system identification methods for aircraft flight control ... · system identification is a...
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National Aeronautics and Space Administration Ames Research Center Moffett Field, CA 94035-1000
US Army Aviation and Troop Command Aeroflightdynamics Directorate Moffett Field, CA 94035-1000
NASA Technical Memorandum 110369 USAATCOM Technical Report 95-A-007
System Identification Methods forAircraft Flight Control Developmentand Validation
Mark B. Tischler, Aeroflightdynamics Directorate, U.S. Army ATCOM, Ames Research Center,Moffett Field, California
October 1995
National Aeronautics and Space Administration Ames Research Center Moffett Field, CA 94035-1000
US Army Aviation and Troop Command Aeroflightdynamics Directorate Moffett Field, CA 94035-1000
NASA Technical Memorandum 110369 USAATCOM Technical Report 95-A-007
System Identification Methods forAircraft Flight Control Developmentand Validation
Mark B. Tischler
October 1995
System Identification Methods for Aircraft Flight Control Development andValidation
MARK B. TISCHLER
Aeroflightdynamics Directorate, U.S. Army ATCOM
Ames Research Center
Summary
System-identification methods compose a mathematicalmodel, or series of models, from measurements of inputsand outputs of dynamic systems. The extracted modelsallow the characterization of the response of the overallaircraft or component subsystem behavior, such as actua-tors and on-board signal processing algorithms. Thispaper discusses the use of frequency-domain system-identification methods for the development and integra-tion of aircraft flight-control systems. The extraction andanalysis of models of varying complexity from nonpara-metric frequency-responses to transfer-functions andhigh-order state-space representations is illustrated usingthe Comprehensive Identification from FrEquencyResponses (CIFER®) system-identification facility.Results are presented for test data of numerous flight andsimulation programs at the Ames Research Center includ-ing rotorcraft, fixed-wing aircraft, advanced short takeoffand vertical landing (ASTOVL), vertical/short takeoff andlanding (V/STOL), tiltrotor aircraft, and rotor experimentsin the wind tunnel. Excellent system characterization anddynamic response prediction is achieved for this wideclass of systems. Examples illustrate the role of system-identification technology in providing an integrated flowof dynamic response data around the entire life-cycle ofaircraft development from initial specifications, throughsimulation and bench testing, and into flight-testoptimization.
1. Introduction
System identification is a procedure for accurately charac-terizing the dynamic response behavior of a complete air-craft, subsystem, or individual component from measureddata. This key technology for modern fly-by-wire flight-control system development and integration provides aunified flow of information regarding system performancearound the entire life cycle from specification and designthrough development and flight test (fig. 1). A similar“roadmap” for application of system-identification meth-ods to rotorcraft development was previously proposed by
Schrage in a comprehensive report dedicated to this topic(Anon. 1991). An excellent historical summary andoverview of system identification is given by Hamel(1995). System identification has been widely utilized inrecent aircraft programs including many of thosedescribed in a recent volume on aircraft flight control(Anon. 1994). Common applications for flight-controlsystem development include: definition of systemrequirements, specification and analysis of handlingqualities, evaluation of proposed control-law concepts,validation and improvement of complex simulationmodels, validation of subsystem components and devel-opment facilities, and flight-test optimization of controllaws.
Frequency-domain identification approaches are espe-cially well suited to the development and validation offlight-control systems. Feedback stability and noiseamplification properties are determined from the broken-loop frequency response, and characterized by metricssuch as crossover frequency, and associated gain andphase margins. Command tracking performance is deter-mined from the closed-loop frequency-response, andcharacterized metrics such as bandwidth and time-delay,and equivalent system eigenvalues. Frequency-domainidentification approaches allow the direct and rapid(including real-time) identification of these frequency
Specifications
Flight test Design
Development Simulation
Figure 1. Road map for fly-by-wire flight-control systemdevelopment and integration.
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responses and metrics, without the need to first identify aparametric (state-space) model structure such as isrequired in applying time-domain methods. Carefultracking of the broken-loop and end-to-end closed-loopfrequency-response behavior from the preliminary designstudies through detailed design and simulation and intoflight test provides an important “paper trail” for docu-menting system performance and solving problems thatmay appear in the later phases of development.
The availability of comprehensive and reliable computa-tional tools has substantially enhanced the acceptability offrequency-domain techniques in the flight-control andflight-test community. Benefits from applying these tech-niques include the reduction of flight-test time requiredfor control system optimization and handling-qualitiesevaluation, especially for complex control-law architec-tures, and improvements in the final system performance.Frequency-domain methods offer a transparent under-standing of component and end-to-end response character-istics that can be critical in solving system integrationproblems.
This paper reviews frequency-domain system-identification methods for development and integration ofaircraft flight-control systems. These methods weredeveloped under a long-term research activity at the AmesResearch Center by the Army Aeroflightdynamics Direc-
torate (AFDD), the NASA and Sterling Software. Manyof the flight applications have been to rotorcraft, whichpose an especially difficult challenge to system identifica-tion (Tischler 1990). The dynamics of these aircraft arehighly coupled, and unstable. Additionally, the rotorcraftdynamics include lightly-damped fuselage and rotormodes. Vibration and low excitation signal content, espe-cially near hover, results in typically low signal-to-noiseratios. Experience in developing and applying system-identification methods to the rotorcraft problem has pro-duced a set of tools that has proven highly reliable for thebroad scope of applications reviewed in this paper. Thefirst section presents a summary of the frequency-domainapproach and the Comprehensive Identification fromFrEquency Responses (CIFER®) comprehensive analysisfacility. The remainder of the paper is organized into fivesections following the flight-control developmentflowchart of figure 1 from specifications and designthrough flight-test optimization. Each section illustratesimportant techniques with examples based on fixed androtary-wing projects at the Ames Research Center.
2. Overview of AFDD/NASA System-Identification Techniques
The AFDD/NASA frequency-domain system identifica-tion procedure is shown in figure 2, and in reviewed in
Frequency Sweep Inputs
AircraftData Compatibility
& State Estimation
Transfer-Function Modeling
Conditioned Frequency-Responses
& Partial Coherences
Identification Algorithm
Initial ValuesMathematical Model
Stability and Control Derivatives and Time Delays
Sensitivity Analysis &
Model Structure Determination
Dissimilar flight data not used in
identificationVerification
APPLICATIONS: FCS design, Handling-Qualities, Simulation validation
Freq.-Response Identification
Criterion
+
–
Multi-variable Spectral Analysis
Figure 2. Frequency-domain system identification procedure.
3
this section. Details of the procedure are found in Tischlerand Cauffman (1992). System-identification methods andrequirements for specific application to high-bandwidthrotorcraft flight-control system design are given byTischler (1990).
Aircraft or subsystem component dynamics are excited bya pilot-generated or computer-generated frequency-sweepinput. The dynamic responses are generally measured bydedicated sensors, and the data are either recorded on-board or telemetered to the ground for processing.Kalman filtering techniques (or simple numerical integra-tion) are used to check data compatibility and eliminatespurious instrumentation system biases, scale factors, anddrop-outs. Here, unmeasured signals may be estimatedfrom the available measured states.
The foundation of the AFDD/NASA approach is the high-quality extraction of a complete multi-input/multi-output(MIMO) frequency-response database. These responsesfully characterize the linearized coupled characteristics ofthe system without a priori assumptions. Advanced multi-variable spectral analysis using the Chirp-Z transform andcomposite optimal window techniques have been devel-oped and exercised over many flight applications. Thesemethods provide significant improvement in identificationquality relative to standard fast Fourier transform (FFT)methods. The frequency-response database directlysupports important flight-control system applicationsincluding: handling-qualities analysis and specificationcompliance testing, simulation validation, and servo-loopstability analysis.
Transfer-function fitting is a rapid procedure for extract-ing simple single-input/single-output parametric modelsof specific frequency-responses pairs. These transfer-function models define the lower-order equivalent sys-tems (LOES) of the fixed wing handling-qualities specifi-cations (MIL-STD-1797) and directly support root-locustechniques for flight-control system design.
