automatic pilot for aircraft (1946)

8/4/2019 Automatic Pilot for Aircraft (1946)

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LibraryU. S. Naval PostgraduateA&aapolis, Mk


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(Inter-Departmental5ETTS INSTITUTE OF 'Cambridge 39, Mass,

MASSACHUSETTS INSTITUTE OF TECHNOLOGY

OF Co So Draper

Memorandum to? Captain W, H BurackerFrom: Dr c C S DraperDates September k y 19A-6Subjects Thesis Work of Lt,Comdr F.M, Ralst:

Coiiidr Ho o EauckCondr Go Ac, WhitesideThe Officers listed above have recently sub-mitted a Masters Thesis done und^r my supervision entitled;

"Control Characteristics of An Automatic Pilo~, ForAircrafto"Good techcique and a sound approach produceda good experimental determination of the operating character-istics to be expected froir. the automatic pilot studied inthe thesis worko The officers concerned should receiveparticular credit for intelligent application of the prin-ciples taught during their year of graduate v/ork Theirworkmanlike attack in designing , building , and using a com-plicated laboratory test installation in the short t .meavailable represents an excellent job

/s/ > So DraperChairman of Graduate CommitteeCSD^pm Department of AeroEii tioalEngineer: ng


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(In'ter-DepartmentalMASSACHUSETTS INSTITUTE OF TECHNOLOGY

Cambridge 39, MassOF C So Draper

Memorandum to? Captain W, H BurackerFrom: Dr C S DraperDates September 4>, 1946Subjects Thesis Work of Lt,Comdr c F.M= Ralston

Coadr H o EauckCotadr G, A WhitesideThe Officers listod above have recently sub=mitted a Master* s Thesis done undsr my supervision entitled;

"Control Characteristics of An Automatic Pilot ForAircraft "Good technique and a sound approach produceda good experimental determination of the operating character*istics to be expected fror. the automatic pilot studied inthe thesis worko The officers concerned should receiveparticular credit for intelligent application of the prin-ciples taught during their year of graduate worko T ^ irworkmanlike attack in designing 9 building t and using a com-plicated laboratory test installation in the short t meavailable represents an excellent job

/s/ C So Draperchairman of Graduate CommitteeCSDcpm )epartmert of AeronauticalEngineering


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CONTROL CHARACTERISTICS OP AN AUTOMATICPILOT FOR AIRCRAFT

by

Lt. Coxndr* Frank M. Ralston, U S* NavyB.S., U S* Naval Academy, Annapolis, Maryland1939Comdr. Hamilton 0* Hauck, U. S. Navy3S, U. S. Naval Academy, Annapolis, Maryland1938Comdr* George A* Whiteside, U. S. NavyB.S., U* S. Naval Academy, Annapolis, Maryland1938

Submitted in Partial Fulfillment of the Requirementsfor the Degree of

Master of Science (Aeronautical Engineering)from the

Massachusetts Institute of Technology1946

Signatures of Authors

Department of Aeronautical Engineering, August 24, 1946.Signature of Professor in Chargeof ResearchSignature of Chairman of DepartmentCommittee on Graduate Students


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August 24, 1946.

Professor Joseph S. Newell,secretary of the Faculty,Massachusetts Institute of TechnologyCambridge, Massachusetts.Dear Sir:

We hereby submit the enclosed thesis entitled,"Control Characteristics of an Automatic Pilot for Air-craft", in partial fulfillment of the requirements forthe degree of Master of Science (Aeronautical Engineering)from the Massachusetts Institute of Technology.

Respectfully yours,

Frank M. Ralston

Hamilton 0. Hauck

George A. Whiteside


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ACKNOWLEDGMENT

The authors wish to take this opportunity to ex-press their appreciation for the valuable suggestions andassistance rendered by Professor R. C Seamans, JT and Mr.Howard Carson.

To Mr. Prank Wllklns we feel Indebted for his as-sistance In setting up and operating the recording equipment.

Grateful acknowledgment Is given to the AeroDivision of the Minneapolis-Honeywell Company for providingsupplementary data about the automatic pilot.


