[American Institute of Aeronautics and Astronautics 20th AIAA Advanced Measurement and Ground...

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VERSATILE SOFTWARE PACKAGE FOR NEARREAL-TIME ANALYSIS OF EXPERIMENTAL DATA

Carol D. Wieseman* and Sherwood T. Hoadleyt

NASA Langley Research CenterHampton, VA

ABSTRACT

This paper provides an overview of a versatilesoftware package developed for time- and frequency-domain analyses of experimental wind-tunnel data.This package, originally developed for analyzing datain the NASA Langley Transonic Dynamics Tunnel(TDT), is applicable for analyzing any time-domaindata. A Matlab®-based software package,TDT_analyzer, provides a compendium of commonly-required dynamic analysis functions in a user-friendlyinteractive and batch processing environment.TDT_analyzer has been used extensively to provideon-line near real-time and post-test examination andreduction of measured data acquired during wind tunneltests of aeroelastically-scaled models of aircraft androtorcraft as well as a flight test of the NASA HighAlpha Research Vehicle (HARV) F-l 8. The packageprovides near real-time results in an informative andtimely manner far exceeding prior methods of datareduction at the TDT.

INTRODUCTION

A Matlab®-based software package,TDT_analyzer, was written to assist in the near real-time and post-test analysis and reduction of time-history data acquired during wind-tunnel tests ofaeroelastically-scaled models of aircraft, rotorcraft andlaunch vehicles in the Transonic Dynamics Tunnel(TDT) at the NASA Langley Research Center. Nearreal-time reduction of dynamic wind-tunnel data anddisplays of results within seconds of data acquisitionare paramount to assess requirements for subsequenttest conditions and model configurations, thereby

* Research Engineer, Senior Member, AIAAf Senior Engineer, Associate Fellow, AIAA

Copyright © 1998 by the American Institute ofAeronautics and Astronautics, Inc. No copyright isasserted in the United States under Title 17, U.S.Code. The U.S. Government has a royalty-freelicense to exercise all rights under the copyrightclaimed herein for Governmental Purposes. All otherrights reserved by the copyright owner.

reducing test time and, in some cases, improvingmodel safety. The software package is highlyversatile and user friendly, taking advantage of thegraphics capability of Matlab®. Although it requiresMatlab® and two toolboxes to be installed andrunning, TDT_analyzer is a stand-alone package ofMatlab® script routines that has evolved over the pasteight years from the on-line, near real-time controllerverification and controller performance evaluationpackage (ref. 1) developed for the NASA/RockwellActive Flexible Wing program in 1989 and 1991(refs. 2).

The TDT analysis package converts time-historydata to engineering units and performs various time-and frequency-domain analyses including statisticalanalyses of the data. Plots of analysis results can beplaced on a page in a user selectable layout. Outputsare provided to the engineers near real-time to 1)assist in determining effective model and tunnel testconfigurations, 2) to provide analyses of steady andunsteady aerodynamics, 3) to evaluate controllerperformance, and 4) assess data quality. Results canalso be used for system identification to improvemodel simulation and control law design.

In addition to processing wind-tunnel data,TDT_analyzer can also process time history datagenerated by other sources, including simulations,after first providing the input time history and signalinformation used by the TDT_analyzer program in astandard Matlab® format. To this end, TDT_analyzerhas a companion pre-processor program,TDT_interface, written in the C programminglanguage that has also evolved over the past eightyears. This pre-processor program converts data froma multitude of sources to the Matlab®-readable inputfile used by TDT_analyzer. TDT_interface provides amechanism for integrating TDT_analyzer with mostdata acquisition systems and can be modified to readdata from other sources as needed.

From its inception, TDT_analyzer was designedto perform on-line data analysis immediately after datawere acquired During the past few years its

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flexibility and capabilities have been enhanced tomeet the data analysis requirements of engineers frommany test programs conducted at the TDT and otherNASA facilities. The TDT analysis package hasmaintained a user-friendly interactive environment,which can be exercised in a batch mode as well. It hasbeen used in close conjunction with the TDT - DataAcquisition System (TDT-DAS) for the past threeyears, and has been used to provide near real-time, on-line and post-test analyses of wind-tunnel data duringthat time. Figure 1 depicts the flow of data from a

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wind-tunnel model through the Data Acquisition Unit(DAU) to computers running TDT_analyzer. Alsodepicted are some of the analysis options availablewith TDT_analyzer and samples of plot outputswhich will be described in detail later.

