Report of the Second Piloted Aircraft Flight Control System - Acgsc.org

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FOREWORD 

For four days beginning on 2 June 1952, representatives 

of the airoraft induatry and the military aervices met 

in Washington, Do C. to phsent and hear papers on the 

deal@ and utilization of piloted aircraft flight control 

sptmr , The eight papara reproduoed in thia report were 

presented at that meeting, 

The lfavy'a appreoiation la extended to the authora of 

theae paperr and to the varioua organization8 they 

repreaent, 

Comment8 or queationa concerning thia report ahould be 

forwarded to the Chief, Bureau of Aeronaut 108, 

Attention AE, Washington 25, Do C 

' ' Rear Admiral, U8rS 

Aarirtrurt Chief for 

Research and Development

CONTENTS 

1, Centering Charauteristics of Power Boosted 

Aircraft Control Systems' (Martin), . , . 

2. Helicopter Powered Control System 

Problem8 (Slkoraky) . . , . . 

. . , . 

3. Flight Research on Force Wheel Control (WAN) 

4, An Analyeis of Fully-Powered Aircraft. 

Control Syatem Inuluding Some 

Reference to Flutter Theory (19orthrop) , , 

5. Parametera for the Design of High-Speed 

Hydraulic Servomotors (NACA) .- , . , . 

3.. Improvement of Power Surfaoe Control 

Systems by Structural Deflection 

Compensation (Boeing). . . . , . , , 

7. A Survey of Suggested Mathematical Methods 

foy the Study of Human Pllotfs 

Response (Franklin) . . . . . . 

8, Synthesis of Flight Control Systems (Purdue).

CENTERING 'CHARACTERISTICS OF POWER BOOSTED 

AIRCRAFT CONTROL SYSTEMS' 

G. H. GOOKE 

I. E. KASS 

The Glenn L. Martin Go. 

Baltimore, Maryland

CENTERING CHARACTERISTICS OF POWER BOOSTED 

AIRCRAFT CONTROL SYSTEMS 

Within fi basically different aircraft, the Glenn L. Hartin Cagp~y h e 

designed and put into service 30 different pouered surface control system of 

Mch 1S wore power operated. The remnining fi power boosted surface control 

eystsaPs have presented an umwual combination of requiremanta for sensitivity, 

stability, and oenterlng, To meet such requiranants while m&Lntabing a 

simple, reliable mchanlsm, devoid of functionally oanplicated acoeesaries, 

the designer muat provide the optimtun system arrangement Md go to a high 

degree of reiinemant in designing the elements. 

i 

The design considerations in a powa: boost& Waft controls ayutcrn 

are as follows: 

1. To provide optimum sensitivity and tbe correct amount of ponm at 

all coaPbinatlo~ of speed and load. 

2. To prevent any fom of imtability such aa ohattor or hunt Yithkl 

. the meohanism in spite of the rensitivity and 1w break-atmy 

iriotion. 

3. To obkin a high degme of system raversibility ro that th. 

mechanism will accurately centor or return fo the t M podtion, 

ud so that a good forcre gradlent will k felt by the pilot at vexy 

low aerodynsrPic moments. 

Theee considerations are close2 y interrelated by m~ll~r 6y8tem perpplbtms 

which generally am determined by one consideration and haw a direct effeot 

on the other tuo. Consideration #1 determines eyetan rate gain, drcuit 

powor, and valve chprrcteriaticr, each of which has a dinat effmt upon 

rtability (consideration #2). Stability ale0 concams the irlction or damp- 

In# throughout the system, the point of application of the actuator, md the 

method of obtaining proportional feel, each of which vitally affwte tho 

csntsrlng charactaristics (considaration #3). 

There an definite perfonaance requirement6 hlch rmst be mat for 

sensitivity, stability, and cgltering to make any system ratirfmtary in 

r&oe. The ability of the designer to maat .those roquiruaatr depend. 

upon hlr undarrknding the effect of woh rymtsrp p.ramstw upon tb, roquirm 

ds. For amupla, to nuke a Judioious deoidon mgardlnq the magnituda 

md dlrtribution of fiiotion, the designer must &tormine the mulmum 

pumisrible frlctlon pattorn from his ertabllahod oentoring roq-mmnb, - 

nut det8rmlne by rnolysis or tat the mlnbmm Mction pattarn ro@s~d to 

arintaln stabill*, and then he our establirh the quality aontrol llritr of 

mation dtbin eaah el-t of the qmtau. 

* 

Centering charrctsrlrtlor M reford to harein ary be dofY.nod u the' 

rolaWonahip be- force, podtion, and rate of motion of a oontrol ~ Ifrr 

in the rlcinity of the tadmned neutral position, Tho oritioal paiotr 

ordinarily oonai&nd rre u followst

1, Break-away friction - defined as the force (as measured at control 

lever) required to begin surface motion from neutral. 

2. Centering force - defined .s the feel force v8. control position 

*en returning to neutral. 

3. Centering error - defined as the poeitioa~l error or distance froa 

neutral at e c h control etalla when being returned taward neutral 

by asr-c 'forces. 

4. Centering speed - defined as the velocity vs. position of control 

lever when being returned toward neutral (from various starting 

positiom) by aerodynamic forces. 

When a power boosted surface control systerm is used in an airplane tho 

aerodynnmic hinge 'momenta on the aurface are approxiatataly directly proportional 

to rmrface deflection and thus taper down to sero hinge moment in 

the trimmed neutral position. A fraction of theee hinge lpomonts must react 

in reverse through the control system to produae feel force at the pilot's 

control lever and to return or center the mechanism (when displaced), to 

the neutral position. Therefore, the degree of raversib1lit.y of the 

mschanim dotsrminss the centering characteristice, 

Figure 1 illustrates the boeic elements and the rigniflaant exterrul 

forces acting upon a power boosted contzol system, The basla arrangemat 

consists of a Wect manual drive h m pilot to ourface with a boost packqp 

inserted at one point in the mechanism. The boost peckage contdm tbs 

differential linkage, actuator, actuator disconnect, control valve, and 

hydraulic accessories. 

When wlysing centering oharu)taristice, tho dosigner is rpeaiiio.lly 

concerned with six relatad v~ables: 

1. Control foroe or pilot offort (F~) 

2, Control surface force (Fs) 

3. Control valve force 0"v) 

4. Actuator force 

5. Surface position 

6. Surface rate and direction of motion, 

The magnitude of aooolmtion forces throughout tho mch.niem hs boon 

negligibh in centaring studios to &to, whiah gnatly rimpUfior tha 

arnlysia by eUahatioa of aooeleration as a variable.

Since pilqt effort and s*face force may become independent variables 

in a centaring problem, it is desirable to expees each other variable as^ a 

function of these two. One soUd link in the boost package serves as a 

foIlow-up loop and also measurhs the error signal. The four forces acting 

upon this link are the first four variables mentioned above. Taking e\moration 

of momnts on this Unk about the piston rod bearing and solving for FV 

ilPdicates thnt valve forces am a direct function of control force and 

surface fome only as dotenninod by the goomtry of the control mechanlsn at 

neutral and as expressed by 

Taking summation of moments about the valve rod bearing which eUminata~ 

Ptf Md eoloiag for FA indicates tht actuator forces are olso a meet 

goometrical function of control force and .surface force only M eqwosmd by 

To aid vimallsation of this problem, a graphical llrsthod has boen 

oployed. (9.0 Fig. 2.) Tho independsnt variables are control fomw 

plotted as ordinates, and aurface forces plotted as absairsa on rscturgulrr 

ooo~ates, By substitution of various constant valuer for Pg in the 

second equation at the top of FQ. 2, valve faroos in pounds are plottoti a8 

a family of prrallrl lines with scales along the sides of the chart. By 

substitution of various co~tant values of FA in the first .quation, aokuhr 

forces in pounds are plotted as a fPrnily of parallel Unes xLth a rcalo .low 

the top of the chart. 

Since ourfaoe position ir appro;ldkately a linear function of surfaao 

load8 it 8bo asy be measured Jong the 8bscissa by using a scale factor (K) 

a h is detded from the oir speed in a given problem, 6 = C v2. 

