding phase control law is given by


ηmax = LANDING_MAX_ANGLE (24)

θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown

The touchdown phase brings the helicopter to rest on the groundby decreasing the collective slowly and attempting to maintain a levelorientation For large helicopters limits on the control inputs may needto be implemented in this phase to keep the blades from impacting thefuselage or empennage after touchdown due to potentially low rotorrotation rates although these limits have not been included here andwould be highly vehicle dependent The touchdown phase control law isgiven by


ηmax = TOUCHDOWN_MAX_ANGLE (27)

θ0 = TOUCHCOWN_COL_DECREASE (28)

A total of 10 controller parameters are defined in the preceding sec-tions In the testing performed as part of this study it was observed thatcontroller response is relatively insensitive to adjustments in almost all ofthese parameters with the notable exception of K_COL and TAU whichare fundamental to shaping the flare trajectory A summary of each of thecontroller parameters is provided in Tables 2 and 3 as well as examplevalues for the AH-1G and a small RC size helicopter derived throughsimulation studies Note that these parameters may be reliably deter-mined from low-to-medium fidelity rotorcraft simulation models suchas the one described in the following section Further note that separatepitch and roll angle parameters may be added as well as separate limits

for positive and negative angles if desired during practical implementa-tion However it was observed that these parameters do not significantlyaffect performance as long as the inner-loop control law is adequatelytuned

Alternate acceleration-free control law

The flare and landing phase collective control laws specified inEqs (22) and (25) require vertical acceleration feedback On some low-cost flight platforms including the RC model used in experimental stud-ies performed here accurate acceleration feedback with suitable noisecharacteristics is difficult to obtain at high update rates In this casean alternative acceleration-free control law formulation is desired Themodified collective control law derived here differs from that shownabove only in the trajectory tracking portion of the flare and landingphases This modified controller uses the same methods to determineTTLE and TTIF described previously however instead of specifying θ0

as shown in Fig 1 θ0 is computed directly This modified control lawattempts to follow an exponentially decaying altitude profile to groundimpact

Consider vertical trajectory dynamics as shown in Eq (19) Assuminginflow changes occur slowly compared to the controller update rate in-flow can be treated in a quasi-static manner and Eq (19) can be rewrittenin a simplified form as

h = 1

Kθ0

(θ0 minus G) (29)

where G accounts for both the inflow and gravity terms Equation (29) isa linear second-order differential equation in terms of h Now consider afeedback control law of the following form

θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)

The solution to the differential equation (29) assuming the control lawgiven in (30) is

h(t) = (h(0) minus A) eminustτT + A e

minustτC (31)

where A is a constant given by

A = h(0) τT + h(0)

1 minus τT

τC

(32)

and t = 0 is defined as the time at which the flare or landing phaseis initiated The altitude solution in (31) can be viewed such thath(0) exp(minustτT ) is the desired descent trajectory with a time constant τT

on the order of the desired time to impact Furthermore A is a measureof the difference between the actual descent rate at t = 0 and the descentrate required to follow the desired exponential trajectory exactly whichis given by hdes = minush(0)τT Thus if τC τT the second term of thetrajectory solution (31) will decay quickly and may be viewed as a tran-sient correction term for the descent rate As long as A lt h(0) h(t) willalways be positive and will approach h = 0 exponentially with a timeconstant of τT after the transient term becomes small This condition onA is guaranteed as long as

h(0) gtminush(0)

τC

(33)

Thus smaller values of τC will result in more robustness to verticalvelocity errors at the initiation of flare and landing

In actual implementation of the acceleration-free control law theappropriate desired time to impact may be substituted for τT based on

022008-6


Table 2 Autorotation controller parameters

Parameter Value for AH-1G Value for TREX 600 Definition

RPM_AUTO 34 rads 160 rads Desired main rotor rotation rate for the steady state descent phaseK_D_SS 003 sminus1 0003 sminus1 Gain on rotor speed time derivative for collective control during steady-state

descentK_P_SS 001 (unitless) 0001 (unitless) Gain on rotor speed for collective control during steady-state descentTTI_L 20 s 10 s Desired time to impact during the landing phaseTTI_F_MAX 6 s 5 s Maximum cap on the desired time to impact during the flare phaseK_COL 666 times10minus4 radmiddots2ft 31 times10minus4 radmiddots2ft Rotor collective gain for flare and landing phasesTAU 005 s 005 s Rotor collective adjustment time constant tuning parameter for flare and landing

phasesFAST_COL_INCREASE 20 s 10 s Collective adjustment rate for rapid adjustments during the flare and landing

phases

Table 3 Autorotation controller speed and angle limit parameters


U_TOUCHDOWN 10 fts 1 fts Desired forward velocity at touchdownU_AUTO 100 fts 10 fts Desired forward speed for the steady state descent phaseLANDING_MAX_ANGLE 8 10 Maximum cap on roll and pitch angles during the landing phaseTOUCHDOWN_MAX_ANGLE 1 3 Maximum cap on roll and pitch angles during the touchdown phaseTOUCHDOWN_COL_DECREASE minus1 s minus1 s Constant collective pitch rate during touchdown phase

the controller phase and several parameters (denoted by fixed width font)must be estimated or tuned The acceleration-free collective control law isgiven by Eqs (34) and (35) for the flare and landing phases respectively(based on Eq (30)) Note that the gain K_COL is scaled inversely withthe square of the rotor rotation speed to correct for the thrust dependencyon 2

Flare

θ0 = K_COLNOMINAL_RPM2

2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)

This control law has several drawbacks compared with the versiondescribed earlier First if the condition in (33) is violated A will betoo large and the velocity correction terms will dominate the responseThis is unlikely to lead to a successful vertical trajectory profile Secondthe alternate law relies on the approximate vertical dynamics given inEq (29) which may suffer from significant error in some flight conditions(especially in ground effect or highly dynamic inflow conditions) Theoriginal control law described earlier only relies on this approximation todetermine how fast to adjust θ0 but seeks the desired acceleration basedon feedback measurements making it significantly more robust For thisreason if suitable acceleration feedback is available the original controllaw is preferred to this alternative

Velocity tracking controller example implementation

An example velocity-tracking controller implementation is requiredto evaluate performance of the autorotation controller in both simulation

and experiment The tracking control used here consists of a standardinner-outer loop PD architecture similar to that used in many productionhelicopter autopilot systems A detailed block diagram of this controlleris omitted here for brevity but may be found in Ref 18 The outer loop ofthe velocity-tracking controller generates desired orientation commands([φcmd θcmd ψcmd]T ) based on udes and the current helicopter velocityFor all the preliminary studies performed here sideslip angles are reg-ulated to zero and thus vdes = 0 The inner loop attempts to track thisorientation using the cyclic and tail rotor controls ([θ1s θ1c θtr]T ) Simplemodifications may be made to this example controller to include windcorrections from a waypoint generation algorithm if one is available