The following sections present details of thecapabilities of this package. Examples are shownwhich use data acquired during some of the testsperformed at the TDT and elsewhere.

Figure 1.- Overview of TDT_analyzer capabilities depicting flow from data acquisition to final plots.

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FEATURES

TDT_analyzer is a menu-driven package whichuses standard Matlab® functions as well as somespecially designed functions. This software can runon any computer where Matlab® and the requiredControls and Signal Processing toolboxes areinstalled. This includes most UNIX workstations andpersonal computers.

During the running of TDT_analyzer, the user isfirst prompted for a file name which contains the datato be analyzed. The user then may input a specifictitle and header information that will be used on allplots. The user then selects the TDT_analyzer plotand analysis options. A list of the analysis optionsthat are available in TDT_analyzer are listed andbriefly described in Table 1. After the selection of theanalysis options, the user is prompted for othergeneral options available to all analyses. Then theuser is prompted to input values of parameters whichare specific to the types of analyses which have beenselected. The user selects channels that s/he wants toanalyze and if the option requires a reference channel,the user will be prompted at the appropriate time toinput a signal number for the reference channel.

All the analysis options currently available inTDT_analyzer are described in this paper. Optionsgeneral to all processing are described first.

General Options Applicable to All Analyses

Units conversion: Prior to data analysis, the usermay select to use one of several units conversions.The raw data are typically in units of the dataacquisition board, namely counts. If this is the case,options are provided to convert data to voltages orengineering units.

Signal selection and processing: The user canselect a subset of available signals or even differencedpairs of signals to analyze. This differencingcapability might be exercised, for example, to analyzeantisymmetric acceleration by analyzing the differenceof accelerometer data from signals on the right andleft side of a full-span model. Differential pressurescould be analyzed using the difference of upper andlower surface pressures. Some analyses in both thetime- and frequency-domain require a reference signal.This reference signal may be either a single signal ora differenced pair of signals.

Decimation or resampling: The data can be 'n*-pointed' before processing, meaning that every n"1

point is selected for analysis. Appropriate digitalfiltering is automatically performed where necessary.The value of "n" is user selectable. The default is 1,which corresponds to selecting all points within theuser-selected time interval of the data.

Plot page layout: Many of the analysis optionsprovide graphical output. The user can select thenumber of plots vertically and horizontally on thepage. Though there are no hard coded limits, thepractical limit is 7 vertically and 3 horizontally. Theanalyses may be performed in any order and plots willbe generated in sequence either vertically orhorizontally, as selected by the user.

Repetitive Processing: One of the mostconvenient features of TDT_analyzer is the capabilityto easily repeat analyses by reexecuting the code inthe same Matlab® session. Additional analyses canbe performed on data previously processed or the sameanalyses can be performed on different time-historysignals. During processing, the user input values arestored in temporary variables. During reexecution ofthe code, the user will be prompted for the values ofthese parameters. If s/he doesn't specify differentvalues and just inputs a carriage return, the previouslydefined values will be used. This feature is whatmakes TDT_analyzer very convenient for repetitiveprocessing. For example, if a user wants to repeat afrequency-domain analysis with a different block size,when prompted to input values for any otherparameters s/he can just hit carriage returns and thepreviously defined values will be used. Whenprompted for the blocksize, s/he provides the newvalue which s/he wants to use during processing.This is the same procedure used for any one ormultiple variables. All parameters except for thesignal numbers can be kept constant thus resulting inthe same analyses being performed on different data,or the values of the options can be changed whilekeeping the signal numbers the same resulting in thedifferent analyses on the same time-history signals.Any combination of changes is available to the user.