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TABLE OF CONTENTS

PagTitle PageLetter of TransmittalAcknowle dgme nt sList of IllustrationsList of TablesDefinition of SymbolsSummaryIntroduction 1-3Equipment and Procedure 4-8Results and Discussion 9-16Conclusions 17 - 19Recommendations 20 - 21Illustrations and Figures 22 - 45Tables 46 - 55Sample Calculations 56 - 57Bibliography 58


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ILLUSTRATIONS

Figure 1 - Photograph of Equipment,Figure 2 - Photograph of Equipment.Figure 3 - Viscous Damping Coefficient vs. True Airspeed.Figure 4 - Spring Stiffness Coefficient vs. Indioated

Airspeed.Figure 5 - Elevator Torsional Elasticity vs Indicated

Airspeed.Figure 6 - Diagram of Discriminator Circuit.Figure 7 - Torque Calibration for Recording Oscillograph.Figure 8 - The clA Automatic Pilot as a Servomeonanism.Figure 9 - D.C. Circuit Diagram of ClA Automatic Pilot.Figure 10- Amplitude Response of Servomotor and Elevator

at 200 MPH (Ind).Figure 11- Phase Response of Servomotor and Elevator at

200 MPH (Ind).Figure 12- Amplitude Response of Servomotor and Elevator


250 MPH (Ind).Figure 14- Amplitude Response of Servomotor and Elevator


350 MPH (Ind).Figure 16- Polar Plot of Servomotor and Elevator Response

at 200 MPH (Ind).


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Figure 17 - Polar Plot of Servomotor and Elevator Responseat 250 MPH (Ind).

Figure 18 - Polar Plot of Servomotor and Elevator Responseat 350 MPH (Ind).

Figure 19 - Transfer Loci of ClA Automatic Pilot at 200,250 and 350 MPH (Ind).

Figure 20 - Elevator Torque Characteristic Curves at 200MPH (Ind).



Figure 23 - Effect of Cable Stretching (Transfer Functionof Cable).

Figure 24 - Sample Oscillographic Record.


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TABLES

Table ITable II

Table IIITable IVTable V

Table VITable VIITable VIII

Table IXTable X

Data for 200 MPH Airspeed.Original Data Referred to Input Wiper

(200 MPH).Results for 200 MPH Airspeed.Data for 250 MPH Airspeed.Original Data Referred to Input Wiper

(250 MPH).Results for 250 MPH Airspeed.Data for 350 MPH Airspeed.Original Data Referred to Input Wiper

(350 MPH).Results for 350 MPH Airspeed.Calibration Data for Recording Oscillograph.


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SYMBOLS

A - Aeronautical Engineering.Oq~ Standard acceleration of gravity * 32.174 ft/see

or 586 in/seo .P- Standard density of dry air at sea level .002378

lb ft"4 sec2 .P- Density of air at altitude.

S ~ Area.Sw- Area of wing.S^-Area of tail.V - True airspeed.#"- Dynamic pressure * 1/2^ v .CG~Angle of attack.Qr Hinge moment coefficient due to elevator angle

setting.H- Hinge moment,^tf- Torsional elasticity of elevator.^..Elastic coefficient of spring (pounds per inch).X- Moment of inertia.w- Natural frequency of oscillation of second order system.C- Viscous damping coefficient.c~ Chord length - Appropriate subscripts added to specify

surfaceS- Distance travelled by airplane, measured in 1/2 wing

chords


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SYMBOLS(Cont'd)

B Servomechanisms./- Angular motion of flight gyro wiper - measured in

degrees.6m - Angular motion of servomotor cable drum - measured

in degrees*Qc - Angular motion of elevator m measured in degrees*Qm . - Angular motion of servomotor cable drum referred tothe flight gyro wiper. Under conditions of perfect

motor response, &m = 28j_. Hence e^ = dm .B . -Angular motion of elevator referred to the flight gyro

wiper. Under conditions of perfect motor responseand no cable stre toning. 8 s 468i . Hence e0l **o 2.135 e .

^-Angular error of cable drum from flight gyro wiper,Em e i - 6^ where quantities are vectors.