Simulation Model

A helicopter simulation model is used to validate the proposed con-trol law based on the ARMCOP model developed by Talbot and Chen(Refs 19ndash21) The main rotor model provides increased fidelity over thestandard ARMCOP model by incorporating effects from dynamic inflowground effect and blade stall Detailed descriptions of each model com-ponent are omitted for brevity but can be found in the cited references

Main rotor forces and moments

Forces and moments generated by the main rotor are calculated usinga numerical blade element approach in which the main rotor blade isdivided into 15 elements and two-dimensional aerodynamic analysis isperformed for each The calculation is repeated at 30 azimuthal stationsevenly distributed over a complete revolution and then appropriatelyaveraged and normalized Main rotor torque is determined by these cal-culations and used to compute the rotor rotation rate derivative whenthe engine is not powering the vehicle Static stall of the rotor blades isimplicitly included in the model through use of a complete aerodynamiclookup table for each blade section (Ref 22) Dynamic stall and com-pressibility effects are neglected Furthermore first harmonic flappingis assumed and higher harmonic flapping dynamics are neglected forthese control law studies Main rotor flapping states β0 β1s and β1c are

022008-7


included in the vehicle state and propagated using a second-order bladeflapping dynamic equation Further details of the main rotor model areomitted here but are provided in detail in Ref 18

Dynamic inflow

A dynamic inflow model is included to increase simulation fidelity inrapidly changing inflow conditions during autorotation Various dynamicinflow simulation techniques have been developed since the 1980s in-cluding linear models (Ref 23) free-vortex wake models (Ref 24) andstate-space wake models derived from indicial theory (Ref 25) Thesemodels range in complexity but the relatively simple linear model struc-ture developed by Peters et al (Ref 23) is used most often in flight dy-namic studies However free-vortex wake models likely provide higheraccuracy especially in turbulent wake conditions such as those experi-enced during autorotation at the expense of significant computationalburden Owing to the requirement for extensive Monte Carlo simula-tion in this study the Pitt and Peters dynamic inflow model describedin Refs 26 and 27 was selected for use here as a reasonable trade-offbetween accuracy and computational complexity The model has threestates λ0 λs and λc which describe the induced inflow ratio distributionover the rotor disk according to the equation

λi(r ψMR) = λ0 + λs

r

Rsin ψMR + λc

r

Rcos ψMR (36)

These states evolve according to the dynamic equation

[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)

where C is the vector of body frame force and moment coefficientscalculated using the blade element approach described above [L] is amatrix dependent on the sideslip angle and wake angle and [M] is a massterm based on the mass of air near the rotor Additional details regardingthis model can be found in Ref 27

Ground effect

A simple ground effect correction is applied to the dynamic inflowmodel when the vehicle is in close proximity to the ground Equation (37)shows that when the inflow has reached steady state (ie λ = 0)

C = [L]minus1λss (38)

where λss is the vector of the inflow states at steady state It is assumedthat in ground effect the steady-state inflow can be modeled by

λssIGE =(

1 minus 08w

w0

)λss (39)

where ww0 is a correction term for ground effect in forward flightdescribed by Heyson (Ref 28) The correction terms calculated in Ref 28are only valid at the center of the rotor and decrease spanwise along theblade (Ref 29) Therefore an average value of 80 of the ww0 valuereported in Ref 28) is used over the entire rotor This correction termis applied in the dynamic inflow model by adjusting C so that λ tends

toward λssIGE At steady state

CIGE = [L]minus1λssIGE (40)

= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)

In the dynamic inflow equation (37) C is adjusted using Eq (43) whenthe main rotor is within two rotor diameters of the ground

[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)

The values for ww0 are taken from a lookup table based on Ref 28and data are indexed based on the height above ground and the wakeangle determined from the inflow state and velocity of the helicopter

Simulation overview

The fuselage horizontal and vertical stabilizer and tail rotor com-ponents of the helicopter model provide additional aerodynamic forcesThe tail rotor uses NewtonndashRaphson iteration to calculate uniform tailrotor inflow and blade flapping is assumed to be quasi-steady The tailrotor and main rotor rotation rates are coupled through use of a scale fac-tor Fuselage and stabilizer components use linear aerodynamic modelsand downwash components are included through a simplified fuselagedrag model Details regarding these contributions to the total helicopterforces and moments may be found in Ref 19 Furthermore actuator ratelimits are imposed in the simulation as well as maximum and minimumstops Actuator rate limits are set to 40 degs and are imposed on θ0 θ1s θ1c and θtr (note this limit applies to the actuator response and not thecontroller demand)

The net force on the helicopter (Fx Fy and Fz) and the net momentabout the mass center (Mx My and Mz) are composed of contributionsfrom the main rotor tail rotor fuselage and empennage aerodynamicsand weight Net force and moment components are expressed in thehelicopter body frame and drive the six degree-of-freedom rigid bodyequations that govern helicopter motion These equations of motion areintegrated forward in time using a fourth-order RungendashKutta algorithmwith a timestep of 0001 s Note that the entire vehicle state vector iscomposed of the 12 rigid body vehicle states main rotor rotation ratethree dynamic inflow states three flapping angles and three flappingangle rates

Simulation Results

Example and Monte Carlo simulations are performed to characterizecontrol law performance under different flight conditions Similar simu-lation experiments are conducted for both the AH-1G Cobra helicopterand for the RC-sized Align TREX 600 model helicopter

Bell AH-1G Cobra simulations

Model parameters used for the AH-1G simulations are obtained fromRef 19 Table 4 lists some of the important model parameters All feed-back states are perturbed with Gaussian white noise to simulate measure-ment error and Table 4 provides measurement error standard deviationsTables 2 3 and 5 list the controller parameters used for these tests

022008-8


Table 4 Select model parameters for the Bell AH-1G simulation

Parameter Symbol Value

Helicopter gross weight W 8300 lbNumber of main rotor blades Nb 2 (teetering)Main rotor blade chord c 225 ftMain rotor radius R 22 ftMain rotor blade moment of inertia I B 2770 slug ft2

Main rotor height above ground (water line) WL MR 1273 ftMain rotor normal operating speed normal 3288 radsMain rotor blade airfoil used for simulation NACA 0012Actuator max rate δmax 40 degsController update rate 100 HzVelocity sensor noise standard deviation σvel 10 ftsAcceleration sensor noise standard deviation σaccel 30 ft s2

