Flight Test Validation of a Frequency-Based System Identification … · 2013. 6. 27. · Gerard S....

NASA Technical Memorandum 4704

July 1995

Flight Test Validation of a Frequency-Based System Identification Method on an F-15 Aircraft

Gerard S. Schkolnik, John S. Orme and Mark A. Hreha

Technical Memorandum 4704 July 1995


Gerard S. SchkolnikNASA Dryden Flight Research CenterEdwards, California

John S. OrmeNASA Dryden Flight Research CenterEdwards, California

Mark A. HrehaMcDonnell Douglas AerospaceSt. Louis, Missouri

FLIGHT TEST VALIDATION OF A FREQUENCY-BASED SYSTEM IDENTIFICATION METHOD ON AN F-15 AIRCRAFT

Gerard S. Schkolnik* and John S. Orme†

NASA Dryden Flight Research CenterEdwards, California

Mark A. Hreha**McDonnell Douglas Aerospace

St. Louis, Missouri

Abstract

A frequency-based performance identificationapproach was evaluated using flight data from the NASAF-15 Highly Integrated Digital Electronic Controlaircraft. The approach used frequency separation toidentify the effectiveness of multiple controlssimultaneously as an alternative to independent controlidentification methods. Fourier transformationsconverted measured control and response data intofrequency domain representations. Performancegradients were formed using multiterm frequencymatching of control and response frequency domainmodels. An objective function was generated using theseperformance gradients. This function was formallyoptimized to produce a coordinated control trim set. Thisalgorithm was applied to longitudinal acceleration andevaluated using two control effectors: nozzle throat areaand inlet first ramp. Three criteria were investigated tovalidate the approach: simultaneous gradientidentification, gradient frequency dependency, andrepeatability. This report describes the flight test results.These data demonstrate that the approach can accuratelyidentify performance gradients during simultaneouscontrol excitation independent of excitation frequency.

Nomenclature

ACTIVE Advanced Control Technology for Integrated Vehicles

*Aerospace Engineer, Senior Member AIAA†Aerospace Engineer, Member AIAA**Aerospace Engineer, Member AIAACopyright 1995 by the American Institute of Aeronautics and

Astronautics, Inc. No copyright is asserted in the United States underTitle 17, U.S. Code. The U.S. Government has a royalty-free license toexercise all rights under the copyright claimed herein for Governmentalpurposes. All other rights are reserved by the copyright owner.

1American Institute of Aero

AdAPT Adaptive Aircraft Performance Technology

ADECS Advanced Engine Control System

AJ nozzle throat area, ft2

estimated derivative of longitudinal force coefficient with respect to symmetric nozzle throat area during separate control excitation

estimated derivative of longitudinal force coefficient with respect to symmetric nozzle throat area during simultaneous control excitation

estimated derivative of longitudinal force coefficient with respect to symmetric cowl position during separate control excitation

estimated derivative of longitudinal force coefficient with respect to symmetric cowl position during simultaneous control excitation

derivative of longitudinal force coefficient with respect to control deflection

CIVV fan variable vanes, deg

DEEC Digital Electronic Engine Control

DFTP discrete Fourier transform points

EAIC electronic air inlet controller

EPR engine pressure ratio

FFT fast Fourier transform

F.S. control full-scale range

FTIT fan turbine inlet temperature

g gravitational acceleration, 32.174 ft/sec2

HIDEC Highly Integrated Digital Electronic Control

CxδAJS

CxδAJS ′

CxδCS

CxδCS ′

Cxδu

nautics and Astronautics

n frequency bin number of FFT

N1C2 corrected fan speed, rpm

Nx longitudinal acceleration, g

Nz normal acceleration, g

Pn normalized spectrum

PSC Performance Seeking Control

average dynamic pressure, lbf/ft2

RCVV compressor variable vanes, deg

RHO inlet first ramp or cowl position, deg

S reference wing area, 608 ft2

SNR signal-to-noise ratio

SNR signal-to-noise ratio of Nx with respect to nozzle throat area during separate control excitation

SNR signal-to-noise ratio of Nx with respect to nozzle throat area during simultaneous control excitation

SNR signal-to-noise ratio of Nx with respect to cowl position during separate control excitation

SNR signal-to-noise ratio of Nx with respect to cowl position during simultaneous control excitation

SR sample rate, samples/sec

u control effector

ω excitation frequency, Hz

Wt average aircraft weight, lb

∆ excitation control amplitude

Subscripts

c symmetric cowl trim, positive leading edge down, deg

i control effector number

n symmetric nozzle throat area trim, positive larger area, ft2

Superscripts

steady-state trim condition

Introduction

An onboard optimization algorithm can increaseaircraft performance without the additional penalty ofweight or modification to control system architecture,

resulting in significant cost savings. Performance andreduced life-cycle cost are critical factors in the decisionto procure commercial and military aircraft. Smalladvantages in range, payload, and endurance separatecontract winners from the competition. For over 15 years,NASA Dryden Flight Research Center, Edwards,California, has pursued and demonstrated controlmethodologies for improving aircraft performance inflight. Digital control, the key enabling technology, hasprovided a means by which previously independentsystems, such as the flight and engine control, can sharedigital data and achieve improved performance.