If q v two variables are known8 a aystsla condition is establlrrhui oo 8 

pod& on this chart. A value for each other &able om then bo obtPined 

A.om the cbut. 

Surface rate and direction of motion nay be detenalned by applying 

the valve load8 obtained irOll Figure 2, to the characteristic8 of. tho valve. 

To proceed further with the analysis, reliable dab must be obtained 

concerning the operating friction and loads for each eloment of the ayatAP. 

Figure 3 b a plot of laboratory test data obtained from a mica bnlrnned 

piston boost cylindar. During frequent intelnittent duty, the stall ond 

atarbing friction piston fome in pounds, indicated by the lower solid Ila6 

on Fig. 3, can be exp~esaed arr 

FA ' 12 + .OU x internal pressure (psi)

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The centering characteristics except centering speed are determined, in this 

case, from the friction of the system elements. Break-away force indicated 

by poirrts (1C) and (16), is simply a combination of cylinder and control 

friction. The centering poaitional error at point (6) is the intersection 

of the 12 lb. cylinder friction line and the 2 lb. conk03 friction Une. 

Figure 6 illustrates a surface deflection cycle in a boost syatem 

. employing a balanced slide valve with no centering spring. The operating 

load of this valve consists of 2.5 lbs. constant friction as indicated by 

b w slope diagonal line of Fig. 6. Starting again frcm point (I), equilibrim 

in neutral, a slowly applied control force proceeds vertically to (2) 

b 

where valve friction first is overcome. The valve dl1 direct presume to 

the c;ylinder proceeding along the 2.5 lb. valve action line until control 

force ie no longer increased. The system will continue to move, proceeding 

horizontally to point (3) where the valve readjusts toward neutral Pnd the 

system atolls at point (3). With a slow decrease in control force, the 

valve dll immediately readjust and assist (as demanded) the return of 

surface to neutral proceeding along valve action line until the control 

force reduces to 2 lb. forward control friction (0 force at pilot). Tbs 

system will continue across the 2 lb. line to point (2) where a reverse 

valve load will bring the valve to neutral and stall the mechanism. The 

outer loop pobts (4), (5), (6) and (1) are again the path of control follees 

at the pilot and was constructed by adding or subtracting forward control 

friction fmm the previously determined points. 

Starting at point (3), if the control load is rapidly released, the 

valve load will exceed 2.5 lb., thus fully opening the valve and centering 

the mechanism at f'ull flow rate. The values of valve friction and forward 

controls friction selected result in zero positional error. However, the 

analysis waa simplified thus far by neglecting friction in the driven linbge. 

" 

* 

Figure 7 illustrates a surface deflection cycle similar to Figure 6 with 

the valve friction increased to 3.3 lb ., a control friction of 2 Ib., and 

uith a driven linkage friction of 10 lb. introduced. The break-awry force 18 

b.6 lb. With this system condition the centering stall point (4) oocurs at 

-10 lb. surface load meesured at the boost package. Diamond shaped points 

(9), (10) and (11) are surface loads as measured at the surface. These points 

are offset horizontally by + 10 lb., which is the driven linkage fzLction from 

the oorresponding system co-ndition points. Poht (11) indicates that the 

actual surface load is zem at the mechanism stall point and thus zero canterlug 

positional error is. achieved. Thia is accomplished, as illustrated in 

the upper left corner of Figure 7, by establishing optimum valve friction f'rom 

the intersection point of the controls friction and driven linkage friction. 

This tzLck of power operation to a perfectly centered position is 

damndent upon certain qualifications: 

1. No centering spring within control valve.

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speed cbpracteristica cannot be represented by a line. Rapid release of 

control force results in centering epee& located at the broken llne for a 

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for open-center valve dth sprlng. 

3 

CONCLUSIONS 

In the pant, centeriag chulpctaristios of mroy power boostad mfaae 

corrtrol aysta~~ have boa evaluated only by pilot eeti.Otion late in the 

fllght teat program of the alrplatm. Prlor to this point in the life of 

the project, MXU~ cmpromises have made to facilit8to Isuwirature and 

to met other performeace requirements, mrch as pomr and stability, dtb 

no analysis of their Pdtarw effect upon centeriq characterlstlcs. At 

this point in the life of the project, lo thing but rFrror detall changes cur 

be made to improve performance without excessive penalties of oost and dew. 

This papar proposw tht oentering characteristics be oo~ldarod 8 

baalo design problem to be ~olysed early in the engineering phaue ,of eaoh 

projscrt Md tO be permed by test Md by quallty control throughout the 

e m projeot Ufe. To illustrate hw this can be mcompliahed, cent* 

characteristics have been dofined in abple englnwrlng toms, 8 technique 

of amlysis has bean preasnted, a test pmc-e bas been ~utllned, Pnd 

appYcation of the analysis and test to four different systas vP118tlons hra 

been illustr.kd.

HELICOPTER POWERED CONTROL SYSTEM 

PROBLEMS 

WALTER GERBTENBERGER 

of 

lPikorrky Aircraft Divirion 

United Airc raft Corporation 

Bridgeport, Connecticut

HELICOPTER POWERED CONTROL SYSTEM 

PROBLEMS 

INTRODUCTION 

Since the audience comprises mostly "fixed wing1' engineers, it is 

felt that some introductory remarks about the operation of the helicopter, 

as related to power controls, might be in order. The type of control for 

maintaining a pitch and roll attitude has gradually boiled down to a single 

type. It is a nethod of tilting the rotor thrust vector by tilting the 

tip path plane of the rotor. It is a reasonable assumption, for a control 

discussion, that the rotor thrust remains essentially perpendicular to the 

tip path plane. Hence to go either forward or sidewards, it is merely 

necessary to tilt the thrust vector in the desired direction. Although a 

rotor may be mounted on a Gknbal joint and rotated by brute force in the 

desired direction, the more practical way of accanplishing this is to hinge 

tne blades at tneir roots so that they may feather and flap; then applying 

an oscillating change in blade angle at exactly one times rotative speed, 

&ich will excite a one times rotative speed flapping of the blade@. An 

observer on the ground would see a constant tilt of the tip path plans 

rather than the one times rotative speed flapping relative to the rotating 

drive shaft of the rotor. This type of control is desirable, because the 

low inertia of the blades about their feathering &s and tne smaller lnanenta 

of the blades about the feathering ~s result in smaller control forces 

necessary to be overcome by the pilot through his control stick. The 

feathering is accomplished by a simple swash plate on a transfer bearing 

directly under the rotor hub. Vertical control is obtained by up and down 

motion of the swash plate as contrasted to the tilt required for azknuth 

control, and an increase in the thrust vector results from an increase in 

the blade angle of all the blades. 

Before describing in more detail some of the problems of the azimuth 

control system, a few introductory remarks will be made concerning the 

directional control. The type of directional control of the helicopter 

depends largely on its basic configuration, that is, whether the helicopter 

is a single rotor helicopter or a multi-rotor helicopter. The single rotor 

helicopter is more analogous to the present day amlane except that the tail 

surface is instead a small rotor to counteract the aerodynamic torque acting 

on the main rotor and to provide for directional Control above or below the 

thrust required to oppose the torque. The tail rotor thrust is vericd by 

changing the blade angle of the tail rotor. In multi-rotor helicopters 

directional control can be varied by controlling the torque distribution 

between two counter rotating rotors or by tilting two rotors, so that the 

horirontal projections of the thrust vectors form a couple to oppose the sum 

of the torques applied to each individual rotor. The foregoing statements 

apply to mechanically driven rotors. If the rotor is jet driven at the tip 

of the blade there is no torque compensation required, but some meana of 

directional control must be available either in the form of ,a tail surface 

operating in the slip stream of the rotor, a variable, horizontal jet thrust 

at the tail, an azdliary rotor or a combination of these devices.

Returning to the discussion of the azimuth control where the tip 

path plane is tilted by means of the tilt of the swash plate, we can 

appreciate the problems resulting from the f ollotdng considerations. 

The friction resulting from the feathering bearings, which are required 

to support a centrifugal force of approhately 5,000 lbs. is appreciable. 