Accurate MIMO state-space models are often needed tosupport multivariable control-law design, simulationmodel validation and improvement, and validation ofaerodynamic theory or wind tunnel results. Here, sophisti-cated nonlinear search algorithms are used to extract ageneral state-space model that matches the completeMIMO input/output frequency-response database. A sig-nificant advantage of identifying parametric models fromfrequency responses is the capability to individuallydefine the appropriate frequency range for each responsepair based on the associated coherence function—a valu-able accuracy and linearity metric. The coherence func-tion is also useful for automatically selecting errorweighting in the cost function independent of the modelstructure. A methodical and integrated model structure
determination procedure simplifies the model to a mini-mum set of reliable parameters that accurately character-izes the MIMO frequency-response database. Finally, theidentified state-space model is validated by comparingpredicted time responses with the actual flight responsesfor test inputs not used in the identification procedure.
The frequency-domain system-identification procedure isincorporated in a sophisticated interactive computationalfacility known as CIFER®–Comprehensive Identificationfrom FrEquency Responses. Integrated data-basing andextensive user-oriented utilities are distinctive features ofCIFER® for organizing and analyzing the large amountsof data which are generated for flight-test identificationprojects. A screen-driven interface is tied to the databasefor rapid user interaction. Previous program set-ups andanalysis results are retrieved by simply referencing casenames. Then, changes can be easily made by moving thecursor around on the user screens and modifying thedefault or previously saved program parameter values.The changes are then updated in the database with a singlekey stroke. Utilities are available for quick inspection,searching, plotting, or tabulated output of the contents ofthe database. Extensive analysis modules within CIFER®
support: 1) rapid identification of transfer-function mod-els; 2) signal spectral analysis; 3) handling qualities andclassical servo-loop analysis; and 4) time and frequency-domain comparisons of identification and simulationmodel predictions with flight data. Aircraft applications ofCIFER® have included the full life-cycle of flight-controlsystem development depicted in figure 1. The DeutscheForschungsanstalt für Luft- und Raumfahrt (DLR) Insti-tute for Flight Mechanics (Braunschweig, Germany) hasalso developed and widely applied excellent methods forfrequency-domain system identification. Applications toflight-mechanics and flight-control studies at the DLRinclude rotorcraft, transport aircraft, and high-performance aircraft (Kaletka and von Grunhagen 1989,Kaletka and Fu 1993).
3. Design Specifications and SpecificationAcceptance Testing
Formulating design specifications is the starting point forflight-control system development, while validating theachievement of these design goals is the concluding stepin the process (fig. 1). Dynamic models of expected sys-tem behavior are determined in the design process usingsystem identification and are tracked and updatedthroughout the aircraft development and flight testing.This documentation provides an important “paper trail”that minimizes flight-control development time andreduces the need for costly flight-test tuning. This sectionpresents system-identification methods for defining and
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verifying design specifications. Flight test examples illus-trate the analysis of handling qualities and servo-loop sta-bility characteristics.
Early handling-qualities specifications for fixed-wing air-craft (MIL-F-8785A, Anon. 1954), and for rotary-wingaircraft (MIL-H-8501A, Anon. 1961) were based on sim-ple dynamic modeling concepts and time-domain metrics.These specifications were suitable to aircraft in whichstability augmentation systems (SAS) did not significantlyalter the character of the (classical) bare-airframe flight-mechanics responses. Compliance testing techniquesdepended on standard step and doublet inputs long used inthe flight-test community, with little requirement forsophisticated post-flight-data processing.
Modern fly-by-wire aircraft employ high-bandwidth digi-tal flight-control systems to achieve greatly increasedagility and disturbance rejection across a significantlywidened operational flight envelope as compared with theolder generation of aircraft. The flight control includescomplex feedback and feedforward shaping and advancedcontrol moment devices that profoundly alter the bare-airframe characteristics and invalidate the classical stabil-ity and control modeling concepts and testing methods.For example, modern combat aircraft achieve independentpitch pointing and flightpath control with direct liftdevices and vectored thrust, rather than the coupledattitude-path response to elevator for conventional air-craft. This capability greatly enhances weapon pointingand air-to-air combat maneuvering. Another common fea-ture of advanced aircraft is side-stick controllers whichreduce weight, space, and cockpit complexity comparedto standard center-sticks. Classical static stick-stabilitytesting is an invalid method for determining speed stabil-ity since the side-sticks possess automatic trimming atneutral stick position and feedback loops provide therequired stability independent of the trim gradient.
A new concern that arises for modern fly-by-wire aircraftis the potential for the accumulation of effective timedelays due to digital flight-control computations, flight-control system filters, and fly-by-wire actuators. Actuatorrate-limiting can also contribute large equivalent timedelays in modern aircraft (Buchholz et al. 1995). Exces-sive delays have been repeatedly cited as a key cause forhandling-quality problems and stability-loop margindegradation in modern aircraft, yet equivalent time delaycan not be reliably measured using the standard testingtechniques. Clearly the dynamics modeling concepts,specifications, and testing techniques must be appropriateto the unique characteristics of modern highly-augmentedaircraft.
System identification provides an accurate, rapid, andreliable approach for defining design specifications and
for validating aircraft flight performance for highly-augmented flight-control systems. The modern U.S. fixed-wing specification (MIL-STD-1797; Anon. 1987) androtorcraft specification (ADS-33C; Anon. 1989) are basedon extensive frequency-domain system-identificationanalyses of flight-test and simulation responses. Numer-ous examples from these and comparable Europeanhandling-qualities specifications are presented in theaircraft control volume (Anon. 1994) and in the refer-ences of this paper. Two common handling-quality spec-ifications are the bandwidth/phase-delay criteria and theLOES criteria. The former is checked directly fromfrequency-response identification, and the latter ischecked from a transfer function fit of the frequency-response result. An illustration of flight-test and handling-qualities analyses based on these specifications is nowpresented.
The Advanced Digital Optical Control System (ADOCS)demonstrator (fig. 3), developed by Boeing’s HelicoptersDivision under contract to the U.S. Army, was a UH-60Ahelicopter highly modified with redundant processors,instrumentation, and side-stick controllers (Glusman et al.1987). The overall program objective of the ADOCS wasto provide the technology base for the engineering devel-opment of an advanced battlefield-compatible flight-con-trol system that: 1) enhanced aircraft mission capability;2) improved handling qualities; and 3) decreased pilotworkload. System identification flight tests and analysesusing CIFER® were conducted to document the responsecharacteristics and to compare handling-qualities charac-teristics with the (proposed at that time) ADS-33 designspecifications (Hoh et al. 1988). Aircraft excitation wasachieved via piloted frequency sweeps using the side-stickcontroller as shown in figure 4. Real-time telemetry ofpilot inputs and aircraft responses ensured that pre-established aircraft flight limits were not exceeded.
The ADOCS frequency response for pitch response due tolongitudinal input is shown in figure 5, along with the
Figure 3. Advanced digital optical control system (ADOCS)demonstrator.
5
δ LO
N (
%)
q (
deg
/sec
)50
25
0
0
20
–20
–25
–50
1251007550Time (sec)
250
Figure 4. Longitudinal side-stick frequency-sweep in hover;(a) pitch input, (b) pitch rate.
θ/–δ
LO
N (
dB
)θ/
–δL
ON
(d
eg)
γ2δ L
ON
q
0
–20
–200
–100
0
–300
1.0
.6
.2
–40
(a)
6 dB
45 deg
ωBW = ωGM
ω135
ω180
2ω180
–60
101Frequency (rad/sec)
0.1
τp = –Φ2ω180
+180°
57.3 x 2ω180
(b)
(c)
Figure 5. Identification of ADOCS pitch-rate response inhover.
determination of bandwidth and phase delay as requiredby the ADS-33 specification. The value of the coherencefunction (fig. 5) is consistently above 0.8 for the fre-quency range of 0.2–8 rad/sec indicating excellent identi-fication. At higher frequencies, the coherence drops,which reflects the intentionally reduced piloted inputs.The pitch bandwidth and phase delay values obtainedfrom the hover identification results are shown on theADS-33 specification boundary in figure 6. Level I (satis-factory) handling qualities for moderate pilot-gain taskssuch as the helicopter “bob-up” are predicted, which isconsistent with the Cooper-Harper pilot rating displayednext to the data symbol. A good correlation of pilot ratingand the predicted handling qualities result was also indi-cated in pitch for the 80 kt flight condition.