The Advanced Engine Control System (ADECS)program was the first to use digital data communicationbetween the engine and flight control computers toincrease engine performance (ref. 1). The ADECSapproach improved performance by trading stall marginfor increased thrust or by reducing fuel consumptionusing fixed control schedules. This system did notcontain an adaptive capability, so it was unable to sensethe operating condition of the engine and to compensatefor levels of degradation. The Inlet Integration programsimilarly shared digital data among flight, engine, andinlet controls to improve the integrated engine and inletperformance, but it also relied upon predeterminedcontrol schedules generated from models.

The Performance Seeking Control (PSC) programfollowed the ADECS program and was the first toincorporate a model-based, real-time adaptive onboardpropulsion system optimization algorithm (ref. 2–3). ThePSC algorithm’s adaptive capability came from aKalman filter that identified the state of deterioration ofthe engine components. The Kalman filter updated anintegrated system model to represent the current enginestate. The optimization process used linear programmingtechniques to determine the optimal engine operatingcondition for the selected performance measure. ThePSC performance improvements derived primarily fromreducing engine stability margins are based uponcomplex models that are in error by an unknown amount.Additionally, model dependency reduces transportabilityof mature systems to different applications. Thesecomplications, which are intrinsic to the model-basedapproach, have spurred research in a new direction.

This new approach uses flight measurements andfeedback control to provide the adaptive capability. Alimited experiment was performed during the PSCprogram to establish the feasibility of using onboardsensors and step inputs to the cowl, nozzle area, andvariable vanes to identify longitudinal force derivatives(ref. 4). These performance derivatives were identifiedpostflight using two methods. The first, a

q

NxAJ

NxAJ ′

NxCS

NxCS ′

′

2American Institute of Aeronautics and Astronautics

computationally intensive approach, used a maximumlikelihood estimator that modeled the longitudinal axisresponse in three degrees-of-freedom. The second, asimplified approach, contained a least-squares estimatorthat modeled the longitudinal axis response in onedegree-of-freedom. Both methods were successful andproved that measurement-based performanceoptimization using available sensors is possible andcomputationally feasible.

Subsequently, a new approach to measurement-basedperformance optimization evolved from the forced-oscillation technique used to compute dynamic stabilityderivatives from wind-tunnel test data (ref. 5). Thisapproach identified frequency domain input–outputrelations using Fourier analyses. Performance gradientsare formed using multiterm frequency matching ofcontrol and response frequency domain models. Anobjective function is generated using the performancegradients and formally optimized to produce acoordinated control trim set (ref. 6). This technique,called the Adaptive Aircraft Performance Technology(AdAPT) approach, was evaluated in a high fidelity,nonlinear, six degree-of-freedom simulation of theNASA Advanced Control Technology for IntegratedVehicles (ACTIVE) aircraft (ref. 7). Excellent resultsfrom the simulation prompted evaluation of thefrequency-based approach using flight test data.

The frequency-based approach has two theoreticaladvantages. The first is the ability to identify multiplecontrol gradients simultaneously. By targeting distinctexcitation frequencies for each control, theircorresponding effect on the performance index can beaccurately separated. This approach reduces the requiredexcitation period because individual control excitationdoes not need to be performed in a serial fashion. Theapproach also enables simultaneous optimization ofdistinct control effectors. Secondly, the approachexhibits an inherent ability to reject noise. Targetingspecific excitation frequencies of known low noise levelsminimizes corruption of the gradients. For example, adiscrete frequency bin adjacent to the one selected maycontain high noise levels caused by structural vibrationor atmospheric effects. This noise will not affectidentification of the selected frequency bin because theapproach uses control and response data only at theselected frequency.

This paper describes results of flight test on the NASAF-15 Highly Integrated Digital Electronic Control(HIDEC) aircraft during the PSC program to validate thedescribed frequency-based system identificationapproach. Three criteria were investigated to validate the

approach across the flight envelope: simultaneousgradient identification, gradient frequency dependency,and repeatability.

Aircraft and Engine Description

Performance optimization was studied on the NASAF-15 HIDEC research aircraft, a high-performancemilitary fighter aircraft capable of speeds in excess ofMach 2 (fig. 1). Two Pratt & Whitney (PW) (West PalmBeach, Florida) F100-PW-1128 derivative, afterburning,turbofan engines power the NASA F-15 aircraft. Theaircraft has been modified with a digital electronic flightcontrol system (ref. 8).

