aiaa 2000-1560 flight control using distributed shape ...mln/ltrs-pdfs/nasa-aiaa-2000-1560.pdf1...

1American Institute of Aeronautics and Astronautics

AIAA 2000-1560Flight Control using DistributedShape-Change Effector Arrays

David L. Raney, Raymond C. Montgomery and Lawrence L .Green

NASA Langley Research Center

Hampton, VA 23681-2199

Michael A. Park

George Washington University

Joint Institute for the Advancement of Flight Sciences (JIAFS)

41st AIAA/ASME/ASCE/AHS/ASC Structures,

Structural Dynamics, and Materials Conference &Exhibit

3-6 April 2000

Atlanta, Georgia

For permission to copy or to republish, contact the American Institute of Aeronautics and Astronautics,1801 Alexander Bell Drive, Suite 500, Reston, VA, 20191-4344.


FLIGHT CONTROL USING DISTRIBUTED SHAPE-CHANGEEFFECTOR ARRAYS

David L. Raney , Raymond C. Montgomery† and Lawrence L .Green‡

NASA Langley Research CenterHampton, VA 23681-2199

Michael A. Park§

George Washington UniversityJoint Institute for the Advancement of Flight Sciences (JIAFS)

Research scientist, Dynamics and Control Branch, MS 132, Member AIAA.

† Research scientist, Dynamics and Control Branch, MS 132, Senior Member AIAA.‡ Research scientist, Multidisciplinary Optimization Branch, MS 159, Senior Member AIAA.§ Graduate Student, NASA Langley Research Center, Multidisciplinary Optimization Branch, MS 159, Member AIAA.

Copyright © 2000 by the American Institute of Aeronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The Government has royalty-free license to exercise all rights under the copyright claimed hereinfor government purposes. All other rights reserved by the copyright owner.

ABSTRACT

Recent discoveries in material science andfluidics have been used to create a variety ofnovel effector devices that offer great potential toenable new approaches to aerospace vehicleflight control. Examples include small inflatableblisters, shape-memory alloy diaphragms, andpiezoelectric patches that may be used to pro-duce distortions or bumps on the surface of anairfoil to generate control moments. Small jetshave also been used to produce a virtual shape-change through fluidic means by creating a recir-culation bubble on the surface of an airfoil. Anadvanced aerospace vehicle might use distributedarrays of hundreds of such devices to generatemoments for stabilization and maneuver control,either augmenting or replacing conventionalailerons, flaps or rudders. This research demon-strates the design and use of shape-change devicearrays for a tailless aircraft in a low-rate maneu-vering application. A methodology for assessingthe control authority of the device arrays isdescribed, and a suite of arrays is used in adynamic simulation to illustrate allocation anddeployment methodologies. Although theauthority of the preliminary shape-change arraydesigns studied in this paper appeared quite low,the simulation results indicate that the effectorsuite possessed sufficient authority to stabilizeand maneuver the vehicle in mild turbulence.

INTRODUCTION

A number of concepts for novel controleffector devices have recently been developedwhich offer great potential to enable entirely new

approaches to aerospace vehicle flight control.Examples of such devices include smallinflatable blisters, shape-memory alloydiaphragms and piezoelectric patches that maybe used to produce distortions or bumps on thesurface of an airfoil, as well as smallpiezoelectric pumps that can produce oscillatorysurface jets. Potential applications of thesedevices include forebody vortex asymmetrymanagement (Roos), control and manipulationof shear flows (Smith, Glezer), fluidic thrustvectoring (Pack), and low angle-of-attack liftaugmentation (Nae). 1-4 Pulsed blowing has alsobeen used to actively vary the reattachmentlocation of a separated flow over specificallydesigned portions of an airfoil (Seifert, Pack).5,6

The Aircraft Morphing Program under way at theNASA Langley Research Center focuses on thedevelopment and application of these noveleffector devices, covering a spectrum researchtopics which include materials development,actuator design and testing, CFD modeling andoptimization methods, dynamic simulation andcontrol using such devices (McGowan).7 In thisstudy we will examine the potential to usedistributed arrays of shape-change devices toprovide a basis for aircraft flight control. Anadvanced aerospace vehicle might use hundredsof small shape-change devices to generate forcesand moments for stabilization and maneuvercontrol, without the need for conventional,hydraulically actuated ailerons, flaps or ruddersas investigated by Scott and Montgomery, andby Allan.8,9 Potential reasons to consider suchalternatives include reduced observability,redundancy, and possible weight reduction of theoverall effector complement.


Given this goal, how might the bestlocations for placement of such devices on theaircraft surface be determined, and how mightthe devices be used in a control system toactually maneuver and fly the vehicle? Thisresearch attempts to address such questions byapplying arrays of a generic shape-change deviceto a representative aircraft configuration in adynamic simulation. This work builds upon aninitial investigation that was conducted by Scottand Montgomery8, extending the research toinclude an effector placement study followed bya revised effector suite, a new allocation anddeployment method, and a new control design.The control system deploys distributed arrays ofthe shape-change devices in a “quantized”fashion. That is to say that each small bump inan array is either completely on or off, and moreof them are turned on to produce larger forces asneeded. Using these arrays, the control system isable to stabilize and maneuver the vehiclewithout conventional hinged surfaces such asailerons or a rudder. The predicted authority ofthe designs studied in this paper is rather lowwhen compared to conventional effectors, so thetarget for utilization of this technology iscurrently low-rate maneuvers (roll rates of 10degrees per second or less).