- Transfer function, Output of unit (vector)Input to unit (vector;"Y - Damping ratio m system damping coefficient system critical damping coefficient


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SUMMARY

Hie purpose of this Investigation was to determinethe control characteristics of an automatic pilot for aircraft.The automatic pilot used was the Minneapolis -Honeywell typeC-lA autopilot* The load applied to the autopilot consistedof inertia, elastic restraint, and coulomb friction, all em-bodied in a test apparatus. For the purpose of this investi-gation, the test apparatus was made to simulate the elevatorsof a Douglas A-26 attack bomber. Three different values ofindicated airspeed were simulated, 200, 250, and 550 milesper hour. The conditions assumed were that the airplane wasin normal flight and was not allowed to respond to the elevatoraction.

As a result of this Investigation tte characteristicsof this autopilot were determined. Increasing the indicatedairspeed increases the torque output of the servomotor and de-creases the elevator shaft rotation for a given Input signal.The resonant frequency of the system Increases slightly withan increase of Indicated airspeed. The effective damping ofthe system decreases with an increase of airspeed. The effectof the control cable is to decrease the magnitude of the elevatorshaft rotation, this effect increasing as indicated airspeedincreases. The automatic pilot is stable throughout the rangeof airspeeds investigated and is a satisfactory servomechanism.

This investigation was conducted at the MassachusettsInstitute of Technology Aeronautical Engineering Laboratoryfrom June to August, 1946,


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A

UTTRODUCTIOHIII I I I - H I 'Although automatic pilots for aircraft have been

In use far many years, comparatively little data is avail-able coijcerning their actual performance as servoxaeehanismsunder the aerodynamic load conditions encountered in .Cli^ht #The purpose of this investigation was to determine the per-formance of a typical autozaatic pilot, and its components,under artificial loads calculated to duplicate those imposedupon the mechanism under various flight conditions* It Isemphasized that this investigation includes only the automatic-pilot, the control oables, and the control surface - consideredas a servomechaniSBW The response of the airplr.no to the re-sultant control surface moveiaent has not been Included and theassumption has been mads that the airplane continues essentiallyunchanged alone Its flight path at the proscribed airspeed.

The automatic pilot employed in this study was theMiniieapolis-Honeywsll, Type ClA# This pilot was selected be-cause it appears typical of the designs to be encountered inthe future and because several concurrent investigations, usingthis autopilot In actual aircraft, are being conducted,

The test assembly for the investigation was con-structed to duplicate the elevator control system of a mediumbomber type aircraft. Since the necessary structural and aero-dynamic data for the A-26 Attaok Bomber were available, ths


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The transfer locus system of analysis is employedherein to evaluate the performance of the system as a whole,and to evaluate the contributions of the system components*In submitting thi3 report, the authors pre-suppose a familiar-ity on the part of the reader with transfer loci studies, theHyquiot diagram and stability criteria, and transfer functionsemploying the LaPlaoe transform* To augsent the transfer lociplotted herein, plots of the amplitude and phase response ofvarious system components have been made on Cartesian coordinates.

This investigation was conducted in the InstrumentationLaboratory of the Massachusetts Institute of Technology by theauthors of this report.


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BqUIPMSffT AHP PROCgPUHE

Photographs of the equipment employed In the testsare provided In Figs. 1 and 2* The equipment may b groupedIn three major components* Referring to the photographs,group A includes the units of the recording oscillographwhich provided timed records of the various performance data*This unit possessed twelve separate data channels, of whichsix channels were used* Group B includes the necessary unitsof the Minneapolis-Honeywell CIA automatic pilot for conduct-ing the tests. Only the elevator channel of the automaticpilot was employed. Group C is the test assembly which simu-lates the levator control arrangement of an A-26 airplane,agd further provides for imposing artificial aerodynamie loadsen the system*

In group E, (1) is the sine drive mechanism whichmoves fcba wiper (2) of the elevator flight gyro potentiometer(removed from the flight gyro unit for these testa) sinusoid-ally through an amplitude of 7 l/S degrees each side of thecenter of the potentiometer - or a total swing of 15 degrees*5Jie position of this input wiper was recorded by the synchro(3) mounted on the wiper shaft* Its output voltage was appliedto the recording oscillograph* The synchro was adjusted toprovide zero voltage on the reoord when the input wiper was inmid-poaibion. The frequency of the input motion was adjusted


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by Variae control of the sins drive eleotrio motor, provid-ing a frequency range from .05 to 4 oyoles per second.