The F100-PW-1128 engine is a low-bypass ratio, twin-spool, afterburning turbofan technology demonstrator,derived from the F100-PW-100 engine. A full-authorityDigital Electronic Engine Control (DEEC) similar to theone for the current production F100-PW-220 enginecontrols the engines. The DEEC software has beenmodified to accommodate PSC trim commands, but thenormal DEEC control loops (i.e., corrected fan speed,N1C2, and engine pressure ratio (EPR)) were notmodified. The DEEC trim commands for subsonic,nonafterburning conditions are perturbations on fanvariable vanes, CIVV; compressor variable vanes, RCVV;N1C2, and nozzle throat area, AJ. Reference 9 providesa more detailed description of the F100-PW-1128 engine.

The NASA F-15 aircraft was also modified with anelectronic air inlet controller (EAIC) which allows PSC

EC-90-312-3

Fig. 1. The NASA F-15 Highly Integrated DigitalElectronic Control aircraft.


trim commands to be added to first and third inlet rampscheduled positions (fig. 2). These inlet ramp scheduleswere tailored specifically for the F100-PW-1128 enginesduring supersonic flight to account for the increasedengine airflow.

The aircraft was equipped with a NASA flight testinstrumentation package which recorded all PSC engineand airframe data as well as the standard set of stability,control, and airdata parameters. These data wererecorded at 40 samples/sec for the postflight analysis.Longitudinal acceleration data were gathered from aflight test instrumentation sensor mounted in thenoseboom. Engineering units range and resolution ofthe accelerometer were ±1.37 and 0.00268 g/bit, usingthe aircraft 10-bit digital-to-analog instrumentationsystem (ref. 4).

Performance Seeking ControlSystem Description

The PSC program advances the capability for a fullyintegrated propulsion flight control system. Whereasprevious algorithms provided single variable control foran average engine (ref. 1), the PSC algorithm controlledmultiple propulsion system variables while adapting tothe measured engine performance. The PSC algorithmoptimizes aircraft propulsion system performance duringsteady-state engine operation. This multimode algorithmminimized fuel consumption at cruise conditions,maximized excess thrust (thrust minus drag) during

aircraft accelerations, extended engine life by decreasingfan turbine inlet temperature (FTIT) during cruise oraccelerations, and reduced supersonic deceleration timeby minimizing excess thrust. Onboard models of theinlet, engine, and nozzle were optimized to compute a setof control trims. Then, these trims were applied asincrements to the nominal engine and inlet controlschedules (fig. 3). The onboard engine model wascontinuously updated to match the operatingcharacteristics of the actual engine cycle through the useof a Kalman filter, which accounts for unmodelledeffects. Subsonic and supersonic flight testing wasconducted at NASA Dryden covering the fourPSC optimization modes and over the full throttle range(ref. 2–3).

To support future work with a frequency-basedoptimization program, an excitation mode was added tothe PSC system. Although the excitation mode was notan original component, it was rapidly prototyped andimplemented into the architecture. The implementationof the PSC excitation mode was based on the minimumfuel mode. This approach allowed the algorithm tooperate at any power lever angle setting. The PSC trimadder and scale factors zeroed all trim outputs of theoptimization and applied sinusoidal trims to the nozzlethroat area, inlet first ramp, and cowl (fig. 4). Frequencyand amplitude trim characteristics were selected in flightfor each control through a variable gain structure.Aircraft control and acceleration data were recorded onthe instrumentation system for postflight analysis.


Fig. 2. Side view of the F-15 inlet.

Engine face

Third ramp deflection

Cowl deflection

950279

Oblique shock

Normal shock

Cowl lip

Fig. 3. Performance Seeking Control system.

Fig. 4. Performance Seeking Control excitation mode.

Integrated system model

Inlet parameters

Inlet and horizontal tail Component

deviationsparameters

Real-time parameteridentification (Kalman filter)