The need for a fine balance is necessary between the aerodynamic thrust 

on each blade and the centrifugal force component projected along the line . 

of thrust which prevents the rotor from llconinglt too much. Also, the 

variety of vibratory and gust disturbances transmitted into the control 

system from the aerodynamic surfaces which support the fulJ. weight of the 

helicopter and which move as a complicated piece of machinery miqfit be 

d 

disconcerting. On top of this a helicopter is inherently unstable in 

hovering having an unstable mode with a period of the order of magnitude 

of 10 seconds or more. mile the pilot can cope with this unstable oscillation 

because of the long period, it is desirable that he make frequent 

corrections without undue effort. The problem was not insurmountable on 

helicopters of the 5,000 lbs. pose weight category, but did limit the size 

of the helicopter unless suitable potjer controls were developed. Various 

aerodynamic and gyroscopic devices have been incorporated on hellcopters. . 

Three of particular interest are the Bell stabiliqer bar, the Hiller control 

rotor and the Kaman blade tab. The Bell stabilizing bar is a large rate 

gyro rotating at rotor speed (its undamped natural frequency ie hence one 

times rotor speed) with viscous damping, which can be adjusted to optMze 

the stabilization obtainable with a raze gyro alone. The Hiller control 

rotor is a similar device which uses the blades of the control rotor to 

obtain aerodynamic damping. Another feature of this control rotor is that 

the feathering produces flapping on the small control rotor which introduces 

feathering on the large rotor. In short, there is an extra stage of an 

aerodpadc .servo in the control loop. The Kainan rotor, the tab is located 

on the blade near the tip. A preloaded cable control regulates the angle of 

the tab which introduces a twisting moment on the blade, which in turn twists 

the very flexible blade to the desired angle without the use of featheflng 

bearings. *Each of these devices solve the problem in part, but have certain 

disadvantages as well. Power requirements for aerodynamic actuated torques 

should be considered, and tests run at Sikorsky Aircraft with tab controlled 

rotors wlth featherlne bearings indicated that the additional drag, due to 

this type of aerodynamic servo, resulted in power loss fran 5 to 1% of total 

power absorbed by the rotor. 

The use of hydraulic power appeared to be the most economical method of * 

improving the control of the helicopter. In 1949 a hydraulic pmr control 

for the three inputs of the swash plate was installed on the S-51 model 

helicopter (gross wei@t 5500 lbs.) The power control had infinite booet 

Q 

ratio, that is no feedback from the output to the input, operated at a 

pressure of 800 to 1,000 psi obtained from a constant displacement pump 

and unloading valve charging an accumulator. The awragle power requirement 

for this system was practically nil, being less than a quarter horeepaser. 

Although the original purpoeb of the control was to prove that the hellcopter 

could be flown with this type of control in order to pave the way for the

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loaded by-pass valve closes, and freedom for the valve of the emergency system 

to operate is introduced simultaneously, so that the emergency system, which 

was previously idling in the control aystem, assumes its burden before a q 

of the control forces are allowed to reach the pilot's stick. There is 

an automatic check by the pilot at every start, because the eng5n.a must. 

be started before the rotor, and during the intern between engine starting 

and rotor olutch engagement the emergency system is the only power control 

which can function at that time. It is true that engine oil is not a 

very good fluid for a hydraulic system, especially from the standpoint of 

high Piscousity at low temperature, but with lagging on the lines and with 

a large by-pass located dlrectly in the actuating cylinder, satlafactory 

cold mather operation can be obtained. The utilization of the casting 

engine oil system makes the emergency aystem a convenience which is feasible 

from an eoonomio standpoint and weight standpoint, since only an extra 

aotuator plus oonneotlng lines are required. There still romoins the 

undosirable oondition of having a oyllnder wlth l1O1l rings with their inherent 

friotlon wnneotod direotly in .tihe control system during mrPrrl operation, 

and offortr are baing ma& to roduoe this friction, although the fome in 

tho rtiok ir rpproxhakly 1 pound. 

Problrmr onoountorod on tho prevlouely mentioned helicopters we r 

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The desirability of the spring force gradient was partially off-set by 

the need for trimming this force after changing to a new flight condition. 

This configuration may not be important in fixed wing aircraft, but the 

helicopter is more apt to be operating over a variety of flight conditions 

and there will be more of a tendency for the pilot to forego the trim 

changes and cope with the bungee force in the trimned position. This does 

not mean he will not camplain about the difficulty of flylns in these 

conditions. In fact, complaints of a trimnable bungee on the rudder pedals 

of the S-5s type helicopter has resulted in the developnent of a paver 

control for the tail rudder even though it was not considered necessary 

after the initial flignt tests of tne helicopter. After flight testing 

the first rudder servo with no feel it was evident that the rudder pedals 

were entirely too light and they would still be too light even at'ter 10 

or 50 hours of flying with them. A pneumatic cylinder was attached to the 

pedal control with a bleed across the piston so that temporary centering 

could be obtained, but after a time the pedal force was independent of 

pedal position. It must be remembered that there is an appreciable 

difference in pedal position between climb and descent because of Wxerences 

in rotor torque for these conditions, which have to be compensated for by 

the tail rotor. The rate feel of the prleumafic cylinder invokes no objections 

but the temporrry position feel did. As a result, the type of feel device 

proposed for this control was me which consisted of centering springs across 

the valve of the power control so that a given rate of servo travel would be 

produced by a given force from the pilot. 

- - -. .- 

THE OVERALL FLIGHT CONTROL SYSm 

The artit'icial feel device should be integrated in fhe overall control 

system to aid the pilot in flying the aircraft. It supplements the pilot's 

vision and should. not transmit any confusing signals. In fact it is believed 

that the feel requirements for any aircraft may vary considerably depending 

upon what is required to xly that aircraft most proficiently. In the case 

of a helicopter, assuming that good flying qualities at hi& speed have been 

obtained with properly designed aeromamic surfaces, hovering stability 

should be approved. At the present time it is a question &ether helicopters 

will become big enough to afford tne added weight of a suitable auto-pilot, 

or whether a sufficiently light weight auto-pilot can be developed to install 

in the present helicopters. SikorsQ Aircraft is engaged in a program to 

attempt the latter. As flight tests have not been made on the initial proposal 

it is difficult to say whether the auto-pilot will be successful; but it is of 

the differential input type so that the pilot may fly with the stabilizing 

effect of the auto-pilot always present. The system is integrated with the 

existing hydraulic power control units, which makes it possible to keep weight 

at a minimum. Several types of feel are being considered including a type 

where the actual gyro signals convey, by means of a force, what the auto-pilot 

considers a proper way to fly a helicopter. There is certainly mamy problems 

connected with such a device which pending flight tests will reveal and lead 

to hoped-for solutions.

FUGET RESEARCH ON FORCE WHEEL CONTROL 

by DUNSTAN GRAHAM, Lt., USAF 

RICHARD C. LATHROP, Capt., USAF 


Wright Air Development Center, 

Wright-Patterson Air Force Base, Oio 

In order to sccomplirh precieion flying, etatic ad dpnaaio rtability 

of the sirplane'fi flight path ie required. The prorlrion of 

tbir rtability need not intorfore with the pilot 1 r control of tho 

flight path. Bbroe tranrdwrr connected to the pilot's cockpit oontrolr 

oan be wed to biar the referencor of the rtabiliring eyetem. 

This romultr in easy aontrol by the pilot of fliat whioh is artificially 

rtabilired and coor0inated. 

Tho practical mccerr of Neb a war demonrtrated on the 

All Weathu Branah's #ore@ Wheel B-17. Qpeeiment r were made in the 

atateerr llke a caras natural handliag q~ulitiet~ and nonlimar force 

gradient configurationr. 

All Woathor Branohla future rerearch plan8 oom&rire experiment8 

with the C+ (dercribed in anothor pcqpor), and the application of 

force uhwd control to other airframe antomatic control combination 

in an atternpt to meet spcrcific operational requirmentr.

The military or economic value of an airplane depends on its ability 

to traverse a controllable flight path. It is, often neoerurrp or 

desirable that the flight path or certain reotionr of it be traverrd 

with great precision. Conriderations of enroute and terminal ares 

navigation, landing approach and lending, interception and pursuit, 

formation flying, and bombing ma, illastrater the point. 