02he servo motor (15) which drives the control cabledrum is provided with a potentiometer, the wiper of which isdirectly connected to the cable drum shaft. The input poten-tiometer and the motor potentiometer are connected electric-ally so that with the motor drum position matched to the inputwiper oonition, no error voltage is developed between thewiper*. When the cable drum position is not matched with theinput, an error voltage is developed between the wipers* Shisvoltage is applied to the amplifier (4) which amplifies theeraser voltage, discriminates between errors on either side ofthe matched condition, and energizes the correct relay (5) todrive the servo motor in a direction to erase the error. Asketch of the disoriadnator circuit is shown in Fig, 6. Sheelectrical system is so arranged that one degree of motion atthe input wiper results in two degrees of motion of the cabledrum. Under perfectly matched conditions, therefore, thecable drum moves through a total swing of 30 degrees, or asine amplitude of 15 degrees*

' She construction of this automatic pilot is suchthat the following action of the servo motor is not continuous.ie action is better described as a "peoking" action wherebythe, motor is driven in pulses until the error is erased. Duringthose pulses, the motor brake is off and voltage is applied tothe motor terminals. Between pulses, no voltage is applied to


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4

the motor terminal*, and the solenoid-operated brake pre-vents rotation of the cable drum. If the error exceed* aet amount, pecking action ceases and the proper relay isheld down until the error ha decreased to the pecking ac-tion range. !The frequanoy of pecking ie determined by atime-delay network incorporated in the discriminator circuit.

A synchro, like that installed on the input poten-tiometer, was attached to the cable drum shaft to provide ameans of recording the servo motor response.

In group c, the units were made to duplicate asclosely as possible the more important dimensions of the A-26elevator assembly. The cable (6) distance from servo motorto elevator hinge (8) and the dimensions of the elevator horn(7) are the same as those in the A-26. Inertia wei^its (9)were added to increase the inertia of the system to that ofthe A-26 elevator about its hinge axis, (see "Sample Calcula-tions"), coulomb friction of the A-26 elevator control systemwas duplicated by adjustment of the prony brake (10) bearingagainst the friction disc (11). a viscous damper fitting (12)was provided at the end of the elevator shaft. During thetests, no viscous damper was installed because of shortage oftime, and because the magnitudes, as developed in "Sample Cal-culations" and shown in Pig. 3, were deeded negligible. Itwas found that coulomb friction alone was sufficiently large todamp out oscillations rapidly. However, the data of pig. 3 has


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been included bo that further testa with this equipment mayprovide the viscous damping feature.

2he elevator torsional elasticity was simulated bysprings (15) installed at the ends of torque arms (14) mountedon the elevator shaft* Use springs were fixed to the testtable at their lover ends* The required elastic coefficientsof the springs were determined as shown in "Sample Calcula-tions". A plot of these coefficients is given in Pig. 4, whichwas derived from the torsional elasticity computations in"Sample Calculations" - a plot of which is shown in Fig. 5.

A synchro (16) was fitted to the elevator shaft toprovide a record of the elevator position versus time. Straingauges (17) were installed on the elevator horn to provide arecord of the torque on the elevator versus time.

In order to obtain sufficient data to plot the fre-quency response of the system and, subsequently, to analyze theperformance of system components, the following data items,arranged in their order of appearance (vertically downward) onthe record (Fig* 8), were obtained!

(a) Angular position of flight gyro potentiometer.(b) Angular position of serve motor cable drum.(c) Motor relay closure, or times of application

of voltage to the motor - and direction ofapplied voltage.

(d) Angular position of elevator.


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(e) Error voltag, measured at the grid of the am-plifier (7P7) tube.

(f ) Torque, Measured at the elevator shaft - calibratedin lb. ft. aa ahown in Fig. 7.Teats were made with aerodynamic loads corresponding

to 200, 250 and 360 miles per hour, indicated. During each ofthese tests, the input sinusoidal frequenoy was varied fromapproxi me.tely .05 to 4 cycles per seoond and simultaneous valuesf the data listed above were recorded by the oscillograph.Upon completion of the tests, the oscillograph records weredeveloped, printed, and data was taken from them for entry onthe enclosed data sheets.