Batch processing: To facilitate batch processing,TDT_analyzer automatically creates a command filewhich replicates all the user inputs generated during



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Table 1. Summary of TDT_analyzer Analysis Options

Type of analysisTime-history plot

Channel statistics

Auto-correlation(normalized)

Cross-correlation(normalized)

Power Spectral Density-standard- non-dimensionalized- normalized- smoothed standard- smoothed normalized

Cross-spectrum-standard- smoothed

Frequency Response-standard- smoothed standard- inverted- smoothed inverted

Coherence-standard- smoothed standard

Magnitude/Phase

FFT-standard- smoothed standard

Harmonic Analysis

Cumulative DynamicResponse Analysis

DomainTime

Time

Time

Time

Frequency

Frequency

Frequency

Frequency

Frequency

Frequency

Frequency

Frequency

DescriptionPlots any channel or multiple channels over a user-selectedtime segment. Overlays of time histories from severalchannels are available. Some channel statistics are includedon the plots.Generates table of minimums, maximums, means, and rootmean square calculated using standard Matiab® functions.Shows how well a signal is correlated with itself in time.Calculated using a standard Matiab® function.Shows how well a signal is correlated with another signal intime. Calculated using a standard Matiab® function.Calculates PSD's using modified spectrum functions. Themaximum and the frequency at which it occurs are included onthe plots. For a purely oscillatory signal, the peak amplitudefor a standard PSD is the square of the signal amplitude, whilethat of a normalized PSD is V2 times the amplitude. InTDT_analyzer, non-dimensionalizing is accomplished bydividing by q, dynamic pressure. This would most likely beused to non-dimensionalize pressure data. Other options fornon-dimensionalizing could easily be incorporated inTDT_analyzer.Calculates cross-spectrum of two signals using a modifiedMatiab® function.

Calculates frequency responses using built-in Matiab®functions. Additional processing is provided which uses thefrequency-response functions generated by this option. Theyare listed and described in table 2. Frequency responses can besaved on file for any other desired post-processing, such assystem identification in the frequency domain.Measures the quality of the frequency responses. Calculatedusing built-in Matiab® functions

Generates tabular results with respect to a reference channel ata specific frequency calculated using a reference signal. Thephase is referenced to the reference phase. The magnitude canbe normalized by the reference magnitude. The magnitude andphase are calculated using a specialized single frequencydiscrete fourier transform function (SFDFT)Calculates Fast Fourier Transforms using built-in Matiab®functions.

Calculates response harmonics with respect to an oscillatorysignal. Used for rotor analysis to provide response at theharmonic frequencies.Determines the RMS over user-selected frequency bandwidths.

Outputsplots

files withtables

plots

plots

plots

plots

plotsMatiab®

outputfiles

tables

plots

tables

plots

plotstables

plotstables



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an interactive session. This command file can thenbe used to generate a Matlab® input file to be used forexample in a batch mode to perform the samecalculations on a different set of experimental data.This file can be modified to add parameters to identifydata points or other options. This capabilityfacilitates the rapid setup of batch procedures forprocessing data acquired at different test conditions.

The following sections describe the time-domain,frequency-domain and extended function capabilities ofTDT_analyzer. Examples of some of the capabilitiesare shown in the Sample Results section.

TIME-DOMAIN ANALYSIS CAPABILITIES

The types of time-domain analyses availablewithin TDT_analyzer are listed in the beginning ofTable 1. These include time-history plots, auto-correlation, cross-correlation, and tables of channelstatistics: mean, minimum, maximum, root meansquare, and peak-to-peak magnitude. A briefdescription of each time-domain analysis option isincluded in the Table 1. For all the options that arelisted, the user can select the entire time history orselect the initial and final times of a subset of theentire time history. The selected time interval is usedfor all the time-domain analyses performed byTDT_analyzer during a Matlab® session until changedby the user.

FREQUENCY-DOMAIN ANALYSISCAPABILITIES

The types of frequency-domain analyses availablein TDT_analyzer along with a brief description ofeach are also listed in Table 1. For all the optionsthat are listed, the user can select the entire timehistory or select the initial and final times of a subsetthereof for processing. The selected time interval willbe used for all the frequency-domain analyses untilchanged by the user. This time interval is independentof that selected for time-domain analyses. Thisselection option allows the user to easily combineboth time- and frequency-domain related plots on thesame page without requiring the same time intervalfor both.