WIPdammtally, the aimam in flight ir a velocity vector in 

space. It has a direction in which it is going and a mpeeb with which 

it is going there. The time integral of thin velocity vector is the 

flight path. (If instantaneous velocities are nmltiplied by little 

bits of time to get little bits of distance travelled, in the direction 

of the velocity vector, and these are rtnrrrg end to end, the result ir 

the airplane88 flight path.) When the velocity vector ie steady the 

flight path is nstraightn, and when the vector i r dunging the participle 

flmaneuverfngUescribes the flight path. The wse with whiah r 

pilot may fly rteadily ie a Function of how well the airplane rerirtr 

changes in itr velocity reator, i.e., its flight path rtabilfty; and 

the errre with which a pilot manavers ir a Function of the means 

available to him to alter the magnitude and direction of the velocity 

vector, 1.0.~ control. 

Flight path etability and control has reveral faoes. The first af 

these to ehov iteelf was static 'rtabllfty vith reepect to the relative 

hd. Leonardo da Vinci convinced himrelf that the center of gravity 

of a flying machine ehould be ahead of the center of wind resirtame. 

HIS ngreat birdn of 1506 was desieed with tr longi tudinsl static margin 

of more than fifty percent chord. &host without exception, rince the 

Wright brothers 1902 glider, maceseful airoraft have had both longitudinal 

and directional rtatic rtability with respeat to the relative 

wind. 

The Wright brothare devoted considerable attention to what they 

called nbalancing. The 1902 glider was their first maahine whiah 

imoqorated a fin ad rudder. Together dth their predoas dwelopm 

a t of the elevator for lo~gitu~inel control, wing warping for roll 

control, and finally a power plant, it made flying possible. But 

"balancing" i 8 just what the fir at flights were, and flying ha8 

rmind to a large extent a belending act. 

The shadowy face of flight path stability and control has been . 

attitude stability. Attitude rtability cannot be inherent in an airfreme. 

By manlpulation of the controls a ekillful pilot can provide 

attitude sta3ilieation vith reepect to a natural or artificial horizon 

and a direction indication. Thie la, however, a feat. Bortunetely, 

an automatic pilot can be built to do the eame thing more rapidly and

precisely. The fir at demonstration of automatic pilot control of airplane 

attitude war made by Lawrence Sperry in 1913. Note that thin "nboerdn 

etabiliration, by the pilct or automatic pilot, de-aende on control. It ie 

contrasted with %~tbooard"tabili~ation (8uch ae la provided by fixed 

aerodynamic uurfacee) which intdferee with control. 

The incqatibil ity cf outboard etabilization with control ha8 

fortered the opinion that atability ie achieped only by racrificing 

control. That this ie not neceeearily the cane may be illuetrated 

by conridering the example of a rlmple poeitioning eervomechaniem, 

(Figure 1). The first desim ie deficient in dynamic etability. The 

output shaft reproduore the aagle of the input ahaft only after a 

wdrly damped traneient har died out. The designer hae at leaet two 

alternatiree. He may add mechanical dampiog to the output ahaft, 

%utboardn. Thin waetee control power and opposes rapid and accurate 

control of the output ahaft. (Such a ryetam has a eteady etate error 

den eubjeated to a velocity input.) On the other hand the deeigner 

may, Elnd usually doer, chooee to employ the derivative of error eignal 

to etabilize the eyetan. UInboardn etabilization, accoqpSirhed at the 

eimd level. doee not mete control power, and doer not reeult in a 

eteady etate velocity error. In thie cam etability doee not interfere 

with control. If anything, control of the output ahaft hae been enhawed 

and refined by additional etability. 

The aonaqt, illuetratal by this eimple example of e~taneous 

etability ah control, can be carried over into the airplane handling 

qualitiee field. Note, however, that both the etability and the control 

shown here depend upon feedback. 

Flight path etability, compoeed of attitude etability euperimpored 

on relative uind etability, ie commonly achieved by the feedback 

mechanisms known ae automatic pilote. These may be equipad with 

pedeetal controllere vhich provide a meane of introducing control at 

the eignd level. . Feedback for control purpoeee ie through the hurmrn 

pilot 1s vioual referenore and. hle kineathetic emee for mall finger 

and wriet moveplente. 

We portulate that a euparior form of feedback to the Man pilot 

ie force. There ie coneiderable logic and erne cuperimentd. widonce 

to eubetantiate thie contention. 

Aeauming -that the feel of the controls is .important to flight 

path control and that compliance with the handling qualities qwificatione 

inearee adequate feel characterietice, but poeeible only 

marginal flight path etability chsracterietice, it is logical to 

retain the f'miliar cockpit.controle'and their feel and add flight 

path etability. This is the equivalent of eaying that it ie logical

STABILIZATION OF A POSlTlONlNO SERVO 

LOAD 

0; €, AMPLIFIER . MOTOR 

+ 

POSITIONING SERVO DEFICIENT IN STABILITY 

LOAD 

8; 8, 

OUTB BOAR^ STABILIZATION 

. 

€3; E I 

LEAD 

NETWORK 

AMPLIFIERr 

+ 

MOTOR - 80 

*INBOARD* 

STABILIZATION 

FIblm 1

to hare thq coakpit controle command a control eyetern in tau& a way 

that the forcer epplied at the controlr -produce predictable and prychologiocilly 

acorrecta airplane reeponree while the automatic control 

eyrtam artificially rtabllirer and coordinate8 the flight. It may, 

however, be poeeible or evsn deeirable to take certain libertiee vlth 

the normal or natural reeponeee to control forcee applied at the 

cockpit controlr. 

In general, the natuml reoponree are ae follows: 

novator foroe oommende a proportional normal acceleration (Vg") or a 

proprtional change from the trim airrpeed. 

Aileron foroe commendr a proportional wing tip helix angle (roll rate 

at a given drrpeod). 

Rudder f oroe comnmadr a proportional ddeelip. 

One mn't add ormger and appler, however, and the rchge in which foroe 

ir meamred directly and ie ueed to cornmead an artificial rtability 

rystem to probrrce natural rerponler require8 that the primary referenoer 

for the rtabiliriog ryrtem be the flight variable8 tmich it ir 

&aired to command. 

No nruh ryrtem yet drtr, but in tho fall of 1950, at the behest 

of the late Wor Patriok L. Kolly, the All Weather Flying Mvidon 

undertook to mponaor the dwolopment of 8uch a rtabiliring ryotem at 

the Oornell Aeroneptioal Lsboratory. Thir ryetem ham been described 

in another --or. 

At the mame time a dl 

group under the energetic leaderrhip 

of Major Kelly beg= to conrtnrct a jury artificial rtability eyetsm 

vlth force commandr, ueing ounponentr which were readily aveilable. 

Right uring automatic rtability and force control wae firet achiwed 

by All Weather mng Divirion on 5 Maroh 1951. Throughout the ~mmer 

and. fall of that yaw the automatic rtability and force control rystem 

war terted in reveral oonfigurationr. It ir the rtory of thore experimentr 

that ir the principal mbj ect of thir paper. No rocordr of 

tertr rerultr were ever made. We out and we tried and cut -and tried 

again. Our goal war an airplane that had the feature8 of the ryrtm-- 

to ehow that it odd be mabe to work and that pilot8 did llke it. 

Its operational auccere war to hare been meaaured later.' All Weather 

Plying Sectionlr rerearch on force control var unfortunately out short 

on 7 ITormber 1951 when the tort airplane crashed. 

40 rtart wlth there war an eirplane with an automatic pilot 

inrtalled. !The force control tmb-ryrtm will probably find it8 prinoipd 

uraiulnerr in alr&ft in which rpae and weight are at a prmium 

and the pilot murt be raliod on to do ar much ar he can. The

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conrtsnt speed). While this ryrtem worked and the pilots experienad 

no difficulty in flying it, they were unanimous in condamming 

it. Unfortunately no one flew it who had had no ezperience in aa 

airplan.. TUr might have shorn 'nor natural a method of control it 

in. 