Transfer-function (LOES) models of the key on-axesresponses were generated from single-input/single-outputfits of the identified ADOCS frequency responses. TheLOES pitch response in hover is:
θδLON
ss e
s=
− + −0 876 0 229
0 539 1 82
0 238. ( . )
[ . , . ]
.(1)
The response is dominated by a well-damped second-order mode with a frequency of 1.8 rad/sec. The LOEShandling-qualities specification boundaries of figure 7have been established based on system-identificationanalyses of an extensive flight-test and simulation database (Hoh and Ashkenas 1979). The ADOCS characteris-tics are seen to lie well within the Level I region. A sec-ond important characteristic of the LOES pitch response is
τ pθ (
sec)
0 1 2 3
HOVER
LEVEL 2 LEVEL 1
80 knots
4 5
.1
.23
2
.3
.4
ωBWθ (rad/sec)
Figure 6. Handling-qualities correlation of ADOCS smallamplitude pitch response in hover and 80 kt; average pilotratings are shown next to the data.
6
�����
������������
������ω n (
rad
/sec
)
10
8
6
4
2
0 .30.25.20
F-8 data
NT-33
F-8 data
.15Equivalent time delay, τe (sec)
.10.05
Pilo
t ra
tin
g
0 1 2 3
2ζnωn (sec–1)
4 5 6 7
1
2
3
Fixed base simulation of NT-33 data
High stress taskLow stress task
6
6 5.5
4.5-5
4.5-5
4.5-5
2.5-3 4-4.5 2 3 3 2-3
2.5-3
2.5-333-3.5
2.5
4-4.5
4.5-53 3 3
3-4
2-4 2.5-3 3 2-2.5 2.5-3 3.0
2-2.5
2-2.5
2.5-3 2.5-3 3
2.0 2.5-3 3.52.5-32.5-4
3.5
3.5-4
2.5-3 2.5-3 2-2.52.5-3
3.5 3.5-4 2.5-3
2.5-3
3.5-4
3.0
4-4.252.5-3 2.0
3.0 2.25-3
1.82-1.96
2.25-3 2.75-3.5 3.5
7 3.5-4 2-3 2.5 2.5-3 3.5
2-3
5-5.5 3-3.5 3.5
ADOCS Flight Testω
BW = 2
ωB
W = 1
2.5-3.53-3.52.5
2.0 3.0 2.5
ζ =
0.35ζ =
0.25
Figure 7. Correlation of ADOCS LOES pitch response withhandling-qualities data.
the relatively large equivalent time delay, τ = 238 msec.Handling-qualities experience indicates that the equiva-lent time delay should not greatly exceed τ = 120 msec,thereby suggesting ADOCS handling-qualities degrada-tion for “high-gain” tasks. Comparable levels of equiva-lent time delay in the roll axis were considered to be a keycontributor to pilot-induced oscillations (PIO) for “high-gain” piloting tasks such as slope landing (Tischler et al.1991). Additional examples of handling-qualities analysesusing lower-order equivalent-system modeling are pre-sented in the 1994 volume (Anon. 1994).
The stability characteristics of aircraft rigid-body andstructural dynamics may be greatly affected by the feed-back loops of the flight-control system. Feedback maydegrade the flutter margin stability at the same time itimproves the rigid-body stability and handling qualities.Military specification 9490D (Anon. 1975) defines mini-mum levels of control system gain and phase margin asdetermined from a broken servo-loop frequency-responseanalysis. The specifications are given as a function of fre-
quency range, with larger gain margins required for thestructural elastic modes (table 1). Figure 8 shows the bro-ken servo-loop frequency response of a large single-rotorhelicopter as obtained by computer-generated frequency-sweep flight-test procedures. The rigid-body responsecrossover frequency is 2.0 rad/sec with an associatedphase margin of 28 deg. This margin is slightly below therecommended specification value. The gain margin ischecked at each crossing of the 180 deg (±n360) phaseline as shown in the figure. The critical margin is the min-imum value (GM5), which is 15 dB at a frequency of23.5 rad/sec. This frequency corresponds to the first verti -cal bending mode for the tail boom of this aircraft.Reference to table 1 indicates this gain margin to be wellwithin accepted design specifications. The coherencefunction of figure 8 shows excellent identification accu-racy for this flight test across the broad frequency range ofinterest (1–30 rad/sec). Sharp drops (“holes”) or peaks inthe coherence function reflect structural anti-nodes andnodes respectively. Examples of fixed-wing programs
Table 1. MIL-F-9490D gain and phase margin requirements (dB, deg) from Caldwell (1994)
Airspeed Mode Freq. Hz fM < 0.06 0.06 ≤ fM < 1st ASE 1st ASE < fM
Below Vo min GM = 6dB No Phase Reqt. below Vo min
Vo min to Vo max GM = ± 4.5 PM = ± 30 GM = ± 6.0 PM = ± 45 GM = ± 8.0 PM = ± 60
At Limit Speed VL GM = ± 3.0 PM = ± 20 GM = ± 4.5 PM = ± 30 GM = ± 6.0 PM = ± 45
At 1.15 * VL GM = 0.0 PM = 0.0 Stable at Nominal Phase and Gain
Mag
nit
ud
eP
has
eC
oh
eren
ce
20Stability-loop: AVCS-output/servo-command input
0
–20
–40
–100
–300
–500
.21 10 40
Frequency (rad/sec)
.6
10
PM = 28 deg
ωc = 2.0 rad/sec
GM1 GM2 GM3 GM4
GM5
Figure 8. Rotorcraft servo-elastic stability margin testing.
7
using frequency-domain system identification for elasticmode stability-margin evaluation include the X-29(Clarke et al. 1994) and EAP (Caldwell 1994) aircraft.
4. Design
The design process establishes control system loop archi-tecture and associated control-law parameters that achievedesired handling-qualities and servo-loop stability specifi-cations. During the conceptual design phase, system-identification procedures are applied to simple linear-design models to establish a baseline description of theproposed control system approaches and an initial checkof specification compliance. At the detailed design stage,system-identification methods can extract highly-accuratelinear-control system design models from complex simu-lation models or wind-tunnel data. These applications ofsystem identification in the design process are illustratedin this section.
Conceptual control-system design studies are commonlybased on simple stability and control derivative descrip-tions and transfer function of the airframe dynamics asobtained from first-principles aerodynamic theory.Control-law architectures are conceived and the initialsystem is modeled in a computer-aided design (CAD)environment such as MATLAB® (1992). System identifi -cation provides LOES models which are very useful incharacterizing the end-to-end system dynamics anddelays, and for an initial check against the design specifi-cations. Flight-control system design parameters are thenadjusted until the identified LOES characteristics satisfythe design requirements. In the F-15 S/MTD demonstratorproject, a numerical optimization design tool was devel-oped to automatically adjust control-law parameters tomeet LOES specifications (Moorhouse and Citurs 1994).
Detailed flight-control design efforts are based on verycomplex high-order and nonlinear-simulation models.Force and moment descriptions are developed for each ofthe aircraft elements such as the wings, propulsion sys-tem, and flight-control systems based on wind tunnellook-up tables, component bench-test data, and analyticaltheory. The simulation of multiple rigid-body systems, orflexible bodies involves sets of dynamic equations ofmotion linked by constraint conditions. In many simula-tions these sets of equations are numerically integrated inserial form to reduce the complexity of deriving a fully-coupled multibody simulation. The distributed or serialnature of these complex simulations thus may precludethe extraction of an integrated high-order linear model ofthe fully-coupled system as is needed for accurate control-design studies.