SUBJECT CONFIGURATION

The example aircraft design used in thispaper is the Innovative Control Effector (ICE)aircraft from Lockheed Martin Tactical AircraftSystems, (Dorsett).10 The configuration is atailless, delta-wing fighter, which was developedfor the purpose of investigating novel controleffector concepts and arrangements. NASA isusing the ICE design, shown in Figure 1, as anexample configuration under a cooperativeagreement with Lockheed Martin.

Wing Characteristics

Area .... 75.12 m2 (808.6 ft.2)Span .... 11.43 m (37.5 ft.)Aspect Ration ... 1.74Leading Edge Sweep .. 1.134 rad (65 deg.)

Figure 1. Lockheed-Martin's ICE configuration.

A simulation database of stability andcontrol derivatives was obtained for thisconfiguration from Lockheed Martin. Thepotential of shape change device arrays to serveas alternative control effectors for the ICE

aircraft is examined using the simulation modelwith linearized aerodynamics. A low-speed,potential flow code (the Panel Method fromAmes Research Center, PMARC) is used topredict the forces and moments that would beproduced by the shape-change effector arrayswhich were designed for this configuration.11

The analysis was performed for a flightcondition of Mach 0.6 at an altitude of 15000 ft.The equilibrium trim angle-of-attack at this flightcondition is approximately 4.4 degrees. Controlmoments required to trim at this flight conditionare assumed to be generated by conventionaleffectors. The shape-change effector arrays areused to stabilize and maneuver the vehicle aboutthis equilibrium flight condition. In this paper,the term "device" will be used to refer to anindividual shape-change effector unit or singlebump, the term "array" will refer to a particulargrouping of adjacent devices, and the term"suite" will refer the entire collection of devicearrays with which the vehicle is outfitted.

CONTROL EFFECTOR DEVICE MODEL

The generic shape-change device modelused in this investigation consists of a smallbump which deflects normal to the surface of thevehicle. The resulting shape-change wasrepresented on a panel model of the ICEconfiguration by displacing a given gridpoint aprescribed distance, XN , along a vector which isnormal to the geometry surface, as shown inFigure 2. The perturbed geometry was thenanalyzed using the PMARC code, and theresulting forces and moments were differencedfrom the values for the nominal geometry toprovide an estimate of the forces and momentsthat would be produced by the surface distortion.Several assumptions are implicit in this modelingapproach, including the assumption that thesurface distortion does not produce separatedflow and the assumption that the flow is entirelysubsonic. These restrictions were imposed bythe potential flow code that was used to evaluatethe shape-change devices.

•

XN

Figure 2. Shape-change device modeled asdeflection of gridpoint along normal vector.


The use of the modeling approach illustratedin Figure 2 appears reasonable for shape-memory alloy diaphragms, piezoelectric domesand inflatable blisters which produce real surfacedistortions. The use of fluidic devices, such aspulsed jets and zero-net-mass-flow oscillatoryjets ("synthetic jet"), to produce a virtual shape-change is far less understood and is a subject ofcurrent research. Kral and Donovan haveperformed a detailed study regarding thesimulation of an isolated jet using Reynolds-averaged Navier-Stokes (RANS) equations.12,13

Their result, shown in Figure 3, demonstrates theeffect of a steady-jet on a NACA 0012 airfoil atRN = 8.5 x 106 and α=.0698 rad (4.0°), Thefigure shows streamlines for the Uj/U∞ = 1.0case, illustrating that the effect of the steady jetis to produce a virtual distortion of the surfaceresulting from the generation of a smallrecirculation bubble, as well as an effluent addedto the primary flow. A proper potential modelwould include a surface distortion as well as aneffluent. In this paper we assume there is zero-mass-transfer and therefore no added effluent.

Effluent

Recirculation Zone

Figure 3. Streamlines = .0698 rad (4.0 ), withsteady-jet control at Uj/U = 1.0.

The modeling approach described aboveincludes no description of the actuator dynamics.A recent investigation by Pack found theresponse time of an exhaust flow to a thrust-vectoring pulsed jet to be very fast -- on theorder of 22 ms, including both the actuation ofthe jet device itself and the fluidic response tothe presence of the jet.3 Other means ofgenerating the shape-change, such as inflatableblisters, could presumably be slower since theresponse time would clearly be dependent uponthe particular mechanization employed. The goalof this investigation was to examine the issues ofshape-change effector placement, deployment,and use in control design, rather than to developa high-fidelity model of a shape-change effector,and so an instantaneous response of the devicewas deemed sufficient for this first-order model.