Dynamic engine model

Engineparameters

Identification

Optimization

Real-time on-line optimizationfor thrust, fuel flow, engine life

Aircraft andflight controlparameters

Digital enginecontrol

835

F-15 HIDEC

Stabilator command

950284Compact engineNozzle

Optimalengine trims

Optimal inlet trims

Digital inlet control

Digital flight control

Extended Kalman filter

Integrated system model

Optimization

Inlet parametersEngine

parametersSinusoidal

signal generator

Aircraft andflight controlparameters

Digital enginecontrol

835

F-15 HIDEC

Stabilator command

950280

Engine trimcommands

Inlet trim commands

Digital inlet control

Digital flight control

Test Description

During 5 flights, 31 test maneuvers were flown at9 conditions ranging from Mach 0.7 and an altitude of7,000 ft to Mach 2.0 and an altitude of 45,000 ft. Table 1summarizes the conditions for these tests. Mach numberand altitude tolerances were ±0.01 and ±100 ft,respectively. Twenty-six maneuvers were conductedacross the envelope to validate the accuracy of the

gradient identification during separate and simultaneouscontrol excitations. In addition, five maneuvers wereconducted at one condition to quantify the effect ofexcitation frequency on the identified gradient. Tominimize unmodelled effects, the aircraft was stabilizedin a hands-off, 1-g, wings-level trim. If possible,autopilot was engaged in the altitude-hold mode. Enginepower lever angle was held constant throughout thesetests.


Separate versus simultaneous control excitation test

The separate versus simultaneous control excitationtest determined whether simultaneous control excitationdegraded the quality of the identified gradients. Theperformance index for the test was the body-axislongitudinal acceleration, Nx, measured with thenoseboom sensor (ref. 4). Additionally, body-axisnormal acceleration, Nz, was measured to evaluateorthogonal axis activity during excitation.

Two controls were selected for this test. The first, anaircraft control, was the inlet first ramp or cowl position,RHO, and nozzle throat area. The cowl was selectedbecause of the integrated nature of the effector. Thevariable geometry inlet is an external compressiondesign. First and third ramp positions were scheduledwith Mach number, total temperature, and angle of attackto efficiently channel engine airflow and maximizepressure recovery. The first ramp has a large two-dimensional flat plate configuration and is exposed torelatively undisturbed flow at the forward fuselage. Thisconfiguration produces significant aerodynamic forcesand moments at subsonic and supersonic conditions. Theinlet first ramp primarily affects pressure recovery at theengine face and, in turn, net thrust. In addition to havinga thrust effect, the inlet first ramp position also affects theaircraft aerodynamics, and its effect can be traded withthe stabilator’s to reduce trim drag while maintainingcondition. The second control effector chosen for the testwas an engine control, nozzle throat area. Nozzle throatarea was chosen because it has a significant effect onthrust subsonically and supersonically.

A maneuver block at a specific flight conditionconsisted of an AJ excitation, followed by a RHOexcitation, and ended with a simultaneous excitation ofthe two controls. Once the pilot stabilized the aircraft oncondition, stabilized data were gathered for 30 sec forSNR calculations after which the pilot initiated thecontrol excitation. Each control excitation lastedapproximately 30 sec to 1 min. Between each excitationmaneuver, stabilized data were gathered so that noiseinformation could be quantified. By performing the threemaneuvers in succession, variations in trim, atmosphere,and weight were reduced.

Frequency parametric test

The frequency parametric test established whether afrequency dependency existed in the identified gradients.Ideally, gradients remain independent of the excitationfrequency across the entire bandwidth of the control. Inreality, the response is corrupted by actuator ratelimiting, structural coupling, aeroservoelastic, or controlsurface damping effects as the control excitationfrequency increases. Consequently, the objective of thetest was to quantify the frequency range within thebandwidth of the control that is independent offrequency.

Mach 0.95 at an altitude of 25,000 ft was the flightcondition selected for the test. The performance indexand the control effector were Nx and AJ, respectively.Table 2 summarizes the frequency range tested. Theconvergent actuator that controls the nozzle area ispneumatically driven and exhibits a relatively lowbandwidth. As such, an appropriate frequency rangebetween 0.02 and 0.20 Hz was selected. The commandedtrim amplitude for the five maneuvers was 0.30 ft2. Thistest procedure was similar to that of the separate versussimultaneous control excitation test except all fivemaneuvers were performed in succession.

Table 1. Test matrix.

Testcondition

Machnumber

Altitude,ft

Excitationtest

1 2.00 45,000 AJ/Both

2 1.60 45,000 AJ/RHO/Both

3 1.35 45,000 AJ/RHO/Both

4 0.95 45,000 AJ/RHO/Both

5 1.40 25,000 AJ/RHO/Both

6 1.25 25,000 AJ/RHO/Both

7 0.9525,000 AJ/RHO/Both/

Frequency

8 0.95 10,000 AJ/RHO/Both

9 0.70 7,000 AJ/RHO/Both

Table 2. Frequency parametric test matrix.