Attitude sensor noise standard deviation σattitude 15 degAttitude rate sensor noise standard deviation σrate 30 sAltitude sensor noise standard deviation σh 10 ftClimb rate sensor noise standard deviation σh 10 fts

Table 5 Flight phase fuzzy transitions for theAH-1G Cobra helicopter

Altitude Time-to-ImpactTransition Range (ft) Range (s)

Steady state descent to preflare 200ndash250 5ndash7preflare to flare 30ndash70 3ndash35Flare to landing 5ndash15 05ndash12Landing to touchdown 0ndash2 0ndash01

Since trapezoidal membership functions are used transitions are linear

An example simulation is performed in which autorotation is initiatedfrom a trimmed flight condition at an altitude of 350 ft forward speedof 50 kt and gross weight of 8300 lb A 1-s delay between engineshutoff and the point at which the autorotation controller takes overfrom the normal flight controller is simulated representing the actualtime it would potentially take to confirm power loss and initiate theautorotation controller Figure 3 shows a distance versus altitude flightprofile and Figure 4 shows a time history of body frame velocity u Notethat although the initial state is near the edge of the avoid region of theAH-1Grsquos HndashV diagram the controller handles the maneuver well andbrings the vehicle to a safe landing The vehicle achieves the desiredforward speed for the minimum descent rate of approximately 90 ftsA time history of the vehicle pitch angle not included here shows thatinitially the controller commands a pitch forward maneuver to increaseforward speed followed by a 20ndash25 deg pitch-up maneuver during flareThe vehicle pitches down to an approximately level attitude just after 20 sFigure 5 provides a time history of the rotor rotation rate showing animmediate drop in the rotor rotation rate before the autorotation controllertakes effect followed by the return of to a value slightly higher than thenormal operating value during steady-state descent A time history of themain rotor collective is also shown in Fig 5 Finally Figs 6 and 7 showtime histories of the phase control authority and time-to-impact internalvariables Note that for clarity in presentation the constant velocitytime-to-impact shown in this figure is calculated without sensor noisealthough the controller actually uses the noise-perturbed value Alsonote that TTLE can be derived from the plotted results in Fig 7 as thedifference between TTIF and TTI_L For the example case consideredhere total horizontal velocity and vertical velocity at touchdown are 37

0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)

Fig 3 Example AH-1 distance versus altitude flight profile

0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)

Fig 4 Example AH-1 body frame velocity history

and 39 fts respectively whereas pitch and roll angles at touchdown arenearly level at minus15 and minus07 respectively

Monte Carlo simulations are also conducted using initial conditionsin and around the ldquoavoidrdquo region of the HndashV diagram to demonstrate thatthe controller is able to recover from difficult (low-energy) initial con-ditions To capture the effects of controller handoff delays on controllerperformance Monte Carlo simulations are performed using various delayvalues between the failure event (engine failure tail rotor failure etc) andinitiation of the autorotation controller Typical handoff delays for certi-fication purposes are 1ndash2 s depending on pilot workload (Ref 1) In eachMonte Carlo simulation performance is evaluated based on the state ofthe helicopter upon impact with the ground Conditions for ldquosuccessfulrdquoldquomarginalrdquo and ldquocrashrdquo landings are specified in Table 6 ldquoSuccessfulrdquolanding conditions are designed to represent a landing which would likelycause no damage to the aircraft whereas ldquomarginalrdquo landing conditionswould likely result in damage to the aircraft but be survivable to pas-sengers and equipment Note that potential tail strikes are also recorded

022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)

Fig 5 Example AH-1 rotor rotation rate and collective pitchhistories

0 5 10 15 20 250

02

04

06

08

1

Time from engine stop (s)

Pha

se c

ontr

olle

r au

thor

ity v

alue

Steady state descentPreflareFlareLandingTouchdown

Fig 6 Example AH-1 phase control authority history

and incorporated into the Monte Carlo analysis where tail strikes dur-ing landing are computed based on the orientation of the aircraft and tailboom length If a tail strike is detected in a landing otherwise categorizedas ldquosuccessfulrdquo the category is changed to ldquomarginalrdquo

Figure 8 shows the results of 1000 simulated autorotation landingswith an immediate handoff and Figure 9 shows results using a handoffdelay of 2 s Each solid dot represents a successful landing from theindicated position and a diamond indicates a marginal category landingA times symbol indicates a crash The low-speed ldquoavoidrdquo region of the HndashVdiagram for the AH-1G Cobra is also marked for reference (Ref 30)although it is important to note that this avoid region captures pilotcomfort level and thus is expected to be more conservative than the regionin which the controller can successfully land the helicopter Note that thecontroller is able to perform a safe autorotation in the vast majority ofcases except in helicopter states where the total vehicle energy (sumof kinetic and potential energies) at autorotation initiation is low The

0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)

Constant velocity TTI (calculated)TTI

F (desired)

TTI_L (desired controller parameter)

Fig 7 Example AH-1 time-to-impact parameters history

Table 6 Conditions for successful and marginallandings for the AH-1G

Condition for Condition forParameter Successful Landing Marginal Landing

Roll angle φ lt5 lt10Pitch angle θ minus5 lt θ lt 10 minus5 lt θ lt 15Forward speed x lt20 kt lt40 ktLateral speed y lt3 fts lt6 ftsVertical speed z lt8 fts lt15 ftsRoll rate p lt8 s lt15 sPitch rate q lt10 s lt20 sYaw rate r lt8 s lt15 s

Simulations that do not meet these criteria are considered crashes(conditions applied to absolute value of parameter unless otherwisenoted)

majority of marginal or crash landings in the avoid region occur dueto violation of the vertical velocity criteria Also note that in generalperformance suffers as the handoff delay grows which is expected At lowinitial energies the controller does not have time to build up main rotorrpm and instead must initiate the flare maneuver immediately with lessavailable thrust leading to higher ground impact speeds Other MonteCarlo cases not shown here demonstrate that controller performance inoverweight scenarios (gross weight of 9000 lb) with a 1-s delay largelymirrors performance at a gross weight value of 8300 lb with a 2-s delayThus as expected higher disk loading reduces the controllerrsquos marginfor error but performance is still generally satisfactory The few marginallanding outlier cases outside the avoid region in Figs 8 and 9 showedimpact conditions that exceeded the successful criteria by only a verysmall amount Also note that the majority of cases in Figs 8 and 9 yieldedpitch angles at impact between minus1 and 1 deg It is possible that by addingan additional constraint prohibiting negative pitch angles in the landingand touchdown phases the controller would be biased toward positivepitch angles and negative values may be avoided entirely although suchadditions are not explored here