DESIGN OF EFFECTOR ARRAYS

A major issue to consider in the design ofshape-change effector arrays is where to locatethe devices on the aircraft surface for maximumbenefit. A sensitivity analysis was performedusing a geometry model of the ICE configurationto aid in determining where the device arraysshould be positioned on the vehicle. The analysisinvolved differentiating the PMARC code usingthe "ADIFOR" tool (Automatic Differentiationof Fortran, Carle & Fagan).14 The differentiatedcode was then applied to the ICE configurationmodel to produce the partial derivative of theforces and moments acting on the aircraft withrespect to a displacement along the surfacenormal at every grid point on the aircraftgeometry model, as described by Park &Green.15 The resulting sensitivity database ofpitch, roll, and yaw moment derivatives withrespect to a normal displacement at everygridpoint on the geometry (taken individually) isshown as a set of shaded planform maps inFigure 4. The shaded regions in the figureindicate greater moment sensitivity and thereforesuggest potential locations at which to place theshape-change devices. The sensitivity plots aredescribed in much greater detail by Park &Green.15

Pitch –

Roll –

Yaw –

∂XN

∂Cm

∂XN

∂Cl

∂XN

∂Cn

Figure 4. Moment sensitivity databases forgridpoint displacements produced by applying

ADIFOR to PMARC using the ICE model.


The databases shown in Figure 4 wereincorporated into an interactive design tool thatwas developed to allow an engineer to quicklybuild up and analyze distributed arrays of smallshape-change devices on the surface of the ICEaircraft. The tool was produced using Matlab™ ,which provides basic constructs for generatingthe interactive graphical user interface and data-manipulation functions. It allows the designer touse the sensitivity data in a subjective fashion toguide the placement, size, and shape of the arrayso that it can produce the forces and momentsrequired to maneuver the vehicle.

The graphical user interface for the effectorarray design tool is shown in Figure 5. Usingthis tool, the designer designates the geometrygridpoints at which to place each element of theshape-change array. The designer also defines aunit deflection magnitude for each element of thearray. Once a grouping of shape-change deviceshas been defined, the designer can obtain apreliminary prediction of its effectiveness andgenerate a perturbed geometry grid that includesthe deployed effector array. This geometry filecan then be used with aerodynamic analysisprograms, in this case the PMARC code, to

further assess the effectiveness of the device.Although the design tool provides somesubjective guidance regarding the location andshape of a given device array, it does not provideinsight regarding the appropriate height profile(deflection magnitudes) for the various elementsof the array. Such insight might be provided bya matrix of second derivatives of the controlmoment with regard to normal displacement ofthe geometry gridpoints (the Hessian). TheADIFOR automatic Fortran differentiation codehas recently been endowed with a capability togenerate the Hessian of the dependentparameters in a Fortran program by Carle andFagan of Rice University, but this new capabilityhas not yet been applied to the ICE shape-changesensitivity analysis.

The design tool was used to generate a seriesof 31 candidate effector array configurations. Aplot of the pitch, roll, and yaw effectiveness foreach of the arrays is shown in Figure 6.Candidate arrays were designed for variousregions on the configuration, including upperand lower surface leading and trailing edges,mid-chord locations, and several wingtippositions.

Figure 5. Shape-change effector array design tool graphical user interface.


-8.E-04

-6.E-04

-4.E-04

-2.E-04

0.E+00

2.E-04

4.E-04

6.E-04

8.E-04

0 2 4 6 8 10 12 14 16 18 20 22 24 26 28 30 32

Design Number

Cl

Cm

Cn

Upper TE Lower TE Upper TIP Lower TIP Upper LE Lower LE Upper MID

Figure 6. Control authority plots for 31 candidate shape-change effector array designs.

The candidate designs were evaluated on thebasis of their authority and their ability togenerate a relatively decoupled control moment.The total number of devices included in a givenarray was not considered as a factor in theevaluation. A particular combination of fourdevice arrays was selected based on a subjectiveevaluation of suitability for providing 3-axismoment control. The effectiveness derivativescorresponding to the selected array designs arecircled in Figure 6. An ongoing investigationbeing performed in the MultidisciplinaryOptimization Branch at the NASA LangleyResearch Center is examining the application ofa more rigorous optimization method for theselection of an effector array suite from thecandidate designs.16 The suite of four effectorarrays that was selected for use in the remainderof this study is described below.

SELECTED EFFECTOR ARRAYS ANDDEPLOYMENT SCHEME

The four distributed shape-change device arraysthat were selected to compose the effector suitefor the ICE configuration are shown in Figure 7.The effector suite includes four arrays on eachwing, three on the upper surface and one on thelower surface. The entire suite of shape-changeeffector arrays includes a total of 156 individualdevices, 78 per wing. The upper-surface leading-edge array (ULE) consists of 10 devices - onedevice at each of 10 span stations (chord lines)

distributed along the leading edge as shown inFigure 7. The lower-surface trailing-edge array(LTE) and upper-surface trailing-edge array(UTE) both consist of 22 devices - two adjacentdevices at each of 11 span stations. The upper-surface wingtip array (UTip) consists of 24devices - six adjacent devices at each of 4 spanstations. The lower-surface trailing-edge, upper-surface trailing-edge, and upper-surface leading-edge arrays all have a maximum displacementheight of 2.4 inches. The upper-surface wingtiparray has a maximum displacement height of 1.2inches.