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9.

RESULTS AND DISCUSSIONI I I I I I II II

I

The results obtained in this investigation are verysatisfactory. The virtual absence of "wild" readings isdirectly attributable to the excellent performance of the re-cording oscillograph. For the conduct of experiments ortests where many quantities must be simultaneously recorded,the advantages of this instrument In accuracy, and in savingtime and labor, are great.

Results are graphically presented in Figs. 10 through23 and are tabulated in Tables I through IX* Figs. 10 and 11are plots of the amplitude and phase response, respectively, ofthe servomotor (measured at the cable drum) and the elevator,with an airspeed of 200 mph (ind). It is seen that at frequen-cies below 0.5 ops the amplitude response of the servomotor ispractically constant at a value of 0.88. In this same frequencyrange, the elevator amplitude response Is similarly constantbut with a value of approximately 0.6. It will be noted fromFig. 11 that the phase lags of the servomotor and the elevatorare Identical and that this lag increases almost linearly withfrequency In the low frequencies. As the frequency is in-creased, the amplitude response rises gradually to a peak valueof 0.965 for the servomotor and 0.708 for ths elevator, at aresonant frequency of approximately 1.04 cps. The phase anglecontinues its gradual rise until the resonant frequency is ap-proached, when it rises sharply, swings rapidly throu$i the


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90 degree valua, and thereafter increases more rapidly withfrequency than it did in the low frequency range. Pastresonance, the amplitude responses of both servomotor andelevator drop off sharply and then asymptotically approachzero - with values at the highest recorded frequency (2.9 cps)of .200 and .175 respectively.

Figs. 12 and 13 are the amplitude and phase responsecurves, for an airspeed of 250 mph (ind). Pigs. 14 and 15 aresimilar curves for an airspeed of 350 mph (ind). These curveshave the same general configuration as the curves of Figs. 10and 11 described above, although the constant amplitude re-sponse at low frequencies is no longer present. Th* 250 mphcurves show that the amplitude responses are smaller, through-out the total frequency range, than that for 200 mph, with peakamplitude response for the motor at .950 and for the elevatorat .622.

A further decrease in the general amplitude responseis apparent when the airspeed is increased to 350 mph. Peakamplitude responses become .893 for the motor and .433 for theelevator. The phase lag decreases slightly with increased air-speed, while the resonant frequencies increase to 1.25 cps at250 mph and 1.28 cps at 350 mph.

Figs. 16, 17, and 18 combine the information pre-sented in Figs. 10 through 15 and present it in polar form.Fig. 19 shows the transfer loci of the automatic pilot at 200,250 and 350 mph. These are plots of the transfer functions of


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the autopilot, obtained by vectorially dividing the servo-motor output by the error between the input wiper and thecable drum.

Figs. 20, 21, and 22 show the magnitudes of torquedeveloped at the elevator hinge at the three airspeeds em-ployed, plotted against frequency. The phase lag of thetorques is presented in the same figures.

Fig* 23 is a plot, on Cartesian coordinates, of theeffect of cable stretching at each airspeed. The valuesplotted are the values of the transfer function of the cableat various frequencies.

Fig. 24 is a reproduction of a typical data recordobtained by the oscilloscope. The smallest timed line spacingis .01 seconds. Calibration data for the oscilloscope is givenin Table X.

A comparison of Figs. 10, 12, 14, 16, 17, and 18shows that as the load, i.e., the simulated airspeed, is in-creased, the output angle at the elevator shaft becomes smallerfor a given input signal. For a given load the output ampli-tude is not a constant but varies with the frequency of theinput. There is a greater difference in response between anytwo loads at low frequencies than at high frequencies. Thisis attributed to the fact that the load consisted of inertia,elastic restraint, and coulomb friction. Changes of load wereaccomplished by changes of elastic restraint, the inertia andcoulomb friction remaining unchanged. At low frequencies the


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governing factor of the load is the elastic restraint and athi$i frequencies the governing factor is the inertia. There-fore, larger changes in the response at low frequencies are tobe expected while only minor changes in the response are to beexpected at the hi$ier frequencies.