Even when the simulation architecture allows for thedirect extraction of higher-order linear models using clas-sical numerical perturbation methods, the assumption ofindependent perturbations results in incorrect phasing ofthe state variables within the multidimensional look-uptables. For example, the look-up table for aerodynamicpitching moment may depend both on angle of attack andpitch rate, so Cmq
= f(α ). Thus, the correct determinationof phugoid dynamics depends on maintaining representa-tive phasing of q and α within the linearization process.Selection of perturbation size can also strongly influencethe linearization results. These effects can significantlydegrade the predictive accuracy of the extracted linearmodel. Much more accurate linear models are obtained bysimulating piloted frequency-sweep inputs and extractingstate-space models using system identification just as iffrom flight-test data.
Engelland extracted accurate stability and controlderivative models of a conceptual A/STOVL air-craft from a complex nonlinear off-line simulation(Engelland et al. 1990) to support control-systemdesign studies. The excitation input consisted ofcomputer-generated frequency sweeps and whitenoise. In a procedure described by Ballin and Dalang-Secretan (1991), artificial feedback control loopswere included to keep the aircraft flight conditionnear the reference trim point during the inputs. Start-ing from the perturbation derivative results CIFER®
was used to identify a more accurate 6 DOF bare-airframe model. The perturbation and CIFER® deriva-tives are compared in table 2. Longitudinal-frequencyresponses of the two linear models are compared withthe complete simulation responses in figure 9 for aflight condition of 120 knots. The linear modelobtained using system identification is seen to bemuch more accurate than the numerical perturbationmodel for the high-frequency (3.0–20 rad/sec) pitch-rateresponse q/δθ, and for the low-frequency (0.1–1.0 rad/sec)longitudinal-acceleration response ax/δθ. The modelsare essentially identical in the mid-frequency range.A time domain comparison of the two-linear modelswith the nonlinear-simulation response is shown infigure 10 for a small (1 deg) pitch-doublet input. Thesystem-identification model is seen to track the non-linear behavior much more closely than the numericalperturbation model. The improvements are most notice-able for the long-term response (low-frequency)behavior, which is consistent with the frequency-response comparison of figure 9.
8
Table 2. Comparison of ASTOVL perturbation derivatives and CIFER® results Derivative Xu Xw Xw Xq XPCD XPLA XΘN
Zu Zw Zw Zq ZPCD ZPLA ZΘN
Mu Mw Mw Mq MPCD MPLA MΘN
Perturb. Value –0.03471
0.03958 6.764E-04
0.2451 –7.690E-03
0.02270 –0.5150
–0.04596 –0.3704
–0.01023 –3.754 0.1389
–0.3800 –0.01724
1.661E-04 1.222E-03
–1.286E-03 –0.4971 0.02494
4.993E-04 2.502E-04
CIFER Value –0.03602
0.02852 6.764E-04
0.2451 –8.303E-03
0.02229 –0.5586
–0.03312 –0.2817
–0.01023 –3.754
0.1551 –0.3305
–0.03055 –1.059E-03
3.715E-03 –1.286E-03
–0.6852 0.02818
4.993E-04 4.953E-04
C.R. (%) –5.662
6.910 — —
–7.504 3.731
–2.353 –13.62 –4.386
— —
5.571 –2.254 –4.646 –6.016
5.263 —
–5.561 2.517
— 10.16
Insens. (%) 2.289 2.840
— —
3.584 1.835 1.005 4.579 1.377
— —
2.698 1.016 2.242 1.745 1.283
— 1.873
0.9822 —
4.257
•
•
•
Perturbation value used.
Co
her
ence
Ph
ase
(deg
)M
agn
itu
de
(dB
)
1.0
–200
–100
–100
–80
–60
–40
Ph
ase
(deg
)M
agn
itu
de
(dB
)C
oh
eren
ce
40
0
–40
–80
0.2
0.6
1.0
–300
–200
Nonlinear simulation Perturbation linear model CIFER linear model
–1000
0.6
0.20.1 10 201.0
Frequency (rad/sec)0.1 10 201.0
Frequency (rad/sec)
q δΘ
ax δΘ
Figure 9. Frequency-response comparison of perturbationand identification models with nonlinear ASTOVLsimulation.
These results show that system identification provides anA/STOVL linear model that will be much more accuratethan models extracted using numerical perturbation meth-ods. The improvement obtained by “flying” thefrequency-sweep input is especially apparent at low
Pit
ch c
on
tro
l (d
eg)
Pit
ch r
ate
(rad
/sec
)
2.0
1.0
0
–1.0
–2.0
–.02
–.01
0
.01
.02
Ver
t. v
el. (
ft/s
ec)
7.0
8.0
10.0
9.0
11.0
Lo
ng
. acc
el. (
ft/s
ec2 )
.02
.04
.06
.08
1.0
Ver
t. a
ccel
. (ft
/sec
2 )
–32.8
–32.6
–32.2
–32.4
–32.0
Lo
ng
. vel
. (ft
/sec
)
119δΘ
q w
axaz
u
118
117
116
115
100 2.5 5.0 7.5100 2.5 5.0Time (sec)Time (sec)
7.5
Nonlinear simulation Perturbation linear model CIFER linear model
Figure 10. Time-domain comparison of perturbation andidentification models with nonlinear simulation of ASTOVLaircraft.
frequencies where the dynamic responses are larger, andcorrect phasing of the representative motion variables forentry into the multidimensional look-up tables is impor-tant. A cursory time-domain comparison of the numericalperturbation results with the nonlinear-simulationresponse would suggest the presence of strong nonlineari-ties in the A/STOVL aircraft dynamics. However, thevery close agreement of the system-identification modelwith the nonlinear simulation shows that the method oflinear model extraction is much more important in thiscase than the nonlinear characteristics of the simulation.
Success in achieving maximum control-system perfor-mance and robustness in flight depends heavily on thepredictive accuracy of the linear-design models. The sys-tem identification approach provides highly-accuratedesign models for design at specific flight conditions, butit is clearly more time intensive than the simple numericalperturbation method. This is not a practical approach forchecking control system behavior at the tens or hundredsof off-nominal conditions.
9
5. Simulation
The detailed implementation of the control-system designis evaluated in comprehensive real-time piloted simulationtrials. System-identification techniques are exercised tovalidate the real-time math model implementation of non-linear digital control laws. Also, these techniques are usedto document simulator motion and visual systems. Onceflight-test data are available, system identification pro-vides an important tool for validating and updating thesimulation math models. This section illustrates system-identification techniques for validating simulation mathmodels and simulator validation using XV-15 tilt-rotor(airplane mode) and UH-60A helicopter results. A com-panion frequency-domain format is proposed for specify-ing simulation model fidelity for the on-axis responses.Finally, an analysis based on an A/STOVL piloted simula-tion study illustrates the use of system identification fordetermining actuator authority requirements.
Direct frequency-response comparison of the end-to-endperformance of the complex simulation model with theconceptual design models and specifications constitutesan important “dynamic check” which often exposes unex-pected processing delays such as in the numerical integra-tion procedures, or errors in the digital (Z-plane)implementation of control laws. This technique is alsouseful in exposing degradation in control system perfor-mance due to high-order structural or other hardwaredynamics modeled in the advanced design simulationmodel that may not have been taken into account in theconceptual studies.
Simulator visual and motion systems should track themath-model response as accurately as possible to ensurethat the pilot’s cueing environment is correct and that thehandling-qualities evaluation obtained in the simulatorreflect what may be expected in flight. Nonlinear com-pensation algorithms have been developed by McFarland(1988) that offset visual system delays, thereby minimiz-ing the mismatch between the simulator visual systemresponse and the math model. In work reported byAtencio (1993) and illustrated in figure 11, there is nearlyperfect agreement of the DIG-1 visual system image (withMcFarland compensation) and the UH-60A helicoptersimulation math model. Math-model commands to thesimulator motion drive are attenuated using wash-outlogic. The wash-out parameters are selected to preservethe dynamic behavior in the frequency range of most con-cern to the pilot (e.g., 1–10 rad/sec for pitch and rolltasks), while accommodating the restricted motion envi-ronment of the simulator. Figure 12 from Atencio (1993)compares the (washed-out) cab roll-motion to stick inputwith the math-model response for the UH-60A simulationin the Ames Vertical Motion Simulator (VMS). In the
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)
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20101.1Frequency (rad/sec)
φ/δa math model φc/δa DGI response
Figure 11. Validation of DIG-1 visual-system response.