Lower SurfaceTrailing-Edge(LTE) Array

Upper SurfaceTrailing-Edge(UTE) Array

Upper SurfaceLeading-Edge(ULE) Array

Upper SurfaceWingtip (UTip)

Array

devices activateinboard tooutboard asmore control isrequired

Figure 7. Selected shape-change effector arraydesigns applied to ICE configuration.

Design Number

Mom

ent C

oeffi

cien

t


The effector suite was applied to the ICEvehicle in a simulation and used in a stabilityaugmentation and control system design. Thecontrol system employs a “quantized spanwise”deployment scheme for activation of the devicearrays, as noted in Figure 7. That is to say thateach device in an array is either completely on oroff (rather than proportionally deployed), andmore of them are turned on to produce largerforces as needed, from the most inboard to themost outboard span station of each array. Alldevices located along a particular span station ina given array operate together - turning on or offat the same time. This quantized deploymentscheme addresses a realistic aspect of the controlallocation problem, since a number of existingshape-change device concepts involve this sortof "bang-bang" operation.

Each of the four arrays were analyzed usingPMARC in each of their quantized deploymentstates to generate a database of controleffectiveness for use in a closed-loop dynamicsimulation of the vehicle model. Figure 8 showsplots of the control effectiveness for theprogressive spanwise deployment of each of thedevice arrays. The use of the PMARCpredictions for control effectiveness in thedynamic simulation constitutes a quasi-staticassumption since unsteady aerodynamic effectsdue to the transient deployment of the devicesare neglected.

DYNAMIC SIMULATION

A six degree-of-freedom dynamicssimulation was used to investigate theunaugmented and augmented aircraft dynamics.The body axis coordinate system shown inFigure 9 is used for the formulation of theequations of motion.

The longitudinal configuration aero-dynamics are represented in the simulation as alinear expansion of the longitudinal aerodynamicforce and moment coefficients in angle of attack,α, and pitch rate, q, plus the force and momentcontributions from the shape-change effectordeflections, δ, as in the method of Bryan.17 Thus,the longitudinal coefficients, Cx, Cz, and Cm,are expressed as:

Cx = Cxo + Cxαα + Cxqq(c/2V) + Cxδ δCz = Czo + Czαα + Czqq(c/2V) + Czδ δCm = Cmo + Cmαα + Cmqq(c/2V) + Cmδ δ

Upper Leading Edge (ULE) Array

-2.E-04

-1.E-04

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

0 1 2 3 4 5 6 7 8 9 10

Number of Bump Points Activated

ClCmCn

Upper Trailing Edge (UTE) Array-7.E-04

-6.E-04

-5.E-04

-4.E-04

-3.E-04

-2.E-04

-1.E-04

0.E+00

0 1 2 3 4 5 6 7 8 9 10 11

Number of Span Stations Activated

ClCmCn

Lower Trailing Edge (LTE) Array

-1.E-04

0.E+00

1.E-04

2.E-04

3.E-04

4.E-04

5.E-04

6.E-04

0 1 2 3 4 5 6 7 8 9 10 11


ClCmCn

Upper Wingtip (UTip) Array-3.E-04

-2.E-04

-2.E-04

-1.E-04

-5.E-05

0.E+00

0 1 2 3 4Number of Span Stations Activated

ClCmCn

Figure 8. Control effectiveness buildup for eachof 4 shape-change effector arrays included in

ICE effector suite (right wing).



x, pCx, Cl

Relative Wind V

z, rCz, Cn

y, qCy, Cm,

Figure 9. Body axis coordinate systemdefinitions used in dynamic simulation.

Dependence on both angle of attack, α, andangle of sideslip, β, is retained for the lateral-directional force and moment calculation, so thecoefficients, Cy, Cl, and Cn, are expressed as:

Cy = Cyββ + Cypp(b/2V) + Cyrr(b/2V) + Cyδ δ

Cl = Clββ + Clpp(b/2V) + Clrr(b/2V) + Clδ δ

Cn = Cnββ + Cnpp(b/2V) + Cnrr(b/2V) + Cnδ δ

Where,

Cyβ = Cyβo + Cyβαα

Clβ = Clβo + Clβαα

Cnβ = Cnβo + Cnβαα

The parameters relating to flight condition,including total air speed, V, and dynamicpressure, qbar, are calculated as:

V = (u2 + v2 + w2)1/2

qbar = ρ•V2/2

α = arctan(w/u)

β = arcsin(v/V)