The motor output to signal input ratio is alwaysless than unity at low frequencies. When operating near theminimum error voltage level the peck duration is a functionof the amount of error. The amount of torque delivered by themotor is a linear function of the peck duration. Therefore,the torque output is a function of the amount of error. Forstiff loads with consequent high torques to be overcome, agreater minimum error is required at low frequencies.

The fact that the motor output to signal input ratiois always less than unity at very low frequencies can be ex-plained by the fact that the autopilot does not have a zeroposition error. This fact is illustrated in Fig. 19. For azero position error, the loci would approach the - Jw axisasymptotically. A minimum voltage error must exist before therelays can operate. This voltage level exists independentlyof load and can be considered dead space.

The elevator shaft output to signal input ratio curveis similar in shape to the motor output to signal input ratiocurve. The curves would be identical if the motor and elevatorshafts were rigidly connected. The difference between the two


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curves is then caused by the cable connecting the two shafts.Fig. 23 shows a plot of the transfer locus of the cable. Ifthe motor output to signal input ratio is multiplied by theamplitude ratio from Fig. 23, the elevator shaft output tosignal input ratio is obtained.

The amplitude ratio curves, Figs. 10, 12, and 14,show definite resonance effects and a falling off of responseat higher frequencies. Ike resonant frequency increasesslightly with increase of load. Ihe average resonant frequencyobtained was about 1.2 cycles per second. The resonant effectbecomes more marked as the load increases. This indicates thatthe effective damping is less for larger loads.

Figs. 11, 13, and 15 show the phase response of themotor shaft and elevator shaft outputs. Since there is a zerophase shift occurring in the cable, the motor and elevator shaftoutput phase angles are the same. These curves show that theresonant frequency increases for an increased load and that theaverage resonant frequency obtained for the loads used wasabout 1.2 cycles per second. Other than changing the resonantpoint slightly, the load appears to have little effect upon thephase response. Increasing the load decreases the phase angleslightly.

Ihe torque applied to the elevator shaft is shown inFig. 20, 21, and 22. A comparison of these three curves showsthat as the load increases the torque applied to the load in-


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creases. All curves have a definite resonance effect withthe resonant frequency increasing slightly with load. Theaverage resonant frequency was about 1.2 cycles per second.The phase angle of the torque at the load is essentially un-changed by changes of load. In all cases the phase of thetorque leads the phase of the elevator shaft angle.

Fig. 23 shows a plot of the transfer function of thecable for the three different loads used. The cable used forthis investigation was a 3/32 inch flexible wire cable withan initial tension of about sixty pounds. This correspondedto an ambient temperature of about seventy degrees Fahrenheit.Previous to the investigation for this report, a series of runswere made with a 1/8 inch extra flexible wire cable. From theresults of these two series of runs it appears that decreasingthe size of the cable, increasing the elasticity of the coupling,also decreases the torque and the output angle at the elevatorshaft for a given input. The curves of Fig. 23 were obtainedby dividing the output of the cable, elevator shaft rotation,by the input to the cable, motor shaft rotation. The cableeffect seems to be a scalar effect since the phase angle re-mained zero throughout. However, the cable exerted an effectwhich does not appear as a phase angle. This effect was incausing the elevator output angle to appear distorted from asinusoidal variation. The oscillation began at the same timethat the motor shaft oscillation began, but the maximum ampli-tude occurred at a later time than the motor shaft maximum am-plitude.


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The viscous damping coefficients that are applicableto the various airspeeds used are shown in Fig. 3. No viscousdamping was intentionally Introduced in this test apparatussince the effect was considered almost negligible and becauseof a shortage of time available for the investigation. Coulombfriction was Introduced into the apparatus, however, and wasset to give a force of ten pounds in the control cable. Thisfriction caused an effective damping ratio, 7 , to appear.

The natural frequency of the system is 1.6 cyclesper second as found from Fig. 19. Figs. 10, 12, and 14 showthat the resonant frequencies for the various loads are 1.04,1.25, and 1.28 cycles per second respectively for the 200, 250,and 350 miles per hour conditions. With this Information andPlate 12, Chapter VII, Instrument Analysis (Draper and McKay),the damping ratios can be computed. Using this technique, thedamping ratios are 0.54, 0.36, and 0.34 for airspeeds of 200,250, and 350 miles per hour respectively. This was expectedsince the same amount of coulomb friction would have less effecton large loads than on small loads. The natural frequency ascalculated by this method is again 1.6 cycles per second.