In all tests the controller generally has difficulty at high forward flightspeeds and low altitude (below 40 ft) This is typically a dangerous regionof the heightndashvelocity envelope since there is usually insufficient time toslow the helicopter to a safe speed before ground impact and insufficientaltitude to establish a steady-state descent Suitable performance in suchscenarios would likely require an immediate open-loop climb commandto gain altitude followed by initiation of the standard autorotation descentbeginning with the steady-state descent phase This mimics typical high-speed low-altitude autorotation maneuvers carried out by human pilots

022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800

Initial forward velocity (kt)

Initi

al a

ltitu

de (

ft A

GL)

Successful landingMarginal landingCrashAHminus1 avoid region

Fig 8 AH-1 Monte Carlo test results (immediate handoff)

(Ref 1) Such additions to the autorotation control framework are notexplored here but may improve performance in this specific flight regimeThese modifications potentially involving backward progression throughthe control phases are left to future work

Align TREX 600 simulations

Simulations are also performed using a model of the Align TREX600 hobby-class helicopter to demonstrate controller portability Thesimulation has a similar structure to the AH-1G model with simulationparameters listed in Table 7 The Align TREX uses a semirigid rotorhub in which blades do not have a flapping degree of freedom Thusthe model is modified to incorporate an equivalent hinge offset and hubspring (Ref 1)

An example simulation is shown in which autorotation is initiatedfrom an altitude of 100 ft and forward speed of 10 fts As before a1-s delay between engine shutoff and the point at which the autorotationcontroller takes over from the normal flight controller is used Figure 10shows a distance versus altitude flight profile and Fig 11 shows a timehistory of body frame velocity u Note that the autorotation is completedin approximately 7 s and touchdown occurs with nearly zero forwardspeed and vertical speed of less than 5 fts As in the Cobra simulationsa time history of vehicle pitch angle is not shown but generally indicatesa similar trend of a pitch forward maneuver followed by a pitch backmaneuver during flare Touchdown is initiated at a pitch angle of less than1 deg and a roll angle of less than 5 deg Figure 12 shows a time history of as well as main rotor collective where the 1-s handoff delay is clearlypresent Note that minimum collective (negative for the aerobatic modelhelicopter) is commanded immediately during the steady-state descentphase and maximum collective is commanded near touchdown to slowthe descent Finally Fig 13 shows time-to-impact internal variables

0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)


Fig 9 AH-1 Monte Carlo test results (2-s handoff delay)

Table 7 Align TREX 600 model parameters pertainingto autorotation


Helicopter gross weight W 815 lbNumber of main rotor blades Nb 2 (semirigid hub)Main rotor blade chord c 01771 ftMain rotor radius R 2208 ftMain rotor blade moment of inertia I B 001357 slug ft2

Main rotor height above ground (water line) WL MR 15 ftMain rotor normal operating speed normal 162 radsMain rotor blade airfoil used for simulation NACA 0012Actuator max rate δmax 100 degsController update rate 100 HzVelocity sensor noise standard deviation σ vel 10 ftsAcceleration sensor noise standard σ accel 30 ft s2

deviationAttitude sensor noise standard deviation σattitude 15 degAttitude rate sensor noise standard deviation σrate 30 sAltitude sensor noise standard deviation σh 02 ftClimb rate sensor noise standard deviation σh 05 fts

indicating similar trends as in the AH-1G example case Performancedemonstrated in this example case would certainly be survivable for thismodel aircraft

Monte Carlo simulations are performed using the TREX 600 modelto demonstrate the controllerrsquos effectiveness in a wide variety of initialflight conditions Landings are classified according to the criteria listed inTable 8 Figures 14 and 15 show landing performance with an immediatehandoff and a 3-s handoff delay respectively When the handoff delay is

022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)

Fig 10 Example TREX 600 distance versus altitude flight profile

0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)

Fig 11 Example TREX 600 body frame velocity history

small the controller is able to handle a wide variety of initial conditionsAs the handoff delay is increased performance becomes progressivelyworse due to the decrease in rotor rpm caused by the controller attemptingto maintain altitude before the handoff Additional Monte Carlo resultswere generated with a 50 increase in vehicle gross weight (not shownhere) Performance in this increased-weight case was similar to con-troller performance with the nominal gross weight using a 1-s handoffdelay Overall when combined with the AH-1G results Figures 10ndash15demonstrate reasonable performance of the autorotation controller whenapplied to vehicles of various scales

Flight Test

A limited set of flight experiments was conducted to demonstratecontroller performance given realistic measurement feedback and distur-bances A small RC helicopter the Align TREX 600e was used for these

0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)

Fig 12 Example TREX 600 rotor rotation rate and collective pitchhistories

0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)


Fig 13 Example TREX 600 time to impact parameter history

flight tests For these preliminary flight experiments trajectories werelimited to vertical autorotation only and thus validation of the forwardflight component of the autorotation controller is left to future experi-ments Furthermore limitations in the quality of accelerometer feedbackled to use of the acceleration-free version of the flare and landing controllaws discussed in the Controller Design section

Flight test setup and methodology

The controller parameter values used in the flight experiments weresimilar to those shown in Table 2 The additional acceleration-freecontroller parameters used in the flight tests are given by K_COL =1524 rad s2 ft TAU_CLIMB = 025 s and GRAV = 656 fts2 The au-topilot used for the flight experiments was an ArduPilot model 252which consists of an ATmega2560 8-bit microprocessor running at16 MHz coupled with a sensor package These sensors include a three-axis magnetometer barometric altimeter GPS three-axis accelerometer

022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200

Initial forward velocity (fts)

Initi

al a

ltitu

de (

ft A

GL)

Successful landingMarginal landingCrash

Fig 14 TREX 600 Monte Carlo Test results (immediate handoff)

0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)


Fig 15 TREX 600 Monte Carlo test results (3-s handoff delay)

minus15 minus10 minus5 0 5minus100

0

100

200

300

Alti

tude

(ft)

Time from touchdown (s)


minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)


Fig 16 Altitude versus time and vertical speed versus time Solidlines are experimental data a dark solid line is the experimental casehighlighted in the Discussion and a dashed line is the simulated one


0

10

20

Com

man

ded

colle

ctiv

e (d

eg)


minus15 minus10 minus5 0 50

500

1000

1500

2000

Rot

or r

pm


Fig 17 Collective pitch versus time and rotor rotation rate versustime Solid lines are experimental data a dark solid line is the ex-perimental case highlighted in the Discussion and the dashed line issimulated

and three-axis gyroscope In addition the aircraft was outfitted with acustom rotor rpm sensor and a downward-facing ultrasonic sensor formeasuring precise ground proximity A Kalman filter with outlier re-jection was implemented to combine altimeter and ultrasonic sensormeasurements