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Frequency (rad/sec)10 30
p/δlatMath model Motion follow up
Figure 12. Documentation of VMS motion follow-up forUH-60A roll response in hover.
1–10 rad/sec frequency range, the simulator motion driveresponse follows the math model, although the motion isless than one-to-one as seen by the vertical shift in themagnitude curves. The motion drive wash-out logic isdesigned to minimize phase distortions in this frequencyrange as can be seen in the figure. At low frequencies thelarge motion is washed-out, and considerable errors areencountered in the magnitude and phase response as
10
expected. At high frequency, the motion drive is unable tofollow rapid commands to the aircraft model, resulting inlarger phase lags of the motion follow-up as seen in thefigure.
Once flight-test data are available, system-identificationtools are exercised to validate and update the simulationmath models. The direct comparison of frequency-response behavior provides a clear picture of modelfidelity as a function of frequency. This is critical for val-idating piloted simulations since the requirements on pilotcueing accuracy are also frequency dependent. The sepa-rate display of the magnitude and phase responses allowsthe sources of simulation discrepancies to be more easilydetermined. For example, an excessive time delay ( τ) inthe simulation math model or hardware causes a linearphase shift with frequency (φ = –τω). Scaling errors in thesimulation model appear as a clear vertical shift (in dB) inthe magnitude curve. These effects are all combined in thetime-domain and therefore are not easily discernible in thetraditional time-response comparison methods for valida-tion. Further, the procedure of overlaying time histories isoften not very accurate since the flight responses rarelybegin in a trim quiescent condition.
Tischler (1987) conducted an extensive flight-test pro-gram and simulation math-model validation study on theXV-15 tilt-rotor aircraft shown in figure 13. This tilt-rotormath model is based on comprehensive look-up tables offull-scale wind-tunnel test data, and detailed theoreticalmodels of the rotor-system behavior and rotor-on-airframeaerodynamic interference effects. Figure 14 compares theflight and simulation roll responses for a flight conditionof 170 kts. Excellent dynamic response fidelity is seen inthe close match of the simulation prediction and themeasured flight response. Figure 15 replots these resultsin terms of magnitude and phase errors as a function offrequency. Here 0 dB magnitude and 0 deg phase indicateperfect tracking of the flight and simulation results. Alsoshown in the figure are math model mismatch boundariesproposed herein for the highest fidelity training simula-tions (FAA Level D). These boundaries correspond to theLOES mismatch criteria from the fixed-wing handling-qualities criteria (Hoh et al. 1982). The XV-15 simulationmath model complies with the proposed Level D (high-fidelity) criteria. This result is consistent with the veryfavorable pilot comparison of simulator and flight behav-ior (Churchill and Dugan 1982). The same approach ofmismatch boundaries in the frequency-domain has alsobeen independently proposed and applied by DLRresearchers to detect the effects of unnoticeable dynamicsin the case of helicopters (Hamel and Jategaonkar 1995),and for evaluating the fidelity of in-flight simulation(Buchholz et al. 1995).
(a)
(b)
Figure 13. XV-15 tilt-rotor aircraft; (a) hover configuration,(b) cruise configuration.
p/δ
a (d
B)
p/δ
a (d
eg)
0
–20
Flight data Simulation model
–40
–60
–80
–100
–200
–300
–4000.2 1.0
Frequency (rad/sec)10
Figure 14. XV-15 tilt-rotor simulation model validation for170 kts.
Direct comparisons of stability and control derivativesidentified from flight tests with values identified fromsimulation math models can be used to derive correction
11
Err
or
(dB
)E
rro
r (d
eg)
–20
200
100
0
–100
–2000.1 1.0
Frequency (rad/sec)
Flight data
Proposal Level D fidelity criteria
10
–10
0
10
20
Figure 15. Tilt-rotor math model error functions and pro-posed fidelity criteria for Level D simulators.
factors for significantly improving the model fidelity. Forexample,
L f nonlin sim eqns
L L p
L L
corrected
p flight p sim
flight sim latlat lat
=
+ −
+ − +
( . . )
[( ) ( ) ]
[( ) ( ) ] ...δ δ δ(2)
Identification tools provide a systematic and accurateapproach to determine these correction factors which areroutinely used by the simulator industry to improvedynamic fidelity.
Comprehensive simulation studies are often used to defineflight-control system hardware requirements such as actu-ator and sensor filter bandwidths. Franklin et al. (1991)used CIFER® to determine actuator bandwidth require-ments for a conceptual A/STOVL aircraft. The spectralcharacteristics of the stabilization and command augmen-tation system (SCAS) commands to the aircraft controlsurfaces were obtained for ensemble analyses of simulatedflight tasks, and are shown in figure 16. The results indi-cate a SCAS command signal bandwidth (frequency at–3dB amplitude) of about 4 rad/sec in pitch and roll, witha significantly lower command bandwidth for the thrust(vertical) axis. Actuator hardware response bandwidthsshould be 5–10 times the respective SCAS commandbandwidths to avoid introducing significant phase lag inthe control loops (Franklin et al. 1991). Similar analysistechniques were used by Blanken to determine the effectof control-system design on changes in pilot control
Po
wer
sp
ectr
al m
agn
itu
de
(dB
)
30
0
–302010
CommandsPitchRollTotal thrust
1.0Frequency (rad/sec)
0.1
Figure 16. Power spectra of ASTOVL propulsion systemcommands.
bandwidth (workload) and handling qualities. This studyincluded an interesting comparison of pilot workload forthe simulation and flight-test environments (Blanken andPausder 1994).
6. Development
At the development stage, flight-control system hardwareand software components and subsystems undergo benchtesting to verify that the performance characteristics meetthe design specifications. Sophisticated flight-controldevelopment facilities (DF) or “hot-benches” allow thetest of prototype flight software and hardware integratedwith the simulated aircraft dynamics. In helicopter devel-opment, model or full-scale rotors are dynamically testedin the wind tunnel and the responses are validated againstdesign requirements and comprehensive analysis models.This section presents system-identification techniques tosupport development stage validation. Examples aredrawn from the NASA VSRA project, helicopter actuatortests, and the Sikorsky Bearingless Main Rotor (SBMR)full-scale rotor wind-tunnel tests.
An extensive development facility has been used in theNASA vertical/short takeoff and landing (V/STOL) sys-tems research aircraft (VSRA) project, which equipped aYAV-8B Harrier aircraft with a fly-by-wire researchflight-control system (Foster et al. 1987) (fig. 17). Theoverall flight-control goals of the VSRA program are toassess critical technology elements for advanced shorttakeoff/vertical landing (STOVL) aircraft, including: inte-grated flight/propulsion control, advanced control anddisplay laws, and reaction-controlled bleed-flow require-ments. The role of the DF has been for verification ofcontrol-law flight software, system software, and safetymonitoring. Actual flight computers and flight hardware
12
Figure 17. NASA V/STOL system research aircraft(VSRA).
were included in the DF to validate flight systems duringthe final development stage. The aircraft dynamics aresimulated by the VSRA math model, with inputs from atest console or a rudimentary pilot-cockpit station.CIFER® was exercised extensively to validate broken-loop and end-to-end closed-loop frequency responses ofthe DF flight systems against the design models and theo-retical analyses. Signal processing and conditioning algo-rithms and digital timing were also verified during DFtesting.
Actuator system dynamics comprise an important compo-nent of the overall high-frequency phase lag in modernflight-control systems. Therefore, flight-control systemstability margins and overall closed-loop performance andhandling qualities can be significantly degraded if theactuator dynamics do not meet the design specifications.System-identification bench testing of aircraft actuatorsensures that expected performance is achieved and thatcostly modifications can be avoided at the flight-teststage. Frequency-response identification and transfer-function modeling from a typical helicopter actuator testare shown in figure 18. Excellent coherence is achievedover a broad frequency range (0.2–40 rad/sec) using acomputer-generated frequency-sweep excitation. Theactuator dynamics are well characterized by the dampedsecond-order response obtained by CIFER® (fig. 18).These component system results are used to update simu-lation math models and to optimize flight-control systemgains prior to first flight.