Testpoint

Machnumber

Altitude,ft

Excitationfrequency, Hz

1 0.95 25,000 0.020

2 0.95 25,000 0.049

3 0.95 25,000 0.098

4 0.95 25,000 0.156

5 0.95 25,000 0.195


Repeatability test

The repeatability test established the sensitivity of theidentified gradients to random effects, such as noise anddata windowing. For the identification approach to besatisfactory, only small variations in the results wereexpected for data gathered over the same maneuver. Noadditional maneuvers were required to perform this test.The analysis was performed on the same data as that ofthe separate versus simultaneous control excitation test.The window length selected for the analysis was25.6 sec. Approximately 2 min of excitation data werecollected during each maneuver. By successivelyoffsetting the starting point of the analysis window12.5 sec, 6 or 7 sets of analysis could be performed oneach maneuver. This technique was used to evaluate therepeatability of the identification approach because itminimized changes in unmodelled effects.

Analysis and Results

The frequency-based system identification methodwas validated by investigating simultaneous controlexcitation, frequency dependency, and repeatabilityacross the flight envelope of the F-15 HIDEC aircraft.Results of each test are presented separately.

Separate versus simultaneous control excitation test

A series of steady-state cruise tests was conducted atnine flight conditions throughout the aircraft envelope.Figures 5 and 6 present a typical simultaneous maneuverperformed at Mach 2.0 and an altitude of 45,000 ft. Thenumber of data points analyzed in the discrete Fouriertransform points, DFTP, was 210 or 1024 samples with adata rate, SR, of 40 samples/sec, translating into 25.6 sec.To enhance the likelihood of gradient identification usingfrequency separation, carefully chosen excitationfrequencies, ωi, were calculated using equation 1.

(1)

The excitation frequencies were applied to AJ and RHOat frequency bin numbers nn = 2(ωn = 0.078 Hz), andnc = 7(ωc = 0.273 Hz). This selection reduces theinteraction of the controls and their higher order effects.The AJ and RHO excitation trim amplitudes were±0.14 ft2 (3.9 percent control full-scale range F.S.) and±0.68° (4.5 percent F.S.), respectively, to determine thelinear characteristics, reducing the effects of amplitude.

Figure 5 contains time histories of Nx and Nz measuredduring the excitation period. At this flight condition, bothtime histories show that the aircraft response isdominated by the effect of the cowl. With Nz amplitudesaveraging 0.064 g, the excitation was noticeable to thepilot, but they were not objectionable.

Figure 6 shows the normalized spectrum, Pn, of thecontrols and response before and during the excitationperiod. The normalized spectrum is a useful calculationbecause a unit sinusoid in the time domain correspondsto unit amplitude in the frequency domain.

Pn(x) = 2*abs(FFT(x))/DFTP (2)

The steady-state data gathered just before theexcitation period were used to assess the noise level atthe excitation frequencies. Because the gradientidentification approach uses frequency separation todiscriminate noise from actual response to the control, itis critical to choose an excitation frequency that containslow noise levels.

Figure 6 also shows AJ and RHO excitation trimamplitudes in square feet and degrees as a function offrequency in hertz. Frequency bin 2, nn = 2 (ωn =0.078 Hz), shows that AJ excitation generated an averageperturbation amplitude of 0.14 ft2 during the datacollection period. Frequency bin 7, nc = 7 (ωc =0.273 Hz), shows that RHO excitation produced anaverage perturbation amplitude of 0.68°. Figure 6presents the normalized spectrum of Nx. This graphillustrates the greater effectiveness of RHO over AJduring this maneuver. The cowl produced 6.7 mg of Nx,while the nozzle only managed 1.8 mg of Nx.

At Mach numbers greater than 1.4, shock position iscritical for performance. Small changes in location of thefirst oblique shock significantly affect spillage drag andpressure recovery. Additionally, cowl pitching momenteffectiveness becomes significant when compared to thestabilator. Large trim drag reductions are possible byoffsetting stabilator trim position. Nozzle area becomesless effective as Mach number increases because enginepressure ratio has less affect on thrust than airflow. Noiselevels in bins 2 and 7 were below 1 mg. Thenondimensional derivative, longitudinal forceeffectiveness, was calculated using the followingequation at the excitation frequency of each control:

= abs(FFT(Nx)/FFT(u))*F.S.(u)*Wt/ /S (3)

where

ωi SNR DFTP⁄( )∗ni=

u = control effector, AJ or RHO

F.S.(u)=

full-scale control deflection—3.65 ft2 for nozzle area, 15° for cowl

Wt = average weight over the maneuver, lb

=average dynamic pressure over the maneuver, pfs

S = reference wing area, ft2

Cxδu,

Cxδu

q

q



Fig. 5. Time histories of simultaneous nozzle area and cowl excitation.

2.00

1.95

1.90

46,100

46,000

45,900

Altitude,ft

Mach

Cowl,deg

Nx,g

Time, sec

Nz,g

Nozzle area,

ft2

45,800

0 6.0

5.5

5.0

– 1

– 2

– 3

– 4

0 5 10 15 20 25 30

.04

0

– .04

.2

0

– .2

950281

Nozzle areaCowl

Fig. 6. Normalized spectrum of simultaneous nozzle and cowl excitation.