The velocity-tracking controller used in the flight experiments hasstructure similar to that described earlier except that a waypoint-trackingloop was included to generate commands for udes and vdes This al-lows wind corrections to be included in the feedback control structurebut has negligible effect on autorotation controller performance During

022008-13



02

04

06

08

1


Steady-state descentPreflareFlareLandingTouchdown

Fig 18 Phase progression for selected autorotation flight test

Table 8 Conditions for successful and marginal landingsfor the TREX 600


Roll angle φ lt5 lt10Pitch angle θ minus5 lt θ lt 10 minus5 lt θ lt 15Forward speed x lt6 fts lt12 ftsLateral speed y lt5 fts lt6 ftsVertical speed z lt7 fts lt12 ftsRoll rate p lt10 s lt15 sPitch rate q lt10 s lt20 sYaw rate r lt8 s lt15 s

Simulations that do not meet these criteria are considered crashes (conditions ap-plied to absolute value of parameter unless noted)

autorotation tests a single waypoint is set at the horizontal location ofautorotation entry so that the vehicle will follow a vertical path to theground The velocity-tracking controller is tuned for waypoint follow-ing in powered flight and thus the success of these flight experimentsdemonstrates how the autorotation controller is highly compatible withexisting autopilot control laws

Flight-test results

Several flight experiments were performed from an initial altitude of250 ft above ground level Starting from a trimmed flight condition thehelicopterrsquos motor was powered off and the vehicle landed completelyautonomously Numerous trials were conducted which were largely suc-cessful Figure 16 shows a time history of altitude and vertical speed forfive selected trials Both of these data sets are derived from the Kalmanfilter estimates and thus do not represent truth measurements Throughoutall figures an example time history is highlighted using a thicker blackline for discussion purposes A simulation time history is also shownwith a dashed line This simulation was run from approximately thesame initial conditions as the flight tests and used the acceleration-freeversion of the control law Figure 17 shows time histories of collectiveinputs and main rotor rpm and Fig 18 shows a controller phase timehistory for the example trajectory highlighted in black

Several features are noteworthy in these results and were evident infurther trials not shown here First the controller is able to successfullyland the helicopter in engine-out scenarios demonstrating vertical ve-locities at touchdown of under 3 fts in most cases which is well belowthe damage threshold for the helicopter Second note that shortly af-ter engine cutoff collective is commanded full negative which yieldsan rpm increase nearly back to the nominal value for power-on flightAs the aircraft nears the ground collective is gradually increased caus-ing a reduction in rotor rpm as expected The helicopter consistentlyimpacts the ground with a rotor rotation rate of 30ndash50 of the nom-inal value Note that for this small helicopter this rotor rotation rateis still enough for minor cyclic adjustments and reasonable margin oferror (for full-sized helicopters with larger rotor inertia the decay asa percentage of the nominal rate would be less as shown in Fig 5)Third note that the simulated trajectory and experimental data showreasonable correlation lending credibility to the simulation results pro-vided above Finally it was observed that there was significant inter-action between transient inflow dynamics and altitude measurementsfrom the barometer (which was necessarily placed under the rotor asthere was no suitable alternative location) Thus as shown in the exam-ple case around 6 s from impact sudden increases in collective pitchgenerated momentary high pressure at the barometric sensor due to in-creased induced velocity This type of spurious measurement causedoccasional spikes in vertical velocity feedback which were mitigatedto some extent using shielding around the autopilot sensor package (al-though this effect was never fully eliminated) Overall upward of 10successful vertical autorotations were performed in wind conditions ex-ceeding 10 kt validating the overall control system design in a realisticenvironment

Concluding Remarks

A novel expert system control law for autonomous autorotation hasbeen proposed and validated through simulation and limited experimen-tal tests The multiphase control structure incorporates estimates of thetime-to-ground impact using a simple kinematic model enabling suit-able flare trajectories to be calculated quickly in a feedback mannerThrough calculation of a desired time to impact flare trajectories arefurthermore conditioned based on the total kinetic energy available for

022008-14


maneuver The controller is designed for straightforward integration withexisting autopilots landing site selection algorithms and pilot guidanceSimulations and limited experimental data validate the control algorithmand show suitable performance in realistic environments Overall resultsdemonstrate the portability of the proposed controller as well as its po-tential use as an automated autorotation landing system for single enginerotorcraft

Acknowledgments

The authors thank Bradley Taylor for helping to develop the simula-tion software used in this research Lee Fowler for piloting the flight-testhelicopter and Robert Long for creating flight-test electronics This ma-terial is based on work supported by the National Science FoundationGrant No 1252521

References

1Leishman J G Principles of Helicopter Aerodynamics CambridgeUniversity Press New York 2006

2Johnson W ldquoHelicopter Optimal Descent and Landing after PowerLossrdquo TM-73244 NASA 1977

3Lee A Y Bryson A E and Hindson W S ldquoOptimal Landingof a Helicopter in Autorotationrdquo Journal of Guidance Control andDynamics Vol 11 (1) 1988 pp 7ndash12

4Hazawa K Shin J Fujiwara D Igarashi K Fernando D andNonami K ldquoAutonomous Autorotation Landing of Small UnmannedHelicopterrdquo Transactions of the Japan Society of Mechanical EngineersVol 70 (698) 2004 pp 2862ndash2869

5Abbeel P Coates A Hunter T and Ng A Y ldquoAutonomousAutorotation of an RC helicopterrdquo Experimental Robotics Vol 542009 pp 385ndash394

6Dalamagkidis K Valavanis K P and Piegl L A ldquoAutonomousAutorotation of Unmanned Rotorcraft using Nonlinear Model PredictiveControlrdquo Journal of Intelligent and Robotic Systems Vol 57 (1ndash4)September 2009 pp 351ndash369

7Dooley L W and Yeary R D ldquoFlight Test Evaluation of theHigh Inertia Rotor Systemrdquo USARTL-TR-79-9 US Army Research andTechnology Laboratories June 1979

8Yomchinda T Horn J F and Langelaan J W ldquoFlight Path Plan-ning for Descent-Phase Helicopter Autorotationrdquo AIAA-2011-6601AIAA Guidance Navigation and Control Conference Portland ORAugust 8ndash11 2011 pp 1ndash24

9Tierney S and Langelaan J ldquoAutorotation Path Planning UsingBackwards Reachable Set and Optimal Controlrdquo AHS International 66thAnnual Forum Proceedings Phoenix AZ May 11ndash13 2010