Structural analysis programs such as NASA structuralanalysis (NASTRAN) are rarely able to accurately predictthe flexible response beyond the first elastic modes of anew aircraft. Therefore, structurally-scaled models or full-scale structural test vehicles are evaluated in special rigsto verify the elastic characteristics and make final adjust-ments to the structural compensation (e.g., notch filters) inthe control system prior to first flight. Automatedtest/analysis facilities excite the individual structuralmodes of the aircraft with shakers and then use system-identification methods to determine model characteristics.For modern rotorcraft development, system identification
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20 Actuator test response
Identified model [ζ = 0.74, ωn = 42.2 rad/sec]
0
–20
–40
200
–200
1.0
0.6
0.2
0
40101.0Frequency (rad/sec)
0.1
Figure 18. Helicopter actuator response identification andmodeling.
has also been effective in extracting dynamic responsemodel of subscaled or full-scale rotor systems fromdynamic wind-tunnel test data. The control responsedynamics of the SBMR were determined in a jointNASA/Sikorsky test in the Ames 40- by 80-Foot SubsonicWind Tunnel (fig. 19) (Tischler et al. 1994). Computer-generated frequency-sweep excitation signals to theSBMR swashplate actuator were carefully designed toensure adequate identification within the limitations of therotor and wind-tunnel stand. Rotor blade and hub momentfrequency responses were then extracted using CIFER®
and were compared to comprehensive simulation modelsof the SBMR. CIFER® was also used to extract therotor’s physical parameters based on a linearized 14 DOFanalytical formulation of the SBMR dynamics (Tischleret al. 1994).
Figure 20 shows the identified on-axis roll momentresponse to a lateral stick input. The simulation mathmodel and 14 DOF identified model agree closely withmeasured responses. The off-axis pitching moment tolateral stick input is shown in figure 21. Here, the simula-tion model phase response deviates significantly fromboth the measured response and identified parametricmodel, indicating a poor prediction of rotor cross-coupling.
13
Figure 19. Sikorsky Bearingless Main Rotor (SBMR) test inNASA Ames 40- by 80-Foot Subsonic Wind Tunnel.
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1.0
0.6
0.2
0.6 1.0Frequency (rad/sec)
10 30
Co
her
ence
Wind tunnel extractedGENHEL simulationIdentified parametric model
MX/δlat
Figure 20. SBMR roll-moment response to lateral-stickinput (40-kts flight condition).
The key identified physical parameters of the rotor systemare compared with the GenHel simulation values intable 3 (both are updated from the earlier results ofTischler et al. 1994). Many of the important rotor parame-ters such as Lock number, blade inertia, and effectivehinge off-set compare very favorably, and reflect the goodon-axis response prediction of the simulation model. The
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10 30C
oh
eren
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MY/δlatWind tunnel extractedGENHEL simulationIdentified parametric model
Figure 21. SBMR pitching-moment response to lateral -cyclic-stick input (40 kts).
Table 3. Comparison of SBMR identified parameters with GENHEL values
Rotor Parameter Lock number1 Lift-curve slope Blade inertia1 Blade 1st mass moment1 Blade weight Flapping frequency Effective hinge-offset Lag frequency Lag damper Collective-lag/shaft freq. Collective-lag/shaft damping Trim coning angle Pitch-flap coupling Pitch-lag coupling Control phase angle
Symbol γ a Ib Sb
mbg υβ e υζ Cζ υζ0
Cζ0
βΤ
KPβ KPζ ∆SP
Units
ND 1/rad
slug-ft2 slug-ft
lbs per rev
ND per rev
ft-lb-sec/rad per rev
ft-lb-sec/rad rad
rad/rad rad/rad
deg
GENHEL value
7.46 5.73
552.81 38.76
115 1.081 0.097 0.699
372 — —
0.0768 0
–0.0225 –14.0
Identified value
7.82 5.33
489.8 48.78
142.68 1.080 0.095 0.697
473.29 0.474
1631.49 0.0654
0 –0.184 –23.4
•
IMPORTANT NOTE: 1Mass moment parameters and Lock number are referenced to the hub center and not to the hinge-axis.
important difference between the identified model and theGenHel simulation is the control-phase angle. Thisparameter has a known geometric value of –14 deg in thewind-tunnel tests, but the identified value needed to cap-ture the measured off-axis response of figure 21 is–23.4 deg. This discrepancy in control phasing indicates afundamental problem in the aerodynamic modeling of the
14
rotor. Follow-on analysis of these results have yielded anew approach for correcting the simulation math modeland improvements in the identification methods for free-flight results (Takahashi et al. 1995). Accurate cross-coupling prediction is especially important for the designof decoupling compensators in modern rotorcraft flight-control systems. Corrections to the flight-control lawsprior to final flight software installation and vehicle test-ing reduces development flight-test costs and improvesthe final performance of the system.
7. Flight Testing
The flight-test program for flight-control and handling-qualities validation and optimization has a significantimpact on the overall development schedule and cost formodern fly-by-wire aircraft. System identification pro-vides a critical technology for tracking aircraft dynamicresponse performance into flight, solving problems thatarise in flight tests, and rapidly optimizing control systemparameters. This section presents system-identificationmethods for control system flight testing. Flight dataresults are presented for the VSRA and UH-60A Rotor-craft Aircraft Systems Concept Airborne Laboratory(RASCAL) projects.
Flight test verification of aero-servo-elastic stabilitymargins is an important concern for modern fly-by-wireaircraft, where dynamic coupling of the high-gain flightcontrol system with light-weight structural dynamics candegrade flutter stability. Flutter margin verification usingsystem identification has been adopted by BritishAerospace in the development of a series of fly-by-wirehigh-performance aircraft, as described by Caldwell(1994). Near real-time system identification wasemployed during the X-29 aircraft flight testing (Clarkeet al. 1994) for on-line verification of stability margins ina highly-efficient flight envelope expansion program.Piloted frequency sweeps were used to excite the vehiclestructural modes at each test condition, and the tele-metered data were then analyzed using high-speed arrayprocessing computers. Once the stability margins wereverified, the pilot was cleared to proceed to the next flightcondition, avoiding the normally time-consuming testtechnique of clearing one flutter test point per flight. In asimilar application of near real-time identificationtechnqiues, CIFER® was used to support flight tests ofthe “Pathfinder,” a large high-altitude solar UnmannedAir Vehicle (UAV) (Dornheim 1995). Servoloop stabilitymargins were extracted based on telemetered data fromcomputer-generated frequency-sweep tests, and thencompared with simulation predictions. When the CIFER ®
results indicated a loss of stability margins at a high
altitude flight condition, the ground station pilot executedreal-time switching commands to adjust the Pathfindercontrol law gains.
Theoretical analyses of the XV-15 tilt-rotor aircraft(fig. 13) predicted that the reduction of whirl mode flutterstability margins with increasing flight speed would limitthe aircraft’s usable flight envelope. An extensive flight-test program was conducted to verify the expected mar-gins. Early testing using the traditional dwell-delaymethod proved time-consuming and resulted in consider-able data scatter. Acree and Tischler (1993) conductedautomated frequency-sweep tests using wing flaperonexcitation and subsequently analyzed the data using theCIFER® identification tools. The frequency-domain testtechnique proved to be much more time-efficient, and theresults showed both a reduction in the scatter at specificconditions and an improvement in consistency acrossflight conditions.