.2

.1

0

1.0

.5

0

.010

.005

Nozzle,area,

ft2

Cowl,deg

Nx,g

Frequency, Hz0 .2 .4 .6 .8 1.0

950282

Steady-stateExcitation

Figure 7 shows summary plots of separate andsimultaneous identification of nozzle area and cowllongitudinal force effectiveness as a function of Machnumber for altitudes of 10,000, 25,000, and 45,000 ft.Overall, excellent agreement was exhibited between theseparate and simultaneous identification tests at all flightconditions. Small differences in the two techniquesresult, in part, from interactions between the controlsduring simultaneous excitation and unmodelled effects,such as differences in trim flight and atmosphericconditions. Additionally, the analysis revealed the

relative effectiveness between the cowl and nozzle areato be somewhat unexpected. As expected at low Machnumbers, nozzle area effectiveness was high, and thecowl was practically ineffective. As Mach numberincreased, the cowl rapidly became increasinglyeffective as the nozzle area effectiveness quicklydecreased. At an altitude of 45,000 ft, cowl effectivenesssurpassed the nozzle at Mach 1.6. At Mach 2.0, cowleffectiveness approached the highest levels attained bythe nozzle at low Mach numbers. This reversal ineffectiveness supports incorporating a variable geometry


Fig. 7. Comparison of separate and simultaneous identification of nozzle area and cowl longitudinal effectiveness as afunction of Mach number at varying altitudes.

CxδAJSCxδCS

.020

.015

.010

.005

0.80.60 1.00

Mach

45,000 ft

25,000 ft

1.40 1.60 1.80 2.001.20

Longitudinal force

effectiveness

CxδAJS′CxδCS′

950283

.025

.020

.015

.010

.005

0

Longitudinal force

effectiveness

10,000 ft.025

.020

.015

.010

.005

0

Longitudinal force

effectiveness

inlet into an F-15 aircraft. Increased performance offsetsthe associated penalties of increased complexity andadded weight. At lower altitudes, the trend indicates thatthis reversal occurs at lower Mach numbers. Suchreversals are probably caused by increased dynamicpressure.

To gauge the fidelity of the identified gradients, SNRcalculations were performed for all maneuvers. The SNRwas calculated from the steady-state and excitationportions of the maneuver at the excitation frequency for

each control, allowing a direct assessment of theconfidence of the identification. The inherent assumptionto this approach was that noise characteristics just beforethe excitation were representative of the noise during theexcitation. Because the steady-state noise data weregathered within 60 sec of the excitation data during thesame maneuver, the noise characteristics did not changesignificantly during this period. As a result, the approachwas deemed satisfactory for quantifying the steady-statenoise levels. The steady-state trim data before theexcitation provided base noise levels at the excitation


frequency. This quantity was subtracted from themeasured Nx level during the excitation to calculate theactual response level. Equation 4 shows the calculation.

(4)

where

Figures 8(a)–8(c) present summary plots of SNR forseparate and simultaneous identification of nozzle area

SNR absPn Nx( )

niPn Nx( )

ni ′–

Pn Nx( )ni ′

-----------------------------------------------------

=

ni = frequency bin i during excitation

= frequency bin i during steady stateni′


Fig. 8. Comparison of separate and simultaneous excitation signal-to-noise ratio as a function of Mach number atvarying altitudes.

Signal-to- noise ratio

0.70

Mach

10,000 ft

17.1

5.5

18.4 18.7

15.1

0.3 1.03.3

.95

5

10

SNR NxAJ

15

20

950286

SNR NxCSSNR NxAJ′SNR NxCS′


1.401.25Mach

25,000 ft

2.78.3

0.5

71.5

5.3 8.34.2

21.3

7.22.3

8.03.5

.95

80

70

60

50

40

30

20

10

0

SNR NxAJ

950287



0

Mach

45,000 ft

15.6

2.00.2

4.8

0.21.8 2.4

6.5

0.4

6.0

3.7 3.3

0.8 0.3

14.2

.95 1.35 1.60 2.00

5

10

SNR NxAJ

15

20

950288


and cowl longitudinal force effectiveness as a function ofMach number for altitudes of 10,000, 25,000, and45,000 ft. The SNR calculation provides an effectivemeans of assessing the confidence of the identification.These ratios were consistently high for nozzle area andcowl in regions of the envelope where the respectivecontrol was most effective. Signal-to-noise ratios above2 indicated good confidence in the identification. Signal-to-noise ratios equal to and below 1 indicated responselevels were within the threshold of the noise, and littleconfidence existed in the results. Typically, this thresholdoccurred at effectiveness values below 0.0025. Ingeneral, SNR were consistent between the simultaneousand separate excitation tests. Simultaneous and separateexcitation results were consistent above 2 or below 1.Although there were exceptions, these werepredominantly caused by a change in noise levelbetween the two tests and not by a significant change insignal level.