The geometry constants, c, b, and S are thereference chord length, wing span, and wingarea, respectively. Also (u,v,w) and (p,q,r) arethe translational and rotational rates about thebody-fixed, reference (x,y,z) axes of the aircraft,respectively, and (Cx,Cy,Cz) and (Cl,Cm,Cn) arethe aerodynamics force and moment coefficientsabout the (x,y,z) axes, as indicated in Figure 9.The equations of motion for the rigid bodydynamics of aircraft are well developed andavailable in texts (Etkin).18 They require adescription of the attitude of the vehicle, whichhas traditionally been via Euler angles. These areused herein to represent the orientation of theaircraft with the sequence corresponding to ψabout the z the axis, θ about the y axis, andφ about the x axis. The kinematic differentialequations implemented in the simulation are:

dθ/dt = q•cos(φ) - r•sin(φ)

dψ/dt = (q•sin(φ) + r•cos(φ))/cos(θ)

dφ/dt = dψ/dt•sin(θ) + p

dh/dt= u•sin(θ)-w•cos(θ)cos(φ)-v•cos(θ)sin(φ)

where h is the altitude. For the longitudinalvariables, the dynamic equations of motion usedare:

du/dt = v•r-w•q+g[(T +Cx•qbar•S)/W- sin(θ)]

dw/dt = u•q-v•p+g[cos(θ)cos(φ)+Cz•qbar•S/W]

dq/dt = [Cm•qbar•S•c+(Iz-Ix)r•p+(r2-p2)Ixz -r•HT]/Iy

where g is gravity. Due to inertia terms it isconvenient to define the total rolling moment, L,and yawing moment, N, for the lateral equationsof motion as:

L = Cl•qbar•S•b + (Iy - Iz)•q•r + p•q•Ixz

N = Cn•qbar•S•b + (Ix - Iy)•q•p - q•r•Ixz + q•HT

where T is the engine thrust, and HT is themoment of momentum about the x axis of theengine rotors which are assumed to be alignedwith the body x axis. Assuming symmetry withrespect to the x-z plane, Ix, Iy, Iz are the momentsof inertia about the x,y,z axes and Ixz is therelevant product of inertia about the y axis.Thus, the lateral equations of motion are:

dv/dt = w•p-u•r +g(Cy•qbar•S/W+cos(θ)sin(φ))

dp/dt = (Iz•L + Ixz•N)/(Ix•Iz - Ixz2)

dr/dt = (Ixz•L + Ix•N)/(Ix•Iz - Ixz2)

The geometry constants used in thesimulation are c = 28.75 ft., b = 37.5 ft., and S =808.6 ft.2, and the mass/inertia parameters are W= 32750 lbf, Ix = 35479 slug-ft.2, Iy = 78451 slug-ft.2, Iz = 110627 slug-ft.2, and Ixz = -525 slug-ft2.The aerodynamic coefficients for the ICEconfiguration at the selected design flightcondition of Mach 0.6 and 15000 ft are listed inTables 1 and 2.

Table 1. Longitudinal Aerodynamic Coefficientsfor the ICE simulation.

Subscripto q

Cx 0.0166 -0.1973 0.Cz 0.0395 -2.2475 0.Cm 0.0036 -0.0467 -.39516


Table 2. Lateral Aerodynamic Coefficients forthe ICE simulation.

Subscripto p r

Cy -0.0534 0.2331 0. 0.Cl 0.0109 -0.7846 -.016 .021368Cn -0.0099 -0.1215 -.021789 -.01

CONTROL DESIGN USING SHAPE-CHANGE EFFECTOR ARRAYS

Eigenvalues for the uncontrolled flightdynamic modes of the ICE aircraft model wereobtained from a linearization of the simulationabout the equilibrium trim condition. Table 3presents the mode designations, frequencies anddamping values for the open-loop poles that areplotted as circles in Figure 10.

Table 3. Open-loop poles, frequencies anddamping ratios for the linearized ICE simulation

at Mach 0.6 and 15000 ft.

Eigenvalue DampingRatio

Freq.(rad/s)

Mode

-8.20e-01+2.04e+00i

3.74e-01 2.20e+00 Short- Period

-1.46e-03+6.64e-02i

2.20e-02 6.64e-02 Phugoid

-1.28e+00 1.00e+00 1.28e+00 Roll 5.72e-01+

7.71e-01i

-5.96e-01 9.60e-01 Dutch-

Roll -2.27e-02 1.00e+00 2.27e-02 Spiral

-6 -4 -2

0

2

-4

-2

0

2

4

Real

Imag

inar

y

Dutch RollShort Period

Spiral

Roll

-0.1 0-0.1

0

0.1

Spiral

Phugoid

Figure 10. Open-loop and closed-loop polelocations for the ICE simulation.

The longitudinal phugoid and short periodmodes are stable, but the lateral Dutch-roll modeis not. The lateral instability is not unexpecteddue to the tailless configuration of the ICEaircraft.

A feedback control law was designed thatuses the suite of shape-change device arrays tostabilize the vehicle's lateral dynamics whileproviding a bank-angle command trackingcapability. To accomplish the design, it wasnecessary to develop a feedback architecture,associated filters and control gains, and to devisea control allocation method and deploymentscheme for the suite of shape-change effectorarrays. The controller stabilizes and maneuversthe vehicle using only the shape-change arrays,although the vehicle's steady-state trim isprovided by conventional effectors.