The control position feedback was unnaturally related to the force 

feedbe. The wheel--rigidly connected to the ailerons-followed thin 

emteblimhbg a bank. Ar every pilot knows, the no& requeme of 

wento is romething like this: 

1. The whed is rotated into the turn. 

2. It is held in a deflected position. 

3 Then it 'in returned toward neutral. 

4. Finally it is slightly rotated oat of the turn 

and held there to counteraat the overbanking 

tendell~y. 

With this first 8yst.m the automatic pilot did all tnir while 'tlu 

pilot maintained a conrtant aileron force. It's almort iapoeeible to 

beliwe, but neverthderr tme: not only way control smooth and stray, 

bat nobow objected to this peculiar porition feedback. The objectionr 

ware aoncerned with the magnitude of tbe forcer required to maintain 

tb. aircraft in a steady tm. There objectiona, might have been wercome 

by using wa.hout or nonlinear gradientr or both. Brief eqsrimanta 

ware conducted with a strong centering characteristic and a 

low rtiuk force gradlent for mod'arate diaplacementr. Thir artearr 

like a carn reanr of control, with or without nonlinear gradientr, 

howww, did not meet with agproval and was qulckly abandoned. 

The next configuration which was tried war designed as a first 

step toward making the aircraft control characteristics correspond to 

those of a conventional aircrait. Specifically, the roll control 

channel war alt sred in such a way that whenemor an aileron f orce 

grater than three pounds war applied, the vertical gyro roll signal 

and vertioal gpro roll erection were removed, and, by means of a 

ratchet relay, raalned dilrconnected until a button on the control 

wheel war deprersed. 

The mdder channel was modified as followr: the directional gyro 

rignal was completely removed and a lateral accelerometer was rubstituted 

ar a yau reference device. !Chis configuration reeulted in a 

control characteristic in which wheel force in roll commaaded an aileron 

displacement (and therefore rate of roll at a given airepeed)

and rudder foroe commended lateral acceleration (and therefore ridodip 

angle, epprox5mately). Thn 'action of the lateral acceleometar 

vae such ar to maintain negligible aidedip in the absence of a rudder 

force migaal, 80 that coordinatod turnr were made uripg the vheel 

alone. This rimplified the control of the efrcraft in nornal mancnvarr. 

Pilotr frequently ure little or no rudder in normel mancutere, 

particularly in nailti-e~gin6 or high-.peed drcrait. The 

rudder pedal force pickupr, hovewar, dlo- the pilot to intentionally 

ridedip the aircraft if he eo deeired. (~ntslrtiond. ridedip 

ir urd in making crone vird landingr, for example.) 

No modification8 were made in the elevator control channel; the 

control characterirtic in vhich wheel force conumnded pitch angle wr 

retained. 

Phe roqme of event8 in making a turn vith thir ayrtam war 

romethipg like thin: 

1. The pilot applied a rolling force to the vheel. For 

very -1 uhed forces--muah mailer than thore or 

dinarily usad in rolling into a t&n--wheel. force 

con=nded aircraft bank angle. When the vheel foroe 

reached a value of about 3 poundr, the tartical gro 

roll rignal war smoothly but rapidly (Umonnected from 

the automatic pilot, and roll erection in the rartical 

gyro war 'disabled. At thir point, wheel force commaadad 

eilaron dirplacs~lent, and the force vhsel ryrtcm 

acted merely ar a control booat. 

2. To maintain a conrtsnt turn, the pilot relaxdl the 

vhedt force &en the proper bank angle had bran reached. 

Coordination war aupplied automat i dly. Winor correctione 

to bank angle had to be made in the uoual manner, 

since no artificial rtability elgnalr vare provided. 

3. To return. to straight and lwel flight the pilot hat 

two choicee. Ee oould push the but ton on the rrheel and 

relax uheel force, in vhich care the vertical gyro roll 

rignrrl and roll erecrtion would be reengaged, end the 

aircrait vdd automatically return to lsrel, etabiliswl 

flight. Alternatively, the pilot could return to lmel 

flight in the conventional manner, and then reerrgage the 

vertical gyro etabilisation by bepramring the button, ii 

he 80 derirul. 

Smsral flightr vee ma40 vith thie eyrtsm, and pralirpinery redtr 

indicated that it war a very workable and natural ryrtmn of edrcraft 

control. Some of the pilotr vsre gratifylrrglf enthuriartic 

about the Improved flight path atability ad the sere of fl- path

I I SURFACE I 

AIRCRAFT 

DYNAMICS 

LOAD DISTURBANCES 

ELEMENTARY FORCE WHEEL CONTROL SYSTEM 

A 

FORCE 

FORCE 

WHEEL 

- 

PRE- 

AMPLIFER 

' 

JANPLFER 

SERVO 

ACTUATOR 

I SURFACE DEFLECTION 

FLleHT PATH 

WITHOUT ARTIFICIAL STABILITY 

Fmum 2

AIRCRAFT 

6 

FLIGHT PATH DYNAMICS 


m 

r* 

CONTROL 

SURFACE 

FORCE 

FORCE 

WHEEL 

m 

- 

PRE- 

J 

AMPLIFIER 

4 AMPLIFIER 

SERVO 

' ACTUATOR 

SENSING 

ELEMENT 

a 

f\ 

SURFACE DEFLECTION 

FORCE WHEEL CONTROL SYSTEM 

WITH ART IFlClAL STABILITY 

nQUIU? 3

AUTOMATIC PUT 

DYNAMICS 

a 


I 

I 

I 

I 

I 

I 

I 

E , 

P 

FORCE 

WHEEL 

a 

t 

- 

PRE- 

AMPLIFIER 

- 

- I 

NTE6RATOP AMPLIFIER 

t 

SERVO 

ACTUATOR 

- 

I 

I 

---- - -1 

I 

I 

I 

I 

,--,-----I 

I 

I 

ATTITUDE I CONTROL 

I I 

I 8YRO I SURFACE 

I 

I 

I ,-, ,- , , -, 

- ., 

-,-, 

,-,,,,, -1 

I 

w 

f 

FLINT PATH 

AIRCRAFT 

t 


WITH ATTITUDE - TYPE AUTOPILOT

control. Unfortunately, the test aircraft wae loet before ext ensive 

evaluation of the syetem could be etarted, and before intprovamentr 

could be incorporated which would have rendered the artificial etabilization 

operative at all times. 

A similar but improved installation is currently being ma& in 

a c-54 type traneport aircraft at W~ight-Pattereon Air %roe Baee. 

Unanswered reeeatah queetions concerning much equipment &re legzon, 

and the operational uses to which it may be put renain to 'be explored. 

Coneider sweral possible force wheel configurations: The block 

diagram of an danemtary ,force wheel system for one aircrdt arle is shorn 

in Figure '2. This arrwement operatee a$ a boort only, and no artificial 

etability is provide&. The wheel ie rigidly connected to the control 

surface through the normal control cablee. Thie link, however, doer not 

normally supply an appreciable portion 'of the hinge moment, but merely 

acts as a rurface poeition feedbaak to the pilot. Syrtems'of this tme 

would tend to make the force-biglacement gradient of the control wheel 

relatively independent of airweed. Thie was the characteistic of tho 

later B-17 inetellation. 

A rormewhnt more refined mystem is ahown in block diagram form in 

Bigure 3. In this arrangement, the rigmil from a eeneing element (ma& 

ar a rate gyro or eideslip indicator) is fed back in such a way as to alter 

the effective dgnamiee of the aircraft. Presumably, the syetem ir deefg~ed 

so that the dynamic stability of the aircraft is improved. The rigid link 

betveen the control surface and the control wheel is retained. Thir means 

that control surface deflectione due to both wheel force signals and artificial 

etability eignale me reflected in deflectione of the pilot '8 

controlr. In earno caree, this may be undeeirable. The degree of undosirability 

appear8 to be a function of the magnitude and frequency content 

of the artif iaial stability signals. 

If it ie neceeeary to closely approximate normal aircraft fed charscterietice, 

aignale proportional to airepeed and Q n force may be introduced 

to vary the gain of the force whed prsanplifier and thsrefore altar 

the f orce-dieplacement gradient of the pilot s controls. 