10Keller J D McKillip Jr R M Horn J F and Yomchinda TldquoActive Flight Control and Applique Inceptor Concepts for Autorota-tion Performance Enhancementrdquo AHS International 67th Annual ForumProceedings Virginia Beach VA May 3ndash5 2011

11Bachelder E N Lee D-C and Aponso B L ldquoAutorotation FlightControl Systemrdquo US Patent 7976310 B2 2011

12Padfield G Lee D and Bradley R ldquoHow Do Helicopter PilotsKnow When to Stop Turn or Pull Uprdquo Journal of the American Heli-copter Society Vol 48 (2) 2003 pp 108ndash109

13Padfield G Clark G and Taghizad A ldquoHow Long Do PilotsLook Forward Prospective Visual Guidance in Terrain-Hugging FlightrdquoJournal of the American Helicopter Society Vol 52 (2) 2007 pp 134ndash145

14Padfield G D Lu L and Jump M ldquoTau Guidance in Boundary-Avoidance Tracking New Perspectives on Pilot-Induced OscillationsrdquoJournal of Guidance Control and Dynamics Vol 35 (1) January 2012pp 80ndash92

15Jump M and Padfield G ldquoInvestigation of the Flare Maneu-ver Using Optical Taurdquo Journal of Guidance Control and DynamicsVol 29 (5) 2006 pp 1189ndash1200

16Livchitz M Abershitz A Soudak U and Kandel A ldquoDe-velopment of an Automated Fuzzy-logic-based Expert System forUnmanned Landingrdquo Fuzzy Sets and Systems Vol 93 (2) 1998pp 145ndash159

17Yen J and Langari R Fuzzy Logic Intelligence Control andInformation Pearson Education Zug Switzerland 1999

18Sunberg Z ldquoA Real Time Expert Control System For Heli-copter Autorotationrdquo Masterrsquos Thesis Texas AampM University CollegeStation TX 2013

19Talbot P D Tinling B E Decker W A and Chen R T NldquoA Mathematical Model of a Single Main Rotor Helicopter for PilotedSimulationrdquo TM-84281 NASA 1982

20Chen R T N ldquoA Simplified Rotor System MathematicalModel for Piloted Flight Dynamics Simulationrdquo TM-78575 NASAMay 1979

21Chen R T N ldquoEffects of Primary Rotor Parameters on FlappingDynamicsrdquo Technical Paper TP-1431 NASA Ames Research CenterJanuary 1980

22Sheldahl R E and Klimas P C ldquoAerodynamic Characteristicsof Seven Symmetrical Airfoil Sections through 180-degree Angle ofAttack for Use in Aerodynamic Analysis of Vertical Axis Wind Tur-binesrdquo SAND-80-2114 Sandia National Laboratories AlbuquerqueNM March 1981

23Peters D Boyd D and He C ldquoFinite-State Induced-Flow Modelfor Rotors in Hover and Forward Flightrdquo Journal of the American Heli-copter Society Vol 34 (4) October 1989 pp 5ndash17

24Celi R ldquoState-Space Representation of Vortex Wakes Using theMethod of Linesrdquo Journal of the American Helicopter Society Vol 50(2) April 2005 pp 195ndash205

25Johnson W ldquoTime-Domain Unsteady Aerodynamics of Rotors withComplex Wake Configurationsrdquo Vertica Vol 12 1988 pp 83ndash100

26Pitt D M and Peters D A ldquoTheoretical Prediction of Dynamic-Inflow Derivativesrdquo Vertica Vol 6 1981 pp 21ndash34

27Peters D A and HaQuang N ldquoDynamic Inflow for PracticalApplicationsrdquo Journal of the American Helicopter Society Vol 33 (4)October 1988 pp 64ndash68

28Heyson H H ldquoGround Effect for Lifting Rotors in Forward FlightrdquoTechnical Note D-234 NASA May 1960

29Knight M and Hefner R A ldquoAnalysis of Ground Effect on theLifting Airscrewrdquo Technical Note TN-835 NACA Washington DCDecember 1941

30Free L M and Hepler L J ldquoHeight-Velocity Test AH-1G He-licopter at Heavy Gross Weightrdquo USAASTA Project No 74-19 USArmy Aviation Systems Command Edwards AFB CA June 1974

022008-15


limits to the optimization problem and evaluating initial conditions wellwithin the heightndashvelocity avoid region This analysis concluded that theflight envelope for safe autorotation can be significantly enlarged usingautomatic control More recently in research focused on autonomous ro-torcraft Hazawa et al (Ref 4) created a traditional proportionalndashintegralcontroller for landing a small helicopter in cases of engine failure Abbeelet al (Ref 5) created a reinforcement learning controller that attempts tomatch trajectories recorded from autorotative descents performed by ahuman pilot Algorithm performance was verified experimentally duringsuccessful autonomous autorotations executed with a small hobby-sizedhelicopter Dalamagkidis et al (Ref 6) developed an autorotation controlsystem based on receding horizon neural network optimization althoughthe controller was limited to vertical autorotations only and was testedin simulation using a simplified one-dimensional dynamic model Thesetests were further restricted in the case of full-scale aircraft to includeonly vehicles modified with a high-energy rotor system (Ref 7) provid-ing a high margin for error in control system performance

Additional research has focused on control automation during specificphases of descent or for vehicle path planning Yomchinda et al (Ref 8)have proposed a path-planning algorithm for the steady-state descentphase whereas Tierney and Langelaan (Ref 9) have presented a methodfor calculating the set of flare entry points from which a helicopter cansafely land Others have developed methods to reduce pilot workloadduring autorotation using simple heuristic criteria that communicate to apilot upon approaching a dangerous state (Ref 10) Recently Bachelderet al (Ref 11) developed an autonomous autorotation controller basedon iterative optimization The control law was implemented in an avion-ics package and was meant to provide pilot cues and guidance duringautorotative descents

Many elements common to previous approaches have limited theirutility in practical systems Reinforcement learning algorithms requireextensive training data that may not be available and since they are tiedto a specific flight platform they are limited in flexibility and scalability toother aircraft Iterative optimization algorithms such as those proposedin Refs 6 8 and 11 require significant computational capability and ingeneral lack convergence guarantees Such iterative algorithms may notbe suitable for certification especially given the time constraints inher-ent in autorotation trajectory generation and the robustness guaranteeslikely to be required Throughout the autorotation control literature ithas been almost universally recognized that computation of a feasibleflare trajectory is one of the most difficult control tasks inherent in themaneuver given the variety of initial flight conditions the presence of ex-ternal disturbances and the high dimensionality of the problem (Ref 9)Especially for low-cost platforms new autorotation control laws areneeded that provide suitable flexibility and robustness while avoidingiterative optimization high-fidelity onboard dynamic models or blackbox reinforcement learning approaches