Automated frequency-sweep flight testing was also con-ducted on the VSRA YAV-8B aircraft (Foster et al. 1987)(fig. 17) to determine the locations of the (open-loop) firstand second structural wing-bending modes, and to verifyactuator and sensor processing dynamics. The parametricmodel shown in figure 22 was obtained from CIFER®,and includes the rigid-body response and second-orderrepresentations of the two structural modes. Notch filters,included to avoid coupling of the flight-control and aeroe-lastic dynamics, and control-law gains were subsequentlyupdated based on these identification results. Pilotedfrequency-sweep flight testing was also conducted in theVSRA program to document the final stability marginsand closed-loop response for a number of flight condi-tions. The broken-loop pitch response for 120 knots asobtained from CIFER® is shown in figure 23. The figureshows that the dynamics are conditionally stable, with aminimum crossover frequency of 1 rad/sec required forclosed-loop vehicle stability. The nominal crossover fre-quency of 4 rad/sec yields a phase margin of 40 deg(acceptable). A gain margin of about 8 dB is indicatedover the broad frequency range 15–30 rad/sec were thephase curve has a nearly constant value of about–180 deg.
The identified closed-loop response dynamics are shownin figure 24. In the frequency range of 0.3–5 rad/sec theresponse is accurately modeled by a well-damped second-order system:
θθcom
se=−6 35
0 953 2 47
0 048.
[ . , . ]
.(3)
15
YAV-8B Aeroelastic Identification (120 Kts)
p/δa
Rigid-body First Structural Mode
Higher Modes
Second Structural Mode
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CIFER Results [ζ1 = 0.049;ω1 = 19.4 Hz]
[ζ2 = 0.031;ω2 = 30.1 Hz]
–200
0
1.0
0.8
0.6
0.4
0.210 40
Frequency (Hz)
p
δa
sLδa
(s–Lp)
K1s2
[s2+2ζ1ω1s+ω12]
K2s2
[s2+2ζ2ω2s+ω22]
= + + +…
Figure 22. YAV-8B aero-elastic wing-bending identification(120 kts).
These dynamics closely match the design response of:
θθcom
= 4 0
1 0 2 0
.
[ . , . ] (4)
The small equivalent time delay of τ = 48 msec reflectsthe VSRA high-bandwidth fly-by-wire actuators and rapiddigital calculations, and suggests no time-delay relatedhandling-qualities problems.
In some applications, simulation math models are not suf-ficiently accurate for control-law design prior to firstflight. For example, the current state-of-the-art of rotor-craft flight dynamics simulation yields a fair prediction ofthe on-axis characteristics, but usually an inadequate pre-diction of the cross-coupling response as in the baselinesimulation result of figure 21, often not even correct insign (Curtiss 1992). Rotorcraft math models are still use-ful for initial simulation and control-law developmentefforts, but are less satisfactory for the final determination
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10
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GM
PM
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Co
her
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1.0
0.6
0.2
0
3010Frequency (rad/sec)
1.00.1
ωc
ωcmin
Figure 23. VSRA broken-loop pitch response (120 kts).
θ/θ c
om
(d
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θ/θ c
om
(d
eg)
–300
–200
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20
0
0
100
6.01.00.1Frequency (rad/sec)
Flight data
Identified model [ζ = 0.95, ωn = 2.47]
Figure 24. VSRA closed-loop pitch response (120 kts).
of stability margins and decoupling controller gains.Initial flight tests with the SCAS-OFF or with reducedcontrol system gains can be conducted to identify newaircraft dynamics or to update the simulation for finalcontrol-law parameter selection. The DLR developed ahigh-bandwidth flight-control system for the Bo-105
16
variable-stability aircraft (ATTHeS) based directly onbare-airframe state-space models extracted from flightdata using frequency-domain system identification (vonGrunhagen et al. 1994). This direct use of flight-identifiedstate-space models for control-law design represents themost sophisticated and demanding application of system-identification tools.
An approach similar to that of the DLR has been adoptedby the AFDD/NASA in the development of an advancedfly-by-wire flight-control system for the RASCALUH-60A helicopter (Takahashi et al. 1995), which usesthe same airframe as the ADOCS demonstrator (fig. 3).Extensive theoretical studies of combat rotorcraft control-law concepts for application to RASCAL have been con-ducted by Takahaski (1994) and Cheng et al. (1995) basedon UH-60A simulation math models. At the same time,Fletcher (1995) has conducted UH-60A flight tests andcomprehensive frequency-domain identification studies toextract high-order state-space models of the aircraft forhover and cruise flight conditions. These efforts werebrought together in the RASCAL control-law studydescribed in Takahashi et al. (1995). Figures 25 and 26compare two flight-mechanics-simulation math models(“A” and “B”) used for the control-law designs with thebare-airframe flight-test data. The on-axis roll responseagreement between the math models and the flight-testdata is reasonable at mid-frequency (0.8–10 rad/sec), butis inadequate beyond 10 rad/sec due to errors in the pre-diction of the in-plane rotor response. Large errors arealso seen at low frequency. The simulation models showpoor predictive capability for the cross-coupling responseof roll rate to longitudinal stick input, with large phaseerrors in the critical frequency range of 1–10 rad/sec(fig. 26). While the simulation models were sufficient forthe preliminary flight-control and simulation studies, theyare clearly inadequate for selecting final flight gains—especially for the response decoupling parameters.
The identified higher-order linear model is compared withthe flight data and the simulation models in Figures 25and 26. Significant improvement in the on-axis predictionis seen for both the high-frequency (rotor response) andlower-frequency dynamics. The identified model alsotracks the off-axis magnitude and phase very closely,showing clear improvement compared to the two simula-tion models. The excellent predictive capability of theidentified model is also seen in the time response compar-ison of figure 27.
The identified state-space model was then substituted intothe model-following control system block diagram inplace of the original simulation model (“A”) response tocheck the expected flight characteristics. Figure 28 showsThe identified state-space model was then substituted into
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–90
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p δa
Sim model A
Sim model B
Identified model
Flight results
0.1 1.0Frequency (rad/sec)
10 20
Figure 25. UH-60A on-axis roll-rate response to lateralstick (hover); comparison of simulation and identified state-space model with flight data.
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Ph
ase
(deg
)
0
100
–100
–300
–500
–20
–40
–60
p δe
Sim model A
Sim model B
Identified model
Flight data
0.1 1.0Frequency (rad/sec)
10 20
Figure 26. UH-60A off-axis roll-rate response to longitu-dinal stick (hover); comparison of simulation and identifiedstate-space model with flight data.
17
10
0
–10
10
0
–10
10
0
–10
10
0
–10
16.5
15.5
14.5
Flight data
identification model
8.57.56.55.54.53.52.5
Φ (
deg
)Θ
(d
eg)
p (
deg
/sec
)q
(d
eg/s
ec)
δ e (
inch
es)
Time (sec)
Figure 27. Time response comparison of UH-60A identi-fication model and flight data.
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ase
(deg
)
20 ID model + design gains
0
–20
–40
–100
–200
–30010010
Frequency (rad/sec)1.0
–6 dB
135°
180°
Design modelID model
+ adjusted gains
Figure 28. RASCAL UH-60A broken-loop roll response inhover.
the model-following control system block diagram inplace of the original simulation model (“A”) response tocheck the expected flight characteristics. Figure 28 showsthat the design phase margin is significantly degradedwhen the identified model is incorporated. Further, thelevel of closed-loop cross-coupling (fig. 29) increases by20 dB (a factor of 10) in the critical handling-qualitiesfrequency range of 1–10 rad/sec. The control-systemdesign parameters were then retuned for the identifiedmodel response. Figure 28 shows that the original designcrossover frequency, phase margin, and gain margin arerecovered. Also, the cross-coupling level for the retunedsystem closely tracks the coupling levels for the originalcontrol-system design (fig. 29).
Mag
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20
40
0
–20
–4010010
Frequency (rad/sec)1.0
ID model + design gains
ID model + adjusted gains
Design model
φ/θo
θ/θoc
c
Figure 29. RASCAL UH-60A coupling response of roll-ratedue to longitudinal input for hover.
The full exploitation of system-identification tools earlyin the flight-test development and control system opti-mization effort has been illustrated for the Bo-105(ATTHeS) and UH-60A (RASCAL) programs. Thisapproach will significantly reduce flight-test developmenttime for new aircraft, and will expedite the optimizationof flight-control system performance and handlingqualities.