Methode whereby the force wheel control eyetedu may be ueed with an 

attitude-type automatic pilot are shown in Figure' 4. In this configuration, 

a eignal proportional to the integral of wheel force ie fed into 

the automatic pilot amplifier in such a way ae to command aircraft attitude. 

lrll of the stability aeeocicrted with attitude-type of automatic 

pilot ie retained during all normal manavere. The control wheel 

. theref ore become8 a sort of refined pedestal controllere wlth nfeeln. 

The rigla link between the control surface and the control wheel is 

retained.

FORCE ME- SERVO. 

\ 

- = AMPLIFIER = 

WHEEL AMPLIFIER ACTUATOR 

A I r I r 

I 


- 

d 

me FoRc D L 

I 

SENSINB 

ELEYENTS 

< 

FLIGHT PATH 

AIRCRAFT 


WITH ARTIFICIAL STABILITY 

AND ARTIFICIAL FEEL 

rIam 5

LOAD DIST URBAMS 

(SURFACE I 

.= 

a - 

r AMPLIFIER C 

SERVO 

ACTUATOR 

* FLIGHT WTH 

AIRCRAFT 

DYNAMICS 


WITH ARTIFICIAL STABILITY 

AND ARTIFICIAL FEEL FIGURE 6

The configuration described above remlte in a control char-taistic 

in which, effectively, wheel force commande rate of change of 

attitude. If the integrator is removed, the lateral control ChBSacterirtic 

becomer similar to that of an automobile, in which wheel 

force comr~andr a rate of turn. Integrators for the B-17 inrtellation 

were conrtructed and grand-cheeked but were never inrtalled. Improved 

intagratore will be a feature of the C-54 installation. 

In Figure 5, the pilot 1s controls are not oonnected mechically to 

the control eurfece, and motionr of the control taurface induced by artificial 

atability 8ignd.r from the rensing element are not aocoapded by 

rimilar motionr of the cockpit controle. This mean8 that the pilot ir 

not rubjected to the poesibly disconcerting phenomenon of having the 

control wheel move about in a manner aich he does not command. Ae far 

ar the pilot ir concerned, he ir flying an aircraft which ir more atable, 

but just ar controllable ar the rame aircraft would be if it had a more 

oonvsntional control eyrtcm. 

The force wheel eyetcm of Figure 5 la a ro-callod #full-poweredn 

ryrtear, in which none of the power necessary to more the control rurfacer 

ir mupplied by the pilot. This ie in contrast to the systemr prdourly 

described, which are boost eyetar, eince a emall portion of the power 

neceerary to move the control surfaces is applied by the pilot through 

the rigid mechanical connection between the cockpit controlr and the 

control arrfacer. 

In a full powered ryetem there is no conventional control #feeln 

for the pilot, ro it ie derirable to include artificial feel in the form 

of a bungee rprlng, and bobweight wlth proviaions for variation of the bungee 

characterietior with airspeed. The effect of trim may be rimrrlated by including 

mean. for varying the cockpit control position at which no force ir 

qerisnced. It may be dedrable, however, to fix the rtick and fly with 

forcer alone. Thir war to have been tried on the B-17. In thir case 

there would be no control porition gradient and no dieplacement of the 

rtick wlth varflng trim. 

Another force wheel eyrtem using full-powared control e+rfaoee ir 

ahom in Figwe 6. Thir arrangement ir rimilar to that jaet dercribed, 

arcapt that the artificial feel bungee has bean replaced by a wheel position 

Berm ryrtm. !Che force-displacement gradient be conveniently abjarted, 

and, in fact, may be mede nonlinear if desired. Honlimar gredisntr are 

mupporod to be psychologioally optimum. Proririons are &own for the introduction 

of alrmpeed aad #gn force rignale into the force &eel preamplifier 

to eimultaneaurly alter the control rurface and wheel force gradientr. 

Thir is essentially the aystam which ir to be flown in the w.

The force &eel ryrtms mentioned above are only a fsw of the many 

raible configurations. Testa with systas similar to those of Figurer 

$and 6 rill be cond~tld by the All Weather Branoh in coming months. 

The use of force vheel control, in conJunction with inboard rtabilization 

of airframe dynamics, maker rimulteneous flight pth 

stability and control realizable. All the flexible methods of reroomechaniun 

loop compensation are placed at the disposal of the airplmo 

handling qulities designer. While many research questions conoerirrg 

optimum stability and control remein to be investig~ted in flight, the 

technical practicability and enthusiastic pilot acceptance of force 

wheel control have already been demonstrated. 

1. Graham, D. nglight Path Stability and Control in Relation 

to All Weather blyipgn USdF MB WCT-2372 29 October 1951 

2. Milliken, W. F. @Dynamic Stability and Control Besearah, 

Section VI IIn Cornell Aeronautical Laboratory wort No. 

CLLL-39 (paper presented at tho Third International Conference 

of the B. Ae. 9.-I. A. S. Brighton, IDDglsnd Sept~lber 3-14 1951) 

3. Perkins,C. D. and Graham, 9. tlControl Force Instrumentation For 

Flight Teetn Rinceton University Aeronautical Hbginearing 

Laboratory Report No. 107 30 March 1949 

4. Orlanelry, J. nPsychological Aspects of St i& an8 Rudder 

Controle in AircraftVeronautical Wineering Review vol. g 

no. 1 Janwy1949

AN ANALYSIS OF FULLY-POWERED AIRCRAFT 

CONTROL SYSTEMS 

Including Some Reference to Flutter Theory 

D. T. McRUER 

G. E. CLICK 

J. W. HAGER 


Northrop Aircraft, Incorporated 

Hawthorne, Gal. 

- oa@ination. the 

The rill assrtrol mtr im8lJS.d fwtum8 ap i n t e e 

rarmtd ~vo-cy~er 

peramterm boMd 

ih the derAmtioM of the equatioM are: ooppnsribWty of tho 

rbrkiag fluid, all njor omtr olartieitiar, all apppmt sourear 

oi dmp*,'Md .od a o ~ offact.. c 

Comridmtiaai is glvm to tha affect of th, mjor mtr 

prruotan upon the darinsnt fmcpmq rodeo ami upam mtabillty. 

Pbioibla rodiiiaatiopr to tha clasoical flutter tbmv am a h 

qdlaatod, 

Tha autbn wioh to aclaawledga the valuable aooiotcm~e 

and ouggaotiono offared by tha fo- indiridua108

TUe paper prorents an analysis of a typical valro-q-er 

hydratill6 actuator as ahoun in Pig, lo 

Tho valve, being Integral with the cyliuder, proridear 

- -rsrcnavm um~ Gno 11- 18 1Me lLOn Ud 

ontrainad air will nwer conrtitute an aapreairble part of 

the norklng m1rrp.e of fluid4 

2. Poaltion error ar a function of load, eamon to napcontern 

ryetam, armmer negU&ble proportlaw bouue the 

neutral leakage (region of open eonter tp 

operrtion) ir 

confined to oxbrreb -l.l dirplaemta, (?%go 2,)

"W@J@tI pendm 

ao poqtmeard euofenfouoo eqq uo peouq oq mp8e.x mn eofqomd uZQoep qrq 

@ (1 eouue~q eom) meep tedcud $0 enofqwqoe~~wm ~wfobqd eqq qqp pouxeo 

-Uoa qm mf .redmi queo@~d eq& o ~ q koqo8Jofqw ~ o a Shqxe~oo q q p u 

m epoqwr 

. 

wmoemueo fwmuaa JO uofqwandd. eqq qomn WJ qwm 

VQfmm JO eTeW 099 e p ~ l pw ~ d *eof~=d crF peAelW8 m9.P 

emuodmu &aenbe.rj mnopar qmoead 'roqwqow JO odl:q fareaoS ofqq JO ppom 

TnTqmq8m dn qoo oq ~edd OFqq JO emodmd k-d eqq of q1

Tho plaa ir a8 follarr: 

1. Dorive the flou quatiopo 

2, Dmrin the rilpUf$od -t(i lord eqg.tioa8, 

3. Cambine the trro aqi dircurr the rirplliiod apt-, 

4. Dirollrr tb M tbg carer 'of the rirpllfiod aystr. 

5o Dorive the aquatiom for the g ~emlord oar. incldbg 

effect8 on flutter th.oqo 

Tho tollawing ar.rptloxu will gor.rn tb analpir: 

dlffemse bat- 

2, All elrantr of the rptr can b. rqla8.d W Irsp.d 

COIL8wt8 o 

30 The f l u in tho 8yllular ir elrap crprobrod t6 the 

aatamt tht earitotion ir rragllgibleo 

40 valve ir derlgmed in mch a way a8 to nk. ne&lI@la 

the rate of ohqe of rorartr ef the fluid ar it p88@8 

thmwgh the valve, thr rerrrlt$ng in the all&amtioar of 

camtarh# and decemta~ 

foreer on the valve, 

5. The pirtoor la double dodo 

60 The valr. ir motrieal, iOao, in itr noutral poritioll 

an noutral laakage anar .n .qPal. 