At the same time significant recent research efforts in the handlingqualities community led by Padfield et al (Refs 12ndash14) have noted theimportance of estimated time to contact with a point or obstacle in a widevariety of pilot maneuvers This value termed optical tau and defined asthe ratio between distance to a certain viewpoint and closing velocityhas been demonstrated to be a critical factor in pilot trajectory trackingevasive maneuvers and pilot-induced oscillation Specifically Jump andPadfield (Ref 15) have shown that during flare maneuvers close to theground pilots adjust the estimated motion tau to ground impact throughcontrol inputs to match a pilot-generated reference value Similarly itis shown here that predicted time to impact with the ground plays animportant role in autorotation control and is the mechanism that providesflexibility in flare trajectory generation and tracking

This paper presents a novel multiphase expert control system forhelicopter autorotation The controller is composed of multiple phases

which are executed sequentially as the autorotation maneuver progressesPhase changes are fuzzily defined and are initiated through altitude andpredicted time-to-impact criteria A novel aspect of the control design isits use of time-to-impact predictions during the flare maneuver and its useof a desired time-to-impact reference value conditioned on the vehiclersquoshorizontal velocity vertical velocity and rotor kinetic energy A set oftuning parameters allows the controller to be applied to a wide set ofhelicopter platforms with minimal structural changes Furthermore thesimplicity of the controller design minimizes computational burden andimproves its prospects for flight certification First the control systemis described in detail followed by a brief description of the simulationmodel used to evaluate controller performance Monte Carlo simulationresults are presented for both the Bell AH-1G helicopter as well as fora small remote-controlled (RC) sized helicopter Finally results from alimited set of flight experiments are provided to demonstrate controllerperformance in a realistic environment

Control Law Formulation

The control law is designed based on several requirements and de-sign principles First it must be applicable to forward flight scenarios andshould not be restricted to vertical autorotation only Second the con-trol law must not rely on a high-fidelity dynamic model of the aircraftwhich may not be available or may be too computationally expensiveThird the controller should be portable to various classes of helicoptersboth manned and unmanned Finally the controller should avoid itera-tive optimization and exhibit minimal computational burden This finaldesign constraint is meant to allow the autorotation controller to functionon many low-cost autopilot systems which are becoming increasinglypopular in the small unmanned aerial vehicle (UAV) community

These design principles led to formulation of the autorotation con-troller as an expert system The term ldquoexpert systemrdquo has been usedto describe a wide range of control systems and other computationalstructures Essentially two characteristics define expert system controlarchitectures First such controllers generally imitate control methodolo-gies applied by expert human operators Second these control systemsusually have ldquoexpertrdquo knowledge already available to them at runtime inthe form of a deterministic low-order dynamic model that is there is noiterative learning high-fidelity model prediction or optimization at run-time An example of an expert control law applied to a similar problem isthe controller derived by Livchitz et al (Ref 16) for autonomous landingof a small fixed-wing aircraft Unlike the controller described in Ref 16which relies mainly on a fuzzy logic structure the controller proposedhere uses a combination of several reasoning approaches including crisplogic fuzzy logic and proportional-integral-derivative control

The control structure considered in this paper consists of a standardinner-outer loop control architecture in which an inner-loop controller isresponsible for tracking velocity commands generated by an outer loopcontroller A block diagram of this control architecture is shown in Fig 1During nominal powered operating scenarios a waypoint following con-troller may send velocity commands to the inner loop controller (labeledas a ldquovelocity-tracking controllerrdquo) which is responsible for achievinga suitable vehicle orientation to track these commands The inner-loopcontroller therefore generates main rotor cyclic and collective commandsas well as tail rotor collective commands given desired velocity values Inthe case of autorotation the outer loop waypoint following controller isreplaced by the autorotation controller described here The autorotationcontroller therefore provides forward velocity commands (udes) maxi-mum pitch and roll orientation limits (ηmax) and main rotor collectivecommands (θ0) as shown in Fig 1 The velocity commands and orienta-tion constraints are sent directly to the inner-loop controller for trackingThus the autorotation control system is designed for straightforward

022008-2




radicφ2 + θ2





Alti

tude

AG

L (f

t minus lo

g sc

ale)

SS Descent

Preflare

Flare

Landing

Touchdown

0 2 4 6 8 1010

0

101

102

103






022008-3



udes = U_AUTO (1)






Preflare


udes = U_AUTO (4)




Flare


















022008-4



KEavailable equiv 1

2mu2 + 1

2IR2 (9)



2m(U_AUTO)2 + 1

2IR(RPM_AUTO)2 (10)



2IR(RPM_AUTO)2 (11)











h(t + TT IF ) = h(t) + h(t) TTIF + 1

2h(t) TTI 2

F (15)


hdes = minus 2

TTI 2F

h minus 2

TTIF

h (16)




TTIF le minus2h

h(17)



CT = σclα

(θ0

6minus λ

4

)(18)


h = ρR32Nc

(θ0

6mminus w

4mR

)+ g (19)






θ = kθ0

(θD

0 minus θC0

) = K_COL



K_COL asymp 6m

ρR32Nc(21)


022008-5




θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF


hlt TTIF

(22)

Landing




θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown











h = 1

Kθ0

(θ0 minus G) (29)


θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)



minustτC (31)


A = h(0) τT + h(0)

1 minus τT

τC

(32)



h(0) gtminush(0)

τC

(33)



022008-6







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15




radicφ2 + θ2





Alti

tude

AG

L (f

t minus lo

g sc

ale)

SS Descent

Preflare

Flare

Landing

Touchdown

0 2 4 6 8 1010

0

101

102

103






022008-3



udes = U_AUTO (1)






Preflare


udes = U_AUTO (4)




Flare


















022008-4



KEavailable equiv 1

2mu2 + 1

2IR2 (9)



2m(U_AUTO)2 + 1

2IR(RPM_AUTO)2 (10)



2IR(RPM_AUTO)2 (11)











h(t + TT IF ) = h(t) + h(t) TTIF + 1

2h(t) TTI 2

F (15)


hdes = minus 2

TTI 2F

h minus 2

TTIF

h (16)




TTIF le minus2h

h(17)



CT = σclα

(θ0

6minus λ

4

)(18)


h = ρR32Nc

(θ0

6mminus w

4mR

)+ g (19)






θ = kθ0

(θD

0 minus θC0

) = K_COL



K_COL asymp 6m

ρR32Nc(21)