Fig. 19 shows that the system Is stable throughoutthe entire range of airspeeds investigated. Instability wouldbe denoted by enclosure of the - 1 + j point within the trans-fer locus. Referring to this figure, the system shows suffi-cient stability. The sensitivity of the system could be increasedby a factor of 3.86 j 1 before instability would occur for the


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range of airspeeds investigated. This increased sensitivitywould result in an increasing ratio of elevator shaft rota-tion to signal Input at resonance.


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17.

CONCLUSIONS

An analysis of the results of this investigationsubstantiates the below-stated conclusions of the generalcontrol characteristics of the Minneapolis-Honeywell type C-lAautomatic pilot

(1) Hie "autopilot" is a satisfactory servomechanismwith ample stability. The resonant frequenciesare sufficiently high that no resonance effectwill be encountered during normal flight opera-tions. The use of a series wound D.C. motorcontrolled by relays with "pecking" action closelyapproximates a proportional servo and appears tobe an excellent design practice in view of theweight saving accomplished.

(2) At low frequencies the response of the servo motoris appreciably affected by the load stiffness. Anincrease in load stiffness, i.e., indicated air-speed, decreases the amplitude of the response*

(3) At very higji frequencies the response is governedprincipally by the load inertia and is only veryslightly affected by the load stiffness. Thefrequencies of normal application are well belowthis range.


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(4) The torque output of the motor is proportionalto the motor matching error for small angles ofmatching error after "pecking" action starts.When outside this small linear range the torqueoutput is governed by the torque -speed character-istics of the servomotor. Motor torque outputis increased by an Increase of load stiffnessor a decrease of input frequency.

(5) The servo has a "zero dead space" and is not azero positional error servomeonanism. The mag-nitude of this dead space is a function of thevoltage sensitivity of the potentiometer and ofthe current sensitivity of the relays. The deadspace could be reduced by increasing either ofthese sensitivities.

(6) The elastance of the coupling between the motorand the elevator shaft has a detrimental effecton the overall servomeohanism performance, '[hiseffect becomes greater as torques become greateror as the load to motor coupling becomes lessrigid.

(7) Coulomb friction caused the system to have an ef-fective damping ratio, ^ The effective dampingratio decreased as the indicated airspeed was in-creased. The resonant frequency also shifted.


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increasing as the indicated airspeed was in-creased.

(8) ihe system natural frequency was so governedby the amplifier and motor characteristics thatit remained constant at 1#6 cycles per secondIndependently of load stiffness.


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RECOMMENDATIONS

The below recommendations are divided into twomain groups. Group A is recommendations for improving thecontrol characteristics of the "autopilot", while Group Bis recommendations for further investigations.

A Recommendations for improving the control character-istics.

(1) Increase the sensitivity of the a.C. bridgepotentiome ters

(2) Redesign the relays to be more sensitive andto provide larger contact areas.

(3) Incorporate an integral effect for the relaysby making the "peck" duration a function ofthe magnitude of the error and the lengthof time that the error has existed.

(4) Minimize the elastic effect of the cable byusing gears, multiple cables, or puttingan A.C. bridge potentiometer on the outputshaft,

B - Recommendations for further investigations.(1) The input signal amplitude should be kept to

a maximum value of about 2.0 degrees.(2) Investigate the no load frequency response

of the servo motor.(3) Determine the torque-speed characteristics

of the servo motor.


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(4) Make a series of tests using a series ofvalues of elastic coupling between motorand load,

(5) Investigate the control characteristics withthe motor potentiometer installed on theelevator shaft.

(6) Incorporate a viscous damper on the elevatorshaft,

(7) Investigate the response at frequencies bracket-ing the natural frequency of the output load.


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ss.