For all frequency-domain analyses, the user mayselect windowing, blocksize, and the percent ofoverlap used in averaging. The selected values willbe used as default for all frequency-domain processinguntil changed by the user. Some of the details

regarding the general options available to allfrequency-domain analyses are summarized in thefollowing section.

General Options for Frequency Domain

Windowing: The capability is provided to easilyselect the windowing option of the time history forfrequency-domain processing. A user can select oneof the following options: Manning, Hamming,Rectangular, Triangular, Bartlett, Blackman,Chebyshev and Kaiser (reference 3). TDT-analyzermakes it easy to repeat analyses using differentwindows and plot the results on the same page forcomparison.

Blocksize: The user can select any blocksizewhich is a power of two. If the user does not select apower of two, the closest power of two that fits thedata will be calculated and used.

Overlap averaging: The user can select thepercent overlap of time-history data for overlapaveraging in frequency-domain analyses. There are norestrictions on the percent overlap as long as at leasttwo averages are calculated. Error checking isprovided to assure this restriction is met.

Frequency-domain units: Results for all of thefrequency-domain analyses may be plotted over a user-specified frequency range in either Hertz or in radiansper second. The axes for the dependent variable beingplotted are automatically scaled. In the case of thePSD, the magnitudes are scaled for the specifiedfrequency units.

Analysis Options for Frequency Domain

Standard Options: Frequency-domain analysesoptions include a standard, normalized, and non-dimensionalized Power Spectral Density (PSD), asdefined in Table 1; frequency response (commonlyreferred to as "transfer function" withinTDT_analyzer); coherence; auto- and cross-spectrum;and Fast Fourier Transform (FFT).

Inverted frequency responses can also becalculated and plotted. In TDT_analyzer, when theuser requests frequency responses the desired outputsignals and then an input signal number are specified.The input signal is referred to as the reference signal.When the user requests an inverted frequency responsethe process is as follows. The user specifies thedesired input signals and then an output signal



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number. In this case, the output signal is referred toas the reference signal.

The option to calculate smoothed FFT's, PSD's,frequency responses, coherences and spectra using aspecially-defined smoothing function based onmethods described in reference 4 is also available.

Magnitude and Phase: Magnitude and phase ofdynamic time-history data can be calculated withrespect to an oscillatory reference signal at a specificfrequency. This is useful for evaluating pressures atflutter, or the unsteady pressure responses due tocontrol surface oscillatory motion. The referencesignal is used to determine the oscillation frequency.First, the location of the peak of the reference signalPSD provides an estimate of the oscillatoryfrequency, which is then used as the starting point tozoom in on the actual frequency using a specializedpeak-searching routine. Once this frequency is found,the magnitude and phase of the reference signal and allother requested signals are determined using aspecialized function that calculates the single-frequency discrete Fourier transform (SFDFT) at thereference frequency. The reference phase is thensubtracted from the phase of each requested signal.The magnitude of the signals can be normalized, ifdesired, by the magnitude of the reference signal.Tabular output files are generated.

Harmonic Analysis: Harmonic analysis is thecalculation of magnitude and phase of signals at thefundamental frequency of a reference signal and atsuccessive multiples thereof. The reference signalmay be specified by the user, but for rotorcraft,specifically, the fundamental frequency is calculatedfrom a one-per-revolution signal of a rotor blade. Thisfundamental frequency is calculated by identifying thestarting point of each revolution and determining thedifference in time between revolutions. Again, themagnitude and phase of the signals at the fundamentalfrequency and its multiples are calculated usingSFDFT methods. The time-history of the signals canbe reconstructed from these magnitudes and phasesusing a user-selected number of harmonics and thencompared graphically with the original experimentaldata to display goodness of fit. A tabular output fileis generated of the harmonic results.

Cumulative Dynamic Response Analysis:Cumulative dynamic response analysis corresponds tocalculating the RMS over user-selected frequencybandwidths based on the PSD. The first step is to

calculate the PSD and perform the cumulative integralof the PSD. The RMS is then calculated as thesquare root of the difference in the cumulative integralof the PSD at the two user-selected frequencies foreach selected bandwidth. A table of the frequencylimits and corresponding RMS values is generated.