7* Srrp p rerm ir errantiaw sere. 

mFL - The error, i , of tbir rerra.cknir ir the - 

the 61- di.pkcrant nktive to fiuQ &rU8ttm, 

X, , ud tho 8yUlrd.r dirphcant mktiva to the mum fiUQ & ~ 8 t ~ # 

X, IAt the pmrturbatisnr of the diepkoratr %, . X, . and k!

Ooeo red em;Co* ey tg areqm 

- a d m ~ u u e ~ ~ 

4 -A@ ~0-b 0% so epv -owd qaTq eqq o?w 

urn eqq -I eqq -@a esml-;C ;~arq-u eqq emeq- 4wqq ! a-k 

e.mooad eqq jo moq rq peeentdre fi-0 aim of af 

pa l a uodn eotmaprPsdep pw~qamy eq& 3 d~arqmu arj , quom~oqdefp 

urn eq? pum 4uoqm~d eqq jo em0 uqqre uo l 3 pm eemsoad 

remPo eq3 & 4elmaee.td &ddao eqq jo aoyqomry e of romLa eqq e ~ m 

0% bPF-3 eA'C1BI -3 mU UTWOJSe e1(& - UTVA SH& WWd WJId

4 = gravitational constant 

ur = epecifi c weight of fluid 

Ap- f-4 = pressure drop across orifice 

f= Ptg *t , because of valve s)raetry 

Inside the neutral leakage region the flow frolr the valve mt be expressed 

by more campllcated functions of the above mentioned variable#. 

However, the object of this short discussion is to mnphasizo that tho 

flaw from the valve is predomfnantw dependent upon 

4 , E , pad 

4 , and that the relationship is continuous for all practical purposes, 

Therefore, since 

the first order Taylor98 expansion of the perturbed flow becaror: 

, jc, and 94 are perturbation quantitieso The tern fl 

where 

is a dlsturbaace entering front the per source, and need not be consldqed 

further since this discussion deals on* with the surface actuating 

#~lt(l~.a Therefore, 

mica1 variation8 of valve flow & with preswre differsnce & , 

valve displacarent E befig held constant, and of valve flow with ralvo 

dlsplacarent, pressure difference 4 being held constant, are sham In 

PI& 4, Figo 4 also shows a typical operating point, the o t w state 

values definhg the operating point ( a!" , A* , and e*L ) pad possible 

values of the perturbed quantitieso The partial derivatives of eqrration 

(b) are the slopes of the curves evaluated at the opor@ting point, Note 

that on Fig. (b), the first quadrant shows the flow codition for a 

resisting load, and the second quadrant for an overbadbg load.

Variation of Valve Flcnr 

with Pressure Drop 

ACIPI~ the Piston 

(valve displaeeaent f raa 

neutral constant) 

Variation of Val- Flor 

with Velr. Diaplaccrat 

froa Ueutnl 

(Proreme dlpp aamr 

piston conrtaat ) 

Fino 4 

is abps positive or sero ami tht a&/& 

8 set of ~ t i o nwtrich r ar& almost alnap 

a necessity for srstcn atabilitr, It will be advantaeeoua in the dm-- 

rent that follows to maks the 81or~al siges of these qrumti)iiem appamt, 

that is, 

Hinas si~pl denote8 t 

Figo 4 (a) is ahye 

Then equation (4a) mar be written

The term Cp is analogous to the slope of the torque-speed curve 

of a shunt motor, and gives rise to a similar damping action. The ten 

C, is analogous to the slope of the speed-field currmt curves of a 

shunt motor, and giver rise to a similar gain texm in the overall optr. 

Cp 

r 

varies frm sen, to infinity as a function of E and of 4 ; 

thesemoccur wh~thevalveisinnentralwith~pnosruedrop 

across the pi ton, and the infinity occurring at the system stall. 

flaw from the valve with cylinder motion, piston motion, ad the pn88Ure 

drop across the piston, In developing the equations for cylinder fl# 

the canpressibility of the fluid will be taken into account. 

THE FIIlkl INTO THE CTLINDER - It now becomes necessary to relate the 

. 

is : 

The total maes of fluid on one side of the piston at any ti.s t 

where 

and 

I = volme occupied by the mass 

p-fluiddmsityatthetime 

and the volumetric flow corresponding to this mass flow rate is 

The compressibility of any fluid is characterized by the exprwrlon, 

where 

N = bulk modqlus of fluid (force per unit area)

p - instantaneons density (mare per tmlt -ha) 

P 

insbIltaneotl8 fluid pH88tWe 

Dividing both sides of equation (10) by dt , 

(u) 

f 4-1 & 

dt N dt 

and substitutl~q'equation (ll) into (8) 

and 

where the subscripts, 1 and 2, denote the mglon6 on one and on the other 

side of the piston respectively (see Fie, 3). 

If it is asrnned that the instantaneous flaw into me ride of the 

cyllnder is equal to the instantaneous flow out of the other ride, 1.9.. 

and ii it is farther asuamed that the bulk modulus /V I6 conetaxit and 

identical for both regioae, equations (12a and b) be- 

dY 

dd 

drr 

dt 

Since / r - - , it follaws tbt

ouoqeyd eqq 

eeatoo m3mueJ;rrP emseead eqq ' 9-2 zg 

'(a) o3w (57) pw ('K) eagqmbe BnF~n3~3oqw

where %, , %+ , fi , and A r' are perturbed qwtiti@r, aad 

st* 'd &* are steady-state values. 

Slmpllfication of equation (17) may be obtained conaidespecific 

operating .,conditionso For eutample, since perturbatioarr are. beconsidered 

about a steady-state cyllnder pres8u.m diifemntirl, the tom 

d4 */df must be disregazdedo PPrthernore, it is a recognisd 

fact that hydreullc servos generally are nearest instability at, or nwr, 

the no-load conditiono* This zero laad condition closely correqadr to 

a faired surfaces position, wherein the VO~UIB~B of oil on either ride of 

the piston are very nearly equal. The effective oilrolme bar beem 

previously defined as 

4ra j 

&+G 

and since A = -A - 

then 

d 

rldk dr( 6-c/; 

5+G 

so if 9 c, then fIr'=o , 

or 

a constant bc I* 

The approdmate linearized expression for perturbed fla thw 

obtained under the foregoing conditions is 

The physical representation of the oil within the cyllnder as a 

spring is developed as follows: 

Consider, first, an open ended cylinder that bas bean subJectad to 

force d F and ccmpressed a Uear displacement A A , as shown b, 

Pigo 50 

* The effective damping tern, Cp , approaches eem as 4 , ud 

hmce the cylinder had, dtninishee, See page 8.

Pram eqpatian (9) 

and the volune incranant is 4 r = R (AX) 

so tbat, 

- qaiv(~1ant wring wn8t8nt 

of the oil, 

Act- them is oil in both sides of the pis- so that 

offeetively them are tm springs in parallel; hence the effective spring 

conatant is 

q& 

G+4 

I 

where 8 = - as in oquation (16). 

TEE UllD EQUATIOHS 

The true load upon the cylinder is mther inWd ami w i l l b. 

conriderad later. Bue to, its c4apldty it is desirable to u8e a 8kpliii.d 

mtr to obtain bric deratanding ad than use the at- sptr to 

dotelaino tho offeet of sa. of the less important elaarts upon tho mta 

operation. The sirplrriod sptm is illuutrated kr Figs. 6 .rd 7. It 

will ba noted tbat the piston rod is armmod rigid sld that tho vatvo 

displacaant 3?, is eanaidered identical to tho sono input 8-1 %z .