For example at an altitude of 25,000 ft and atMach 0.95, SNR for nozzle area were 8.3 and 71.5 forthe simultaneous and separate excitation tests (fig. 8(b)).Noise levels changed by a factor of 4 at the excitationfrequency between the two tests. During the separateexcitation test, Nx noise levels were 0.23 mg, a relativelylow level. Subsequently, during the simultaneousexcitation test, Nx noise levels averaged 0.94 mg, a morerepresentative value. This increase directly results in afourfold change in the SNR. Additionally, during thesimultaneous excitation test, the excitation amplitudewas reduced inadvertently from 0.3 to 0.2 ft2. Thisreduction lowered the signal level during thesimultaneous test, precluding meaningful comparison ofthe two SNR.

Frequency parametric test

Figures 9(a) and 9(b) present nozzle area longitudinaleffectiveness and nozzle area trim amplitude as a functionof frequency at a flight condition of Mach 0.95 and analtitude of 25,000 ft. Nozzle area longitudinaleffectiveness remained relatively constant below0.049 Hz. Above 0.049 Hz, rate limiting of the nozzlearea actuators was encountered (fig. 9(a)). Thecommanded nozzle area trim amplitude was heldconstant at 0.30 ft2. Figure 9(b) shows the nozzle areafeedback trim amplitude attenuating as frequencyincreases above 0.049 Hz. By 0.2 Hz, the amplitude hadattenuated by 65 percent. The nonlinearities introducedby the rate limiting spread the excitation energy acrossseveral frequency bins, reducing the apparenteffectiveness at the fundamental frequency. This effectprecluded identifying a bandwidth greater than 0.049 Hz.If the excitation amplitude had been 0.10 instead of0.30 ft2, a greater bandwidth may have been identified.

.01

.02

CxδCS

.03

Time, sec4020 60 800

950292

Time, sec4020 60 80

.01

.02

.03

.04

.05

0

950291

CxδAJS

∆ Nozzle throat area, ft 2

.05Frequency, Hz

.10 .15 .20

.3

.2

.1

0

950290

.05Frequency, Hz

.10 .15 .20

.04

.03

.02

.01

0

950289

CxδAJS

(b) Cowl longitudinal force effectiveness as a functionof data window start time at Mach 2.0 and an altitude of45,000 ft.

Fig. 10. Nozzle throat area and cowl repeatability testresults.

(a) Nozzle throat area longitudinal force effectivenessas a function of data window start time at Mach 0.70and al altitude of 7000 ft.

(b) Trim nozzle throat area amplitude as a function offrequency at Mach 0.95 and an altitude of 25,000 ft.

Fig. 9. Frequency parametric test results.

(a) Nozzle throat area longitudinal force effectivenessas a function of frequency at Mach 0.95 and an altitudeof 25,000 ft.


Although a limited number of frequency test points wereobtained, results of the frequency parametric test of thenozzle area indicate that an adequate frequency bandexists wherein gradient values are independent ofexcitation frequency.Repeatability test

Repeatability analysis was performed at two flightconditions using data from the simultaneous excitationtest. The flight conditions chosen for the analysisrepresent conditions where effectiveness was greatest foreach control. Results of the repeatability test showed thatvariation in identified gradients was small in both casestested.

Figure 10(a) presents nozzle area longitudinaleffectiveness as a function of analysis window start timefor a maneuver performed at a flight condition ofMach 0.70 and an altitude of 7000 ft. Seven sets ofanalysis were performed over 100 sec. The solidhorizontal line indicates the mean value, and the dottedlines indicate the 95 percent confidence bounds on themean value (ref. 10). Results show a 95 percentprobability that the mean AJ longitudinal forceeffectiveness equals 0.023 ±8.3 percent.

Figure 10(b) presents cowl longitudinal effectivenessas a function of analysis window start time for amaneuver performed at a flight condition of Mach 2.0and an altitude of 45,000 ft. Six sets of analysis wereperformed over 90 sec. Results show a 95 percentprobability that the mean cowl longitudinal forceeffectiveness equals 0.0113 ±4.3 percent. With meanconfidence bounds less than 10 percent for the nozzlearea and cowl, the repeatability demonstrated theidentification approach to be satisfactorily robust tounmodelled effects.