Extended Analysis Options:

Frequency-response functions also serve as inputto a number of extended analysis options as listed inTable 2. These sub-options are made available if anyfrequency response option is selected under the mainmenu.

One such extended option is ControllerPerformance Evaluation (CPE). The CPE analysisoption is used to: (1) predict the closed-loop stabilityof a system while the system is open loop; and (2)assess the closed-loop stability and robustness whenthe system is closed loop. The details of the theoryare documented in references 5 and 6. Both of thesecapabilities were critical in some of the wind-tunneltests conducted in the NASA Langley TransonicDynamics Tunnel to protect the wind tunnel andmodel from damage.

Another extended option enables the user toperform CPE using experimental data for the open-loop plant along with analytically generated controllaws. The same graphical output that CPE producesis generated and predicts the performance of a controllaw prior to experimental testing.

The frequency-response functions of control lawoutputs with respect to sensor inputs can also be usedfor controller verification. This extended optionverifies that the control law being executed matchesthe designed control law. It is performed bygenerating plots which overlay frequency responsescalculated from an analytical control law with thosecalculated from the experimental data.

One of the byproducts of CPE is the extractionof the open-loop plant frequency responses for thoseactuators and sensors being used by the control law.The capability to extract frequency responses for otheractuators and sensors not included in the control lawis also an extended analysis capability available inTDT_analyzer. The additional actuators, however,must have been used to excite the model and theadditional sensor time histories must have beenmeasured.



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Table 2. Summary of TDT_analyzer Extended Analysis Options which use the frequency responses.

Type of analysisController performance evaluation (CPE)CPE with loaded control-law and the open-loop plantController verification

Extraction of open-loop plant for additionalsensors and/or control surfaces

Comparison of experimental frequencyresponse with analytical single-pole filterMagnitude and phase at selected frequencies

DescriptionEvaluate the performance of control lawsPredicts closed-loop performance of control lawbefore experimental testingCompare experimental frequency responses andanalytical frequency response using loaded controllaws provided by control law designersCan be used for additional system identification forcontrol law design with different actuators orsensorsUsed for evaluating single-pole anti-aliasing filters.

Assist in evaluating filter performance or controllaw performance

Outputsplotsplots

plots

plots

plots

tables

A digital controller system used in the TDT forseveral active-control wind tunnel tests for fluttersuppression, reducing maneuver loads and for gustload alleviation (reference 7), used single-pole anti-aliasing filters. In order to check these filters anoption was added to TDT_analyzer to compare thefrequency response calculated from experimental datato the frequency response of a single-pole filtergenerated analytically. The user is prompted forparameters defining the filter. Since many digital dataacquisition systems require anti-aliasing filters, TDT-analyzer could easily be enhanced to include higher-order filters in this analysis option.

In addition to the graphical output of frequencyresponses, the magnitude and phase of theexperimental frequency response can be calculated atuser-selected frequencies and output on a tabular file.When evaluating the performance of anti-aliasingfilters where the magnitude and phase of the anti-aliasing filters is known at selected frequencies, thistabular data is extremely helpful in making sure thatthe correct anti-aliasing filters have been chosen.This tabular data in combination with the graphicalcomparison of the experimental and analyticalfrequency-response functions can assist in determiningwhether the proper anti-aliasing filters are being usedand whether the filters are working properly also.

SAMPLE RESULTS

During its evolution over the past 9 years,TDT_analyzer has been used on line on over 20

occasions. Without some of the capabilities ofTDT_analyzer, some of the wind-tunnel tests couldnot have been performed as safely without putting thetunnel and model at great risk. The recent calibrationof the TDT depended very heavily on TDT_analyzer.Two Langley tunnels have used TDT_analyzer andother tunnels around Langley are also starting to useTDT_analyzer. In addition to wind-tunnel tests,calibration tests, and flight tests, TDT was used tohelp diagnose and solve a pipe vibration problem atthe TDT. Tests taken as a whole have exercised alloptions of TDT_analyzer and in fact have motivatedcontinual enhancements of the software capability. Afew examples are presented in this section.