A linear-systems pole-placement approachto the control law synthesis was selected forsimplicity. Since the open-loop longitudinaldynamics are stable, the control design focuseson the augmentation of the lateral-directionaldynamics. Therefore, only lateral dynamic stateswere used in the pole-placement controller. Anoverview of the dynamic simulation architectureshowing the relation of the command generator,control law and allocator, is shown in Figure 11.

6 DOFEquations of

MotionFeedbacks

p, r,

ControlLaw

Bank AngleCommand

DistributionAllocation

DrydenTurbulence

EffectorForces & Moments

Figure 11. Block-diagram overview ofsimulation architecture.

The linearized lateral dynamics of the open-loop aircraft model are represented in state-spaceform as:

˙ x = [A] x + [B] u

where the transpose of the state vector, x, isgiven by:

x T = { β p r φ }

and the transpose of the control deflectionvector, u, is given by:

u T = {δUTER δLTER δULER δUTipR …

δUTEL δLTEL δULEL δUTipL }


where each subscript corresponds to a particulareffector array as defined in Figure 7, and thesuffix R or L refers to the right or left wing,respectively. The matrices, A and B, contain theaircraft stability coefficients and controlcoefficients, respectively, from the linearsimulation model. To generate the closed-loopsystem we define a commanded input vectorwhich drives the shape-change device arraysusing the following control scheme:

ucmd = [P] mcmd

The vector, mcmd , represents the vector of desiredroll, pitch, and yaw moments:

mcmd = {Cl Cm Cn}cmdT

where Cm cmd = 0 and {Cl Cn}cmd is calculatedby the following lateral-directional state-feedback control law:

{Cl Cn}cmdT = [K] x

The feedback gain matrix, K, is calculated usingthe pole-placement algorithm for linear systemsas described by Franklin and Powell.19 Thematrix, P, represents the control allocationfunction, which calculates a combineddeployment of the eight effector arrays that willgenerate an approximation to the desiredmoment vector. In this design, the pseudo-inverse allocation method is used, which isperhaps the most familiar and fundamentalmeans of control allocation for coupled moment-generating effectors.20 The pseudo-inversematrix, [P], of the control effectiveness matrix iscalculated as:

P = BT [ BBT ] -1

But since the shape-change effectors areone-sided, negative deployments of the devicesare undefined. Therefore, negative deflectionsare reflected to the corresponding effector arrayon the opposite wing as positive deflections inthe effector allocation algorithm. An error inpitch moment is generated by the reflection ofnegative asymmetric control deflections to theopposite wing. This effect is compensated bycalculating an appropriate symmetric deflectionof the upper or lower trailing edge arrays,depending upon the sign of the pitch momenterror.

For the closed-loop system, the followingdesired lateral/directional pole locations wereprescribed as targets for the pole-placementcontroller:

Despoles =

- 2 . 2 5 0 0

- 7 . 2 5 0 0

-1.7678e+00 + 1 . 7 6 7 8 e + 0 0 i

- 1 . 7 6 7 8 e + 0 0 - 1 .7678e+00i

These pole locations, shown as pluses on theplot in Figure 10, were selected to stabilize thevehicle's lateral dynamics and provide improveddamping and settling time for gust response. Forturn coordination, a washout filter is applied tothe yaw-rate feedback with a transfer functionthat is given by:

rout

rin=

1.5s

1.5s +1

A final provision for the use of the effectorarrays is the presence of limiters within thecontrol law, with limits that are dictated by thelow authority of the control effector arrays. Thestability derivative, Cnp, generates an adverseyawing moment in proportion to roll rate,tending to produce an undesired sidesliptransient during rolling maneuvers.Additionally, as the vehicle rolls about the bodyaxis, angle of attack is converted into sideslip.Feedback paths in the control law are provided tocounteract these effects so as to generatecoordinated turns. But due to the limited yawauthority of the effector suite, the ability of thecontrol system to reject these effects is minimal,and maintaining turn coordination while rollingbecomes the limiting factor in our achievableroll-rate command. Therefore, a roll-rate limiterwas placed in the bank-angle command path.Iterative simulation runs which examinedvarious values for the roll-rate limit haverevealed that a maximum limit of 10 degrees persecond will prevent loss of control during rollingmaneuvers, so this value was used as themaximum roll rate that could be commanded.

SIMULATION RESULTS

The effectiveness and utility of the shape-change effector array suite was evaluated bysubjecting the dynamic simulation to variousatmospheric disturbance levels and by assessingthe maneuver capability that it provided. Usingthe shape-change arrays, the control system wasable to stabilize and maneuver the vehiclewithout conventional control surfaces. Thepredicted authority of the shape-change arrays israther low when compared to a rudder or aileron,so the control system generates relatively low-rate maneuvers. Figure 12 presents two timehistories produced by the dynamic simulation in


response to a + 20-degree bank angle doubletcommand with and without mild Dryden-spectraturbulence (σ = 3 ft/s).

0 5 10 15-10

-5

0

5

10

Time, sec

p, d

eg/s

ec

0 5 10 15-0.8

-0.6

-0.4

-0.2

0

0.2

0.4

0.6

Time, sec

side

slip

, deg

0 5 10 15-30

-20

-10

0

10

20

30

Time, sec

bank

ang

le, d

eg

Figure 12. Simulation time histories in responseto a 20-degree bank angle doublet command

with and without mild turbulence.