Concluding Remarks

A frequency-based system identification approach wasflight tested on the NASA F-15 Highly Integrated DigitalElectronic Control aircraft during the PerformanceSeeking Control program. Results demonstrated thatperformance gradients identified simultaneouslycompare well with those identified separately. Signal-to-noise ratio calculations provided a means to judgerelative significance of identified values anddiscrepancies. Secondly, although limited data weregathered, a frequency band was identified within whichgradient values are independent of excitation frequency.Additionally, repeatability analysis produced consistentresults and showed the identification approach to berobust to noise and data windowing. These resultsindicate that this approach to measurement-basedperformance system identification possesses inherentstrengths that make it an excellent candidate for a real-time onboard implementation in the future.

Limited flight data were gathered for the frequencydependency test. All data were gathered at a single flightcondition using only one control effector. In futureexperiments, additional engine and airframe controlswill be used throughout the envelope to quantify theeffects of frequency on gradients. For this investigation,two controls were used to substantiate the simultaneousidentification capability. In follow-on research, up toeight effectors will be controlled simultaneously to testthe algorithm. With the success of this experiment, areal-time implementation of this method will be flighttested on an airframe and propulsion integration testbedcalled the Advanced Control Technology for IntegratedVehicles. The capabilities of the aircraft and its systemswill greatly facilitate integrated controls research in thefuture.

References

1. Highly Integrated Digital Electronic ControlSymposium, NASA CP-3024, 1989.

2. Gilyard, Glenn B. and John S. Orme, Subsonic FlightTest Evaluation of a Performance Seeking ControlAlgorithm on an F-15 Airplane, NASA TM-4400, 1992.

3. Orme, John S. and Timothy R. Conners, SupersonicFlight Test Results of a Performance Seeking ControlAlgorithm on a NASA F-15 Aircraft, AIAA 94-3210,June 1994.

4. Schkolnik, Gerard S., Identification of IntegratedAirframe—Propulsion Effects on an F-15 Aircraft forApplication to Drag Minimization, NASA TM-4532,1993.

5. Chambers, Joseph R. and Sue B. Grafton, Static andDynamic Longitudinal Stability Derivatives of a Powered1/9-Scale Model of a Tilt-Wing V/STOL Transport, NASATN D-3591, 1966.

6. Hreha, M., G. Schkolnik, and J. Orme, An Approachto Aircraft Performance Optimization Using ThrustVectoring, AIAA 94-3361, June 1994.

7. Doane, P., R. Bursey, and G. Schkolnik, F-15ACTIVE: A Flexible Propulsion Integration Testbed,AIAA 94-3360, June 1994.

8. Burcham, Frank W., Jr., Lawrence P. Meyers, andKevin R. Walsh, Flight Evaluation Results for a DigitalElectronic Engine Control in a F-15 Airplane, NASA TM-84918, 1983.

9. Meyers, Lawrence P. and Frank W. Burcham, Jr.,Preliminary Flight Test Results of the F100 EMD Enginein a F-15 Airplane, NASA TM-85902, 1984.

10.Coleman, Hugh W. and W. Glenn Steele, Jr.,Experimentation and Uncertainty Analysis for Engineers,Wiley & Sons, New York, 1989.


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WU 505-68

Gerard S. Schkolnik, John S. Orme and Mark A Hreha

NASA Dryden Flight Research FacilityP.O. Box 273Edwards, California 93523-0273

H-2059

National Aeronautics and Space AdministrationWashington, DC 20546-0001 NASA TM-4704

A frequency-based performance identification approach was evaluated using flight data from the NASA F-15Highly Integrated Digital Electronic Control aircraft. The approach used frequency separation to identify theeffectiveness of multiple controls simultaneously as an alternative to independent control identificationmethods. Fourier transformations converted measured control and response data into frequency domainrepresentations. Performance gradients were formed using multiterm frequency matching of control andresponse frequency domain models. An objective function was generated using these performance gradients.This function was formally optimized to produce a coordinated control trim set. This algorithm was applied tolongitudinal acceleration and evaluated using two control effectors: nozzle throat area and inlet first ramp.Three criteria were investigated to validate the approach: simultaneous gradient identification, gradientfrequency dependency, and repeatability. This report describes the flight test results. These data demonstratethat the approach can accurately identify performance gradients during simultaneous control excitationindependent of excitation frequency.

Adaptive control, Aircraft flight tests, Aircraft performance, Control effectiveness,Performance optimization

AO3

17

Unclassified Unclassified Unclassified Unlimited

July 1995 Technical Memorandum

Available from the NASA Center for AeroSpace Information, 800 Elkridge Landing Road, Linthicum Heights, MD 21090; (301)621-0390

Presented as AIAA 95-2362 at the 31st AIAA/ASME/SAE/ASEE Joint Propulsion Conference and Exhibit, San Diego, California, July 10–12, 1995. (Mark A. Hreha is employed by McDonnell Douglas Aerospace, St. Louis, Missouri.)

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