' TABLE XCALIBRATION DATA

INPUT-MOTOR-

7.5 DEGREES 6N POTENTIOMETER *i INCHON RECORDl'5 DEGREES ON CABLE DRUM* 1 INCHON RECORD

OUTPUT- Q.b+"MOTIONAT15"RADIUS ON TORQUEAT\n - 103/2 INCHONRECORD.2. 4-5 DECREES OR ELEVATOR MOTION-- /. 0312 INCH ON RECORD2.31 rE$0FELEV#TOR MOT,* I INCH ON RECORD/'ZbLB.FT. =1 INCH ON RECORD

S YSTEM ALIGNEDERROR VOLTAGE -O

TORQUE-


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&SAMPLE CALCULATIONS

FRWATICN OF TOhLSlQNAL ELASTICITY - sL^iFrom /\-Zi> da ta.

Chs = - . 009 , CHeC =, -. 00s f CH = CHj 4 + Ch^cCMH = CH Se Q V^onph)311Then

*$< U 311 J if* ~ **** s ~.0Q1 (22.31,)(' - S5)V< * - _. OOC153 V* U>ft/t

2. DERIVATION OF -5FPJNG ST/F 5 COEEEJC EN T- K

*- TORQUE AFW - i.OloZ JMh lb/3^3. SIMULATION OF SYSTEM INERTIA -I

from A-2l -\ :Ele\ r Inert/a about h ,ut i 'me * x LZOQ fb in* * JZ+oo

Inertia, of Bievator Test Assembly (calculated) 3H3/b ih*Jvierti


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SI'

- SAHPLE CA L CULATIONS ~i. DERIVATION OF VISCOUS DAMPING COEFFIC'ENT-C

From A-2le data. :Hinge Position s . 75 ft aft of elevator leadmo edaeElevator Chord * I.SSft 73.il Chord 5ASftElevator Su rfac e Area. * 3* nmae Position s q. h>5 nordlM/ng Chord - il+ ft Half Wing Chord * +-Q7'ft = Tli :: OL>lS 4^ = 5JLoer rXKdc c 1 4* do.

From NACA. Technical Report No 709 f

= Z Ol iQ.Ctg s >.Z3g -Iff") o-'** o-*'*- -QW9 L/c y o df 8* a I.Z3Z + 5.11. x .0741 * 1-593 per d* e **)

f C^Oj AS found above applies to elevator angle changes "\per distance alone the fhghtpath,6, to employ the Ivalue found., it must be modified to appju to elevator

[ anqle changes with respect to time, Sis measured Jin ^ hiinq c hovds.'tin = rad - AQJ x ft x '/& chord!2& i sec '/z chord sec ft ^ l4^

'/fi chord ^.V airspeedH*D< (per tad/sec) - "o


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BIBLIOGRAPHY

1* Draper, C* S. and McKay, W. Instrument Analysis .2. Hall, A, C. The Analysis and Synthesis of Linear

Servo-mechanisms .3. A-26 Erection and Maintenance Manual .4. Overhaul Instructions for Automatic Pilot , Type Cl .5. Den Hartog, J. P. Mechanical Vibrations * McGraw-

Hill, 1934,6 Lin, S. N Mathematical Study of the Controlled

Motion of Airplanes . 3c. D Thesis, A.E., M.I.T.1939. ^v

7 Callendar, A, Hartree, D. R, and Porter, ATime Lag in a Control System. PhilosophicalTrans ao ti ons . Royal Society of London, Vol. 235,1936.

8 Theodorsen, T General Theory of AerodynamicInstability and the Mechanism of Flutter . N.A.C.A.Technical Report 496, 1940,

9. Jones, R. T and Cohen, De An Analysis of theStability of an Airplane with Free Controls .N.A.C.A. Technical Report 709, 1941.

10. Mason, C. E. and Philbrick, G. A. Automatic Controlin Presence of Process Lag . Paper A.S.M.E. Meeting,Philadelphia, December 1939.


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I

ThesisR18

ACCOPRESS BBP 2507HADE BY

Acrcu ProductLONG ISLAND CITY. N.

ThesisR18 Ralston

Control characteristicsof an automatic pilot foraircraft.

8097RalstonControl characteristics

of an automatic pilot foraircraft.


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thesR18Control characteristics of an automatic

3 2768 002 05269 8DUDLEY KNOX LIBRARY

automatic pilot for aircraft (1946)

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