Data analyzed using the TDT_analyzer softwarehave been documented in numerous publications,conferences and meetings (refs. 5, 8-12). Examplefigures are described next which use data from someof the tests to show the versatility of TDT_analyzer.In all cases, plot titles and labels have been re-typedto permit readability, and signal names have beenreplaced with more generic terminology.

A typical time history plot of an actuatorcommand signal from the Benchmark Active ControlsTechnology (BACT) model (refs. 9-10) test is shownat the top of figure 2 along with its auto-correlationat the bottom. This example shows the typicalinformation plotted for two of the options availablein TDT_analyzer. In addition to header informationand a title on the figure, some channel statistics arealso printed on each plot. For time history plots, the



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following information about the time history are alsoincluded: the root mean square (RMS) value, theminimum value, peak-to-peak magnitude, themaximum value, and the mean. The subtitle of theauto-correlation plot displays the magnitude of thepeak and the time at which it occurs. The user selectsthe range of the time (lag-lead) in seconds duringprocessing.

Header Information / Page Title

[Time-History]: RMS: 2.29 Min-7.75 Pk-Pk: 15.33 Max: 7.58 Mean: -.0087

0 10 20 30 40 50 60 70 80Time, seconds

[Auto Correlation]: Actuator Command: max 1.000 at 0.000 seconds

-0.50

Time (lag-lead), seconds

Figure 2. Time history and auto correlation of anactuator command acquired during testing of theBACT model.

A comparison of a standard and a smoothedstandard PSD of the difference of two signals(differential pressure) from the ACROBAT F/A-18buffet model (reference 11-13) test is shown in figure3. These results show, first of all, that signals can bedifferenced. Labels on the dependent axis correspondto the actual signal identifiers and for differencedchannels are generated from the individual signalnames. In addition to header information, the RMSand the maximum of the PSD along with thefrequency at which it occurs are documented on bothPSD plots. The blocksize, in this case 4096, andpercent overlap in processing these data are alsoincluded on the plots. The effect of using a special

smoothing function (reference 4) available inTDT_analyzer is clearly shown at the bottom offigure 3. In this case, the smoothing coefficient usedis equal to one as indicated by a = 1 on the subplottitle. This parameter is user selectable and for thisexample was arbitrarily set to one to show thesmoothing capability. When smoothing data, thepeaks of the smoothed data tend to be rounded. Inthis case, this results in a 10% reduction in peakamplitude for the smoothed PSD. A user can veryeasily reprocess the data with different smoothingcoefficients and compare the trade-off betweensmoothing and peak resolution.


* 1(r> [PSD]: RMS: 0.067 Max: .000041 at 31.926 Hz 4096 75% overlap

.'2.5

0 10 20 30 40 50 60 70 80 90 100Frequency, Hz

[SmoothedPSD]: RMS: 0.067 Max .000037 at 31.926 Hz 4096 75% overlap a=l.00

40 50 60Frequency, Hz

Figure 3. Comparison of a standard and a smoothedPSD of a difference of two signals (differentialpressure).

The magnitude and phase of an accelerometer'sfrequency response for an accelerometer with respectto an excitation of a piezoelectric actuator, along withthe corresponding coherence for data acquired duringthe Piezoelectric Aeroelastic Response TailoringInvestigation (PARTI) test (reference 8) is shown infigure 4.

Frequency response results such as these are used



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to experimentally identify the open-loop plant and arethen employed in the design of active control laws.The coherence is a measure of the correlation betweenthe input and output response time histories, and thequality of data acquired. For instance, presence ofnoise in the system, even with highly correlatedsignals, reduces the coherence in the measured data.