022008-5




θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF


hlt TTIF

(22)

Landing




θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown











h = 1

Kθ0

(θ0 minus G) (29)


θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)



minustτC (31)


A = h(0) τT + h(0)

1 minus τT

τC

(32)



h(0) gtminush(0)

τC

(33)



022008-6







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15



udes = U_AUTO (1)






Preflare


udes = U_AUTO (4)




Flare


















022008-4



KEavailable equiv 1

2mu2 + 1

2IR2 (9)



2m(U_AUTO)2 + 1

2IR(RPM_AUTO)2 (10)



2IR(RPM_AUTO)2 (11)











h(t + TT IF ) = h(t) + h(t) TTIF + 1

2h(t) TTI 2

F (15)


hdes = minus 2

TTI 2F

h minus 2

TTIF

h (16)




TTIF le minus2h

h(17)



CT = σclα

(θ0

6minus λ

4

)(18)


h = ρR32Nc

(θ0

6mminus w

4mR

)+ g (19)






θ = kθ0

(θD

0 minus θC0

) = K_COL



K_COL asymp 6m

ρR32Nc(21)


022008-5




θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF


hlt TTIF

(22)

Landing




θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown











h = 1

Kθ0

(θ0 minus G) (29)


θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)



minustτC (31)


A = h(0) τT + h(0)

1 minus τT

τC

(32)



h(0) gtminush(0)

τC

(33)



022008-6







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15



KEavailable equiv 1

2mu2 + 1

2IR2 (9)



2m(U_AUTO)2 + 1

2IR(RPM_AUTO)2 (10)



2IR(RPM_AUTO)2 (11)











h(t + TT IF ) = h(t) + h(t) TTIF + 1

2h(t) TTI 2

F (15)


hdes = minus 2

TTI 2F

h minus 2

TTIF

h (16)




TTIF le minus2h

h(17)



CT = σclα

(θ0

6minus λ

4

)(18)


h = ρR32Nc

(θ0

6mminus w

4mR

)+ g (19)






θ = kθ0

(θD

0 minus θC0

) = K_COL



K_COL asymp 6m

ρR32Nc(21)


022008-5




θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF


hlt TTIF

(22)

Landing




θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown











h = 1

Kθ0

(θ0 minus G) (29)


θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)



minustτC (31)


A = h(0) τT + h(0)

1 minus τT

τC

(32)



h(0) gtminush(0)

τC

(33)



022008-6







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15




θ0 =K_COLTAU

(minus 2(h+hTTIF )

TTI2F

minus h)

for minus 2h

hge TTIF


hlt TTIF

(22)

Landing




θ0 =K_COLTAU

(minus 2(h+hTTI_L)

TTI_L2 minus h)

for minus 2h

hge TTI_L


hlt TTI_L

(25)

Touchdown











h = 1

Kθ0

(θ0 minus G) (29)


θ0 = Kθ0

(1

τC

(minus h

τT

minus h

)minus h

τT

+ G

)(30)



minustτC (31)


A = h(0) τT + h(0)

1 minus τT

τC

(32)



h(0) gtminush(0)

τC

(33)



022008-6







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15







phases





Flare


2

times(

1

TAU_CLIMB

(minus h

TTIF

minus h

)minus h

TTIF

+ GRAV

)(34)

Landing


2

times(

1

TAU_CLIMB

(minus h

TTI_Lminus h

)minus h

TTI_L+ GRAV

)(35)





Simulation Model




022008-7



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15



Dynamic inflow



r

Rsin ψMR + λc

r

Rcos ψMR (36)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ = C (37)


Ground effect




λssIGE =(

1 minus 08w

w0

)λss (39)




= [L]minus1

(1 minus 08

w

w0

)λss (41)

= [L]minus1[L]

(1 minus 08

w

w0

)C (42)

CIGE =(

1 minus 08w

w0

)C (43)


[M]

⎡⎣ λ0

λs

λc

⎤⎦ + [L]minus1

⎡⎣ λ0

λs

λc

⎤⎦ =

(1 minus 08

w

w0

)C (44)


Simulation overview



Simulation Results




022008-8












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15












0 200 400 600 800 1000 1200 14000

50

100

150

200

250

300

350

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 5 10 15 20 250

10

20

30

40

50

60

70

80

90

100

Time (s)

For

war

d ve

loci

ty (

fts)




022008-9


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15


0 5 10 15 20 2520

25

30

35

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 5 10 15 20 258

10

12

14

16

18

Time (s)

Col

lect

ive

pitc

h θ

0 (de

g)


0 5 10 15 20 250

02

04

06

08

1


Pha

se c

ontr

olle

r au

thor

ity v

alue





0 5 10 15 20 250

1

2

3

4

5

6

7

8

9

10


Tim

e to

impa

ct (

s)


F (desired)









022008-10


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15


0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)







0 20 40 60 80 1000

100

200

300

400

500

600

700

800


Initi

al a

ltitu

de (

ft A

GL)










022008-11


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15


0 5 10 15 20 25 30 35 400

10

20

30

40

50

60

70

80

90

100

x Location (ft)

Cen

ter

of m

ass

altit

ude

(ft)


0 1 2 3 4 5 6 7minus2

0

2

4

6

8

10

12

Time (s)

For

war

d ve

loci

ty (

fts)



Flight Test


0 1 2 3 4 5 6 750

100

150

200

Time (s)

Rot

or r

otat

ion

rate

Ω

(ra

ds)

0 1 2 3 4 5 6 7minus5

0

5

10

15

Time (s)M

ain

roto

r co

llect

ive

pitc

h θ 0 (

deg)


0 1 2 3 4 5 6 70

05

1

15

2

25

3

35

4

45

5


Tim

e to

impa

ct (

s)


F (desired)






022008-12


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15


0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)



0 10 20 30 40 50 600

20

40

60

80

100

120

140

160

180

200


Initi

al a

ltitu

de (

ft A

GL)




0

100

200

300

Alti

tude

(ft)



minus40

minus20

0

20

Clim

b ra

te e

stim

ate

(fts

)




0

10

20

Com

man

ded

colle

ctiv

e (d

eg)



500

1000

1500

2000

Rot

or r

pm





022008-13



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15



02

04

06

08

1









Flight-test results



Concluding Remarks


022008-14



Acknowledgments


References































022008-15



Acknowledgments


References































022008-15

Documents

A Real-Time Expert Control System For Helicopter Autorotationireal.gatech.edu/wp-content/themes/twentytwelve-child/... · 2015. 12. 29. · JOURNAL OF THE AMERICAN HELICOPTER SOCIETY