The maximum roll-rate achieved is 10 deg/sdue to the presence of the limiters in thecommand and feedback paths. Sideslip perturba-tions occur during the execution of the rolldoublet. Larger sideslip transients result fromthe turbulence, but the bank-angle commandtime history is minimally impacted. In spite ofthe relatively low authority of the shape-changeeffector array suite, the control law is able tostabilize and maneuver the vehicle within theprescribed roll-rate limits.

Figure 13 shows a comparison of controleffector array deployment with and without theDryden turbulence. The vertical axis on the plotsrepresents the number of devices that wereactivated in each of the eight arrays at any given

time during the maneuver. The figure is notintended to convey specific details regarding anyone particular array, but rather provides a generalindication of the level of control activity andsaturation that occurred during the run.

0 5 10 150

2

4

6

8

10

12

Time, sec

effe

ctor

arr

ay d

eplo

ymen

t

0 5 10 150

2

4

6

8

10

12

Time, sec

effe

ctor

arr

ay d

eplo

ymen

t

Figure 13. Shape-change effector arraydeployment time histories in response to a 20-degree bank angle doublet command with and

without mild turbulence.

In both cases, various arrays in the controleffector suite saturate, that is to say that allelements of a given array are turned on, for muchof the time history. A higher degree of controlactivity and transient saturation results whenmild turbulence is present, but the control systemis still able to stabilize the lateral dynamics andperform the roll doublet. However, when theDryden turbulence level was increased tomoderate (σ = 6 ft/s ), the simulation diverged.The moderate turbulence field introducedperturbations from the trim condition which theeffector suite did not have sufficient authority toreject, as deployed by the pole-placement controllaw design.

Time histories produced by the dynamicsimulation in response to increasing crosswindgusts are shown in Figure 14. The vehicle isable to recover from crosswind gusts of up to 28ft/s, but beyond that the effector suite lackssufficient yaw authority to recover from the

turbulence offturbulence on

turbulence on (σ = 3ft/s)

turbulence off


disturbance. This magnitude of crosswind gustequates to a sideslip angle of approximately 2.5degrees at the simulation flight condition ofMach 0.6 and 15 000 ft. The figure shows theresponse to increasing crosswind gustmagnitudes in 5 ft/s increments, with the 30 ft/scrosswind gust resulting in a loss of control.

0 5 10 15-3

-2

-1

0

1

2

3

side

slip

, deg

Time, sec

0 5 10 15-15

-10

-5

0

Time, sec

bank

ang

le, d

eg

Figure 14. Simulation time histories in responseto increasing magnitudes of crosswind gust (5,

10, 15, 20, 25, and 30 ft/s).

So the shape-change effector array suiteexamined in this report is of limited practicalityin the regard that it provides relatively lowdisturbance-rejection capability. Although theeffector suite appears suitable to stabilize thelateral-directional dynamics in the presence ofmild turbulence, and to perform relatively low-rate rolling maneuvers, the effector suite lackssufficient authority to act as the sole means ofcontrolling the vehicle in all situations. Rather,such a complement of shape-change effectorarrays may be use to augment conventionaldevices, potentially providing a low-observableflight mode that may be flown through anautopilot executing only low-rate maneuvers.They may also be used to provide a certaindegree of control redundancy, reconfigurabilityor damage tolerance as an augmentation to aconventional effector complement. There is alsopotential for new novel effector concepts to bedeveloped that offer much greater authority

through separation control, forebody vortexmanipulation, or other means, and in such casesadditional control schemes for employing thesedevices in the portions of the flight regime atwhich they are most useful will need to bedevised.

CONCLUDING REMARKS

This investigation has examined the use ofdistributed shape-change effector arrays in aflight control system for an example aircraftdesign. The subject aircraft was Lockheed-Martin's Innovative Control Effector (ICE)configuration. The distributed shape-changeeffector arrays were modeled as a series ofbumps normal to the aircraft surface which couldbe deployed to generate control moments.

A sensitivity analysis was performed whichprovided insight regarding favorable locationsfor the placement of the shape-change devicearrays on the ICE geometry. These sensitivitydata were incorporated into an interactive shape-change array design tool, and a suite of arrayswas developed and used in a lateral-directionalcontrol law design to illustrate allocation anddeployment methodologies. A “quantizedspanwise” deployment scheme was devised foractivation of the device arrays. That is to say thateach device in an array was either completely onor off (rather than proportionally deployed), andmore of them were turned on to produce largerforces as needed, from the most inboard to themost outboard span station of each array.

The control design was used in a dynamicsimulation of the ICE aircraft for a flightcondition of Mach 0.6 at 15,000 ft. Though theauthority of the particular device arrays that weredesigned in this investigation was quite low, thesimulation results indicate that the effector suitepossessed sufficient authority to stabilize andmaneuver the example vehicle model, executingrelatively low-rate rolling maneuvers at 10 deg/s.When substantial atmospheric disturbances wereincluded in the simulation (turbulence levels of 6ft/sec or cross wind gusts of >28 ft/sec), thedevice arrays did not possess sufficient authorityto maintain stability of the vehicle's lateral-directional dynamics using the control lawpresented in this report.