8. Concluding Remarks
1. System identification is a full life-cycle technology thatsupports aircraft flight-control system development fromdesign specification through flight-test optimization. Sig-nificant reductions in development time and costs are real-ized by tracking open and closed-loop dynamic responsecharacteristics through the development process.
2. Frequency-domain system-identification methods arewell suited to aircraft flight-control development sincemany current design specifications, design and analysistechniques, and acceptance flight-test techniques arebased in the frequency domain.
18
3. Reliable computational tools for system identificationare available and have been successfully employed inmany recent aircraft programs.
4. System identification is especially effective in provid-ing a transparent and integrated understanding ofhandling-qualities characteristics and system stability.Considerable improvements in system performance arefacilitated by the rapid availability of accurate end-to-endand subsystem dynamic models.
9. References
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Anon.: Military Standard, Flying Qualities of PilotedVehicles, MIL-STD-1797 (USAF), 1987.
Anon.: Aeronautical Design Standard, Handling QualitiesRequirements for Military Rotorcraft, ADS-33C(AVSCOM), 1989.
Anon.: Rotorcraft System Identification. AGARDAR 280, 1991.
Anon.: International J. Control: Special Issue. AircraftFlight Control, vol. 59, no. 1, 1994.
Atencio, A.: Fidelity Assessment of a UH-60A Simulationon the NASA Ames Vertical Motion Simulator.NASA TM-104016, 1993.
Ballin, M. G.; and Dalang-Secretan, M. A.: Validation ofthe Dynamic Response of a Blade-Element UH-60ASimulation Model in Hovering Flight. J. Amer. Hel.Soc., vol. 36, no. 4, 1991, pp. 77–88.
Blanken C. L.; and Pausder, H. -J.: Investigation of theEffects of Bandwidth and Time Delay on HelicopterRoll-Axis Handling Qualities. J. Amer. Hel. Soc.,vol. 39, no. 3, 1994, pp. 24–33.
Buchholz, J. J.; Bauschat, J. M.; Hahn, K. U.; andPausder, H. J.: ATTAS & ATTHeS In-FlightSimulators: Recent Application Experiences andFuture Programs, AGARD Flight Vehicle IntegrationPanel Symposium “Simulation: Where are theChallenges,” Braunschweig, Germany, 1995.
Caldwell, B. D.: The FCS-Structural Coupling Problemand its Solution. AGARD-CP-560, Paper 16, 1994.
Cheng, R. P.; Tischler, M. B.; and Biezad, D. J.:Rotorcraft Flight Control Design Using QuantitativeFeedback Theory, Symposium on QuantitativeFeedback Theory, 2-4 August, Purdue University,West Lafayette, Ind., 1995.
Churchill, G. B.; and Dugan, D. C.: Simulation of theXV-15 Tilt Rotor Research Aircraft. NASATM-84222, 1982.
Clarke, R.; Burken, J. J.; Bosworth, J. T.; and Bauer, J. E.:X-29 Flight Control System: Lessons Learned.International J. Contr., vol. 59, no. 1, 1994,pp. 199–219.
Curtiss, H. C., Jr.: On the Calculation of the Response ofHelicopter to Control Inputs. 18th EuropeanRotorcraft Forum, Avignon, France, 1992.
Dornheim, Michael A.: Aviation Week and Space Tech.,Sept. 18, 1995, p. 67.
Engelland, S. A.; Franklin, J. A.; and McNeill, W. E.:Simulation Model of a Mixed-Flow Remote-LiftSTOVL Aircraft. NASA TM-102262, 1990.
Fletcher, J. W.: Identification of UH-60A StabilityDerivative Models in Hover from Flight Test Data. J.Amer. Hel. Soc., vol. 40, no. 1, 1995.
Foster, J. D.; Moralez, E, III; Franklin, J. A.; andSchroeder, J. A.: Integrated Control and DisplayResearch for Transition and Vertical Flight on theNASA V/STOL Research Aircraft (VSRA). NASATM-100029, 1987.
Franklin, J. A.; Stortz, M. W.; Engelland, S. A.; Hardy,G. H.; and Martin, J. L.: Moving Base SimulationEvaluation of Control System Concepts and DesignCriteria for STOVL Aircraft. NASA TM-103843,1991.
Glusman, S. I.; Dabundo, C.; and Landis, K. H.: Evalua-tion of ADOCS Demonstrator Handling Qualities.Proceedings of the 43rd Annual National Forum ofthe American Helicopter Society, Washington, D.C.,1987.
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Hamel, P. G.; and Jategaonkar, R. V.: The Evolution ofFlight Vehicle System Identification. AGARDStructures and Materials Panel Specialists’ Meetingon Advanced Aeroservoelastic Testing and DataAnalysis, Rotterdam, The Netherlands, 1995.
Hoh, R. H.; and Ashkenas, I. L.: Development of VTOLFlying Qualities Criteria for Low Speed and Hover.Systems Technology, Inc., Hawthorne, Calif.,TR-1116-1, 1979.
Hoh, R. H.; Mitchell, D. G.; Ashkenas, I. L.; Klein, R. H.;Heffley, R. K.; and Hodgkinson, J.: Proposed MILStandard and Handbook-Flying Qualities of AirVehicles. AFWAL-TR-82-3081, vol. 2, 1982.
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Kaletka, J.; and von Grunhagen, W.: Identification ofMathematical Derivative Models for the Design of aModel Following Control System. 45th AnnualForum of the American Helicopter Society, Boston,Mass., 1989.
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Takahashi, M. D.; Fletcher, J. W.; and Tischler, M. B.:Development of a Model Following Control Law forInflight Simulation Using Analytical and IdentifiedModels. American Helicopter Society, 51th AnnualForum, Fort Worth, Tex., 1995.
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Tischler, M. B.: System Identification Requirements forHigh-Bandwidth Rotorcraft Flight Control SystemDesign. J. Guid., Contr., and Dyn., vol. 13, no. 5,1990, pp. 835–841.
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Tischler, M. B.; Fletcher, J. W.; Morris, P. M.; andTucker, G. E.: Flying Quality Analysis and FlightEvaluation of a Highly Augmented CombatRotorcraft. J. Guid., Contr., and Dyn., vol. 14, no. 5,1991, pp. 954–963.
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11. SUPPLEMENTARY NOTES
Unclassified Unclassified
System identification, Flight control, Flight test
A-950097
Mark B. Tischler
Aeroflightdynamics Directorate, U.S. Army ATCOM,Ames Research Center, Moffett Field, CA 94035-1000
505-59-36
22
A03
Point of Contact: Mark B. Tischler, Ames Research Center, MS 211-2, Moffett Field, CA 94035-1000; (415) 604-5563
October 1995 Technical Memorandum
System-identification methods compose a mathematical model, or series of models, from measurements ofinputs and outputs of dynamic systems. The extracted models allow the characterization of the response of theoverall aircraft or component subsystem behavior, such as actuators and on-board signal processing algorithms.This paper discusses the use of frequency-domain system-identification methods for the development andintegration of aircraft flight-control systems. The extraction and analysis of models of varying complexity fromnonparametric frequency-responses to transfer-functions and high-order state-space representations is illustratedusing the Comprehensive Identification from FrEquency Responses (CIFER®) system-identification facility.Results are presented for test data of numerous flight and simulation programs at the Ames Research Centerincluding rotorcraft, fixed-wing aircraft, advanced short takeoff and vertical landing (ASTOVL), vertical/shorttakeoff and landing (V/STOL), tiltrotor aircraft, and rotor experiments in the wind tunnel. Excellent systemcharacterization and dynamic response prediction is achieved for this wide class of systems. Examples illustratethe role of system-identification technology in providing an integrated flow of dynamic response data around theentire life-cycle of aircraft development from initial specifications, through simulation and bench testing, and intoflight-test optimization.
System Identification Methods for Aircraft Flight ControlDevelopment and Validation
NASA TM-110369USAATCOM TR-95-A-007
Unclassified-UnlimitedSubject Category – 08
National Aeronautics and Space AdministrationWashington, DC 20546-0001 and U.S. Army Aviation and TroopCommand, St. Louis, MO 63120-1798