Controller performance evaluation (CPE) hasbeen used in many tests in the Transonic DynamicTunnel. CPE results acquired during the first test of


Accelerometer Response/Actuator Command

20 30Freq.Hz

0.70.6

0)

I 0.5

jj 0.4

<3 0.3

0.2

0.1

020 30

Freq.Hz

Figure 4. Frequency response of an accelerometer dueto a piezoelectric actuator for the PARTI model.

the BACT model are shown in Figure 5. The uppertwo plots show the minimum singular value of theplant input and output return difference matrices.These are used to indicate the sensitivity of the plantto multiplicative perturbations at the plant input andoutput, respectively. The lower left plot indicates thesensitivity of the plant to additive perturbations of theplant. The minimum singular value is related toguaranteed gain and phase margins for multi-loopsystems (references 5 and 6.) The three horizontallines plotted on each singular value plot at values of0.1, 0.2 and 0.3 are used to rapidly identify areas ofdecreased stability. A minimum singular value of

0.3 corresponds to approximately -2.3 and +2.8 dbgain margins for zero phase margins, and for a 10degree phase margin, the gain margins are -1.5 and+2.2 db, as derived in reference 14.

A plot of the determinant of the return differencematrix of the system, which corresponds to a Nyquistplot for a single-input single-output system, isshown in the lower right of the figure. Sinceencirclements of the critical point are important fordetermining system stability, this plot isautomatically enlarged for the user, as shown inFigure 6. The user is prompted to supply a scalingvalue for the axes in order to expand the unit circle tobetter identify encirclements. A specialized functionuses the resulting determinant to calculate the gainfactors and the phase margins. The gain factors,shown in the plot title, are factors by which the gaincan be multiplied to reach closed-loop instability. Thepossibility of two gain factors, greater and less than1, which correspond to positive and negative gainmargins, and two phase margins are possible. In thiscase in which there is no encirclement of the criticalpoint, only the gain factor corresponding to thepositive gain margin exists and is documented on theplot.

The coherence and cross-correlation shown infigure 7 along with the cross spectra, not shown,were used to assess the aerodynamics for the ActiveControl Reduction of Buffet-Affected Tails(ACROBAT) model (reference 11-13).

CONCLUDING REMARKS

TDT_analyzer, a versatile software packagedeveloped at NASA Langley's Transonic DynamicsTunnel, has been used extensively to provide on-line,near real-time and post-test examination of measureddata. The software package provides a compendiumof analysis functions commonly required during wind-tunnel tests in a user-friendly, interactive and batchprocessing environment. It is a stand-alone package,but has a companion pre-processor, TDT_interface,which converts data from a multitude of sources to aMaflab®-readable input file used by TDT_analyzer.This preprocessor provides the mechanism forintegrating the analysis package into any dataacquisition system. The package has been integratedinto the primary TDT-DAS as well as three othersmaller data acquisition systems at the TDT. It hasbeen ported to other platforms which supportMatlab®, including personal computers.



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max = 5.11, min = 0.38 at 6.4 Hz max = 5.11, min = 0.38 at 6.4 Hz

O1 3

10 15 20 0

max = 4.24, min = 0.42 at 6.7 Hz det(I+HG)

-55 10 15 20

Freq (Hz)-5 0

Real

Figure 5. Output associated with CPE indicating stability and robustness.

Gain Factor = 2.333 , Phase margins = -66.6, 26.27 Header Information / Plot Title

Cob: deIta_Pl/delta_P2 Max: 0.545 at 22.34 Hz 4096 75% overlap

0 10 20 30

Cross Correlation

- 5 - 4 - 3 - 2 - 1 0 1 2 3 4 5Real

Figure 6. Enlarged determinant plot from figure 5.

40 50 60 70 80 90 100Freq, Hz

delta_Pl/delta_P2 Max: 0.275 at 0.0101 seconds

oTime Gag-lead), seconds

Figure 7. Results for assessing buffet aerodynamics.



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REFERENCES

1. Wieseman, C. D; Hoadley, S. T.; McGraw, S.M.: On-line analysis capabilities developed tosupport the AFW wind-tunnel tests. AIAADynamics Specialists Conference, Dallas, TX,Apr. 16, 17, 1992, Technical Papers (A92-3565114-08). Washington, DC, American Institute ofAeronautics and Astronautics, 1992, p. 39-47.(Also NASA TM 107651)

2. Perry, B., IE, Cole. S., and Miller, G. "ASummary of an Active Flexible Wing Program,"Special Section: Active Flexible Wing, Journalof Aircraft Vol. 32, Num. 1, Jan.-Feb. 1995, pp.10- 15.