The shape-change device arrays studied inthis investigation present a promising alternativefor use in aircraft flight control. However, it isclear that experimental demonstrations of theirapplication and further development of their

30 ft/s 25 20 15 10

5 ft/s


control authority would bolster their case.Future research will focus on experimentalvalidation of the predicted authority of variousflow control devices and on flight control usinglarge arrays of interacting effector devices. Abroader database that will characterize thevariation of control authority of the shape-change device arrays with angle of attack andMach number is also planned.

REFERENCES

1 Roos, Frederick W., McDonnell DouglasCorporation: "Synthetic-Jet Microblowingfor Vortex Asymmetry Management on aHemisphere-Cylinder Forebody", 28 th AIAAFluid Dynamics Conference, paper AIAA97-1973, Jun 29 - July2, 1997.

2 Smith, B. L.; Glezer, A.: "Vectoring and Small-Scale Motions Effected in Free Shear Flowsusing Synthetic Jet Actuators", 35th

Aerospace Sciences Meeting & Exhibit,AIAA Paper 97-0213, January 1997.

3 Pack, L. G.; Seifert, A.: "Periodic Excitationfor Jet Vectoring and Enhanced Spreading",37th AIAA Aerospace Sciences Meeting andExhibit, AIAA Paper 99-0672, January,1999.

4 Nae, C.: “Synthetic Jet Influence on NACA0012 Airfoil at High Angles of Attack”,AIAA Paper 98-4523.

5 Seifert, A.; Darabi, A.; Wygnanski, I.: “Delayof Airfoil Stall by Periodic Excitation”,Journal of Aircraft, Vol. 32, No. 4, July-August, 1996.

6 Seifert, A.; Pack, L.: “Oscillatory Control ofSeparation at high Reynolds Numbers”,AIAA Paper 98-0214, Aerospace SciencesMeeting and Exhibit, 1998.

7 McGowan, A. R.; Horta, L. G.; Harrison, J. S.;Raney, D. L.: "Research Activities withinNASA's Morphing Program", NATO RTOmeeting - Applied Vehicle TechnologyPanel, October 1999, Ottawa, Canada.

8 Scott, M., Montgomery, R., and Weston, R.:“Subsonic Maneuvering Effectiveness ofHigh Performance Aircraft Which EmployQuasi-Static Shape Change Devices”, SPIE1998 International Symposium on SmartStructures and Materials, paper 3326-24, pp.223-233.

9 Allan, B.; Holt, M., Packard, A.: “Simulationof a Controlled Airfoil with Jets”, NASACR-201750; ICASE Report No. 97-55,October 1997.

10 Dorsett, K. M. and D.R. Mehl, 1996.“Innovative Control Effectors (ICE)”,Wright Laboratory Report, WL-TR-96-3043, January 1996.

11 Ashby, D., Dudley, M., Iguchi, S., Browne, L.,and Katz, J.: “Potential Flow Theory andOperation Guide for the Panel CodePMARC_12”, NASA Ames ResearchCenter, Moffett Field, CA, Dec. 1992.

12 Kral, L., Dononvan, J. Cain, B, Cary, A.:“Numerical Simulation of Synthetic JetActuators”, AIAA paper 97-1824.

13 Donovan, J.F., L.D. Kral, and A.W. Cary:“Active Flow Control Applied to anAirfoil”, 36th AIAA Aerospace SciencesMeeting, paper AIAA 98-0210, Jan. 1998.

14 Carle, A., Fagan, M., and Green, L.:“Preliminary Results from the Applicationof Automated Adjoint Code Generation toCFL3D”, AIAA Paper 98-48078, Sept.1998.

15 Park, M., Green, L., Montgomery, R., Raney,D.: “Determination of Stability and ControlDerivatives using Computational FluidDynamics and Automatic Differentiation”,AIAA Paper 99-3136, June 1999.

16 Padula, S. L.; Rogers, J. L.; Raney, D. L.:"Multidisciplinary Techniques and NovelAircraft Control Systems", pending 8th

AIAA/NASA/USAF/ISSMO Multidisciplin-ary Analysis and Optimization Symposium,September 6-8, 2000.

17 G. H. Bryan, "Stability in Aviation", Mac-millan Co., London, 1911.

18 B. Etkin, "Dynamics of Flight - Stability andControl", John Wiley and Sons, Inc., NewYork, 1959.

19 G. F. Franklin; J. D. Powell; A. E. Naeini:"Feedback Control of Dynamic Systems",Addison-Wesley Publishing Company, Inc.,1986.

20 Bordignon, K. A.; Durham, Wayne C.:"Closed-Form Solutions to ConstrainedControl Allocation Problem", Journal ofGuidance, Control, and Dynamics, Vol. 18,No. 5, September-October 1995.

aiaa 2000-1560 flight control using distributed shape ...mln/ltrs-pdfs/nasa-aiaa-2000-1560.pdf1...

Documents