3. Hardin, J. C. Introduction to Time SeriesAnalysis, NASA Reference Publication 1145,Seccond printing 1990.

4. Gilyard, G. B. and Edwards, J. W.: Real-TimeFlutter Analysis of an Active Flutter-Suppression System on a Remotely PilotedResearch Aircraft. In AGARD ConferenceProceedings No. 339, pp. 20-1 - 20-15.Presented at the AGARD Flight Mechanics PanelSymposium on Ground/Flight Test Techniquesand Correlation held in Cesme, Turkey, October11-14, 1982.

5. Pototzky, A.; Wieseman, C. D.; Hoadley, S.T.; Mukhopadhyay, V.. Development andtesting of controller performance evaluationmethodology for multi-input/multi-output digitalcontrol systems; Fourth NASA Workshop onComputational Control of Flexible AerospaceSystems, Part 2, Mar. 1, 1991, pp. 615-653.

6. Pototzky, A., Wieseman, C. D.; Hoadley, S. T;Mukhopadhyay, V.. On-line performanceevaluation of multiloop digital control systems.(AIAA Guidance, Navigation and ControlConference, Portland, OR, Aug. 20-22, 1990,Technical Papers. Pt. 2, p. 1673-1682) Journalof Guidance, Control, and Dynamics, vol. 15,no. 4, July-Aug. 1992, pp. 878-884. (AlsoAIAA Paper 90-3501, NASA TM 102704)

7. Hoadley, S.T. and McGraw, S.M., The MultipleFunction Multi-Input/Multi-Output DigitalController System for the AFW Wind-TunnelModel, AIAA Paper 92-2083, April 1992.

8. McGowan, A. R., Heeg, J., and Lake, R.,"Results of Wind-Tunnel Testing From thePiezoelectric Aeroelastic Response TailoringInvestigation", Proceedings of the 37thAIAA/ASME/ ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference,Paper 96-1511, April 1996.

9. Durham, M. H.; Keller, D. F.; Bennett, R. M.;Wieseman, C. D.: A status report on a modelfor Benchmark Active Controls Testing. AIAAPAPER 91-1011. Presented at theAIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics, and Materials Conference,32nd, Baltimore, MD, Apr. 8-10, 1991.

10. Scott, R. C. ; Hoadley, S. T.; Wieseman, C. D.and . Durham, M. H. The Benchmark ActiveControls Technology Model Aerodynamic Data ,35th AIAA Aerospace Sciences Meeting andExhibit, Reno, NV, AIAA 97-0829, January 6-9,1997.

11. Moses, R. W. Vertical Tail BuffetingAlleviation Using Piezoelectric Actuators - SomeResults of the Actively Controlled Response OfBuffet-Affected Tails (ACROBAT) Program,SPIE's 4th Annual Symposium on SmartStructures and Materials, Industrial andCommercial Applications of Smart StructuresTechnologies, Conference 3044, San Diego,California, March 4-6,1997.

12. Moses, R. W. and Shah, G. H., SpatialCharacteristics of F/A-18 Vertical Tail BuffetPressures Measured in Flight, presented at the38th AIAA/ASME/ASCE/AHS/ASC Structures,Structural Dynamics and Materials Conference,Paper 98-1956, April 20-23, 1998.

13. Moses, R. W. and Pendleton. E., A Comparisonof Pressure Measurements Between a Full-Scaleand a 1/6-Scale F/A-18 Twin Tail During Buffet,NASA TM-110282, August 1996, pp. 13, Alsopresented and included in the proceedings of the83rd Structures and Materials Panel Meeting ofAGARD held September 2-6, 1996, in Florence,Italy.

14. Mukhopadhyay, V., Pototzky, A.S., and Fox,M.E., "A Scheme for Theoretical andExperimental Evaluation of MultivariableSystem Stability Robustness, Proceedings of the1990 American Control Conference, pp 3046-4047, also Paper FP 14-5, May 1990.


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