The error equation (l), with XI * ir, R b-es 

also, since the piston displacrnmt Xf 

quation (1Ba) becmes 

is ngn-drtant, tho n9r 

The flow .quation8 (4b) (page 7 ) and (Ua') cabhe to form the 

qrerrion 

The sipaplified load systm~ is rrav camplete3J defined 

(21) throggh (231, 

aquationo 

It now becomes a rimple algebreic task to combine equatiOIU (21) 

throu& (23) into the opa~ loap transfor funetian of the r;ystr. 

definition, the open loop transfer fmction 3npUes that all artrmeou 

inpats, or dirturbances, are %em; hmce the aemdpamic feree F ef 

equation (18) is sera.

f 

Ewr valve neutral, vita 4 =O , the open tranrf er 

function becaes simple, since cF r O o (See Fig. 4.) Haling 

tM8 abstitution plus the nlationship 4 = A W 'r 

(the effective spring due ta oil ~ressibillty), 

equation (a) bemar: 

Eqrrgtion (25), though representative of a rirpllfied mtem, is 

still quite qlex. It is therefore of considerable ralue to attrpt 

approximate factarieation, and to consider Uniting case80 

Equations (24) and (25) are of the forp 

as- that the denabator frequencier are wldely separated, it is 

possible to obtain an'appmxbate factorisation of the donainator In 

eneral torrs0 (See Table I,) The mathod originally developed by Lin 

f 

Refemc9 2) is enplopd for the factor is at ion^ it is asmod tbt the 

first trial solution wnvdrges ianediately, In this situation, the Bode 

diagrerp of the rhplUi4 syat~l will appear as r h in Pig, 8, k- 

prlmental point8 are plotted os top of the calculated valuer for a ttpid 

p ~ i ~ s y 8 t ~ .

C C U P m ZERO - (Bulk Modulus infinite,) For the 

limit- case in which the qmpressibility of the fluid beomes vem 

mall, the laop transfer fuuction becanes: 

huad the neutral position, with 5 = 0 

, the open 

loop transfer fuuction reduces to a very simple expression. 

Equation (28) will be recognized as the conventional expression used in 

the analpis of -radio amplifiers when used with mechanisms b a a 

large lags at fmquancies mch lower than those of the wraulie amplifier. 

Epuation (28) is also recognized as that of perfect iategrator ad zem 

podtion error servo, The reason for this is, of course, tbat. in thir 

care there are no spring or friction loads. If the l@raulic amplifier 

itself is ntable, thin approximation is an excellent one when the other 

elanants of a control loop ouch as an autopilot and airframe sene to 

lovrr the possible gain cmsaover frequency, & = cg /A . For 

une In such analpen, than, the hydraulic system is adequately dencrlbd 

am 

- 

The tima constant is capable of being made quite mil with 

proper derQn, down to the order of v100 second in the authorsf emprlmcen. 

C~~IBILITT INFINITE (~ullc Ibiulus zero:) If valve damping, 

Bw Tbetween the valve spool and the valve housing), is included an 

an extension to the simplified load systeu, the open loop transfer function, 

equation (25). can be- nbrmr to be

For the case with Minite campressibility, the above open loap transfer 

functian became8 

Input motion is coupled to output motion only because of the riscons 

drag of the valve an the cylinder, The system is no longer a Gem 

position error device, Physically, the use of the relationship of 

equation (30) appears when two hydraulic ayatans are connected in parallel, 

with the power to one system shut down, or on a single actuator installation 

with per off, If there is no viecaus friction caupllng between 

valve and cylinder, the transfer function beames zero, art them is no 

motion trandtted fmm input to output, 

COUPLING SPRING -4 w - he situation occasio- mires 

where backlash occurs between the cylinder and the surface load. It is 

then desirable to investigate the stability of the systaa within the 

backlash region, though it must be remembered that stability inside the 

backlash region does not necessarily rule out the possibility of a limit 

cycle occurring due primarily to the backlash, 

he open loop transfer function with .A =a then becaer : 

which, when Cp = o reduces to

Canparing equation (32) vith eqation (25), and also canparing 

the Bode charts of Figares 8 and 9, it is apparent tbat stability of the 

lgdraulic apten outaide the backlash region assures stability inaide 

tb bsckLash regime 

DAMPING COEFF'ICIWTS 4 .. . AND Brr 4 < Ce - Whthe 

surface loading produces high hinge m~~ents, the pressure drop, , 

aomss the cylinder approaches the aptan pressure, . This condition 

corresponds to a very steep slope of the flaw-pressure curve (Fig. 4(b)), 

and, hence, the gradient Cp is verg large canpared to all other s@an 

dompine. 

The opem loop transfer function then becauest 

\ 

Approxhats factori&ation of the danaatnator yields the undamped 

natural frequencies: 

.-

Note that d$, is identical to k;', listed in Table I. 

SPDG CONSTANTS AND MASSES EQUAL - A large portion of the foregoing 

discussion has to be based upon the asmmption that approximate 

factorization of the transfer function dmaxbtor is ssible. This 

tacitly aeeumes that the ad /-- are considerably 

separated, If these quantities are wt separated by a wide 

margin, there are no means available to detezmine the effect of change of 

an individual parameter upon the system except by the use of numerical 

values. 

It is, however, valuable to investigate a Umiting case where the 

values of 

' 

=/M, and are close together, the 

case for which Aa/, - 4 

=-A' and M= = Ms = M . For 

simplification it is also assumed that the valve damping, 

zero. The open loop transfe~ function then becomes: 

8, , is 

uhlch, with approximate factors becanes: 

The Bode diagram of this system is shown in Fig. U),

EFFECT OF ADDRIG A SPEUNC IllbD AT THE SUBPACE (see Fig. 7.) - 

The mtire sptm amlysis to this point has separated the hydraulic 8pt.L 

frar eixteraal syataas at the portion of th load schmatic where the 

laad F appears. me ruvierlying mason for this procedure was to prorido 

a maans of hwxllhg the flutter analysis of the hydraulic system. However, 

in the operation of a Wraulic syatem under fUght conditiono, the 

force F wlll be tho major load, and a portion of this force may bo a 

definite function of ZS . Whem such a force dots, the force F 

ceases to be purely an external disturbance and became8 a p h q element 

of the inner loop. The sinplest example of this situation exists when 

F =As X , or a pun, spring load mch as a static hlnge mment 

gradimt is applled to the 8pteno In this went: 

An approximate value of the naminal lawest &pal 

with Cp ro o 

natural frequency is, 

As is much less tlnn 4 , so that the lowest undamped 

Ilo-Uy 

natural f reqamcy is essentially unchanged, 

!CEE GEaaaAL mAD CASE 

The purpose of this wction is to present the equations for the 

eullc opt- with all of the terns taken into account, to indicate 

the use of the lgdmullc syaten data in flutter calculations and to Inroetigate 

the effects of various stmctural caerponents upon the Mest 

&pal natural. frqumcy of the open loop transfer function.

Q 

- 

The laad equations, (40 throagh (43), are writtat frrrm Fig. Il 

(bat with C, and C, as follmr: (See Fig. ll). 

In addition to the above load equations, me further empmsrion 

is neceraaq for the am48ia of the oclplete h y d ~ ~ c - awtm: 

e ~ c 

This equation i n obtainad fna the relationships givon by equation8 (I), 

(4% (a). 

The characteristic detembumt for the above array 18:

The outtmt 4 is then 

-tion 

(a) may be remitten, 

in which case (46) becomes: 

(The nprlmesw denote the new fom of A, 

equation (4.44 for (44) 

aft)r substitution of 

/ 

where = CE - 5s. 

4 

RecalJ3q that

Oesua pliq 

pe~m.dqs eqq roj suo~qdmnoea epq jo euo sw s~gq 2wqq mwae?~ i

71 

It is of interest to anmine the lowest a roaPlate mdqmd 

natural frequanq of tho d..ointor of oquation747a) W pin a certain 

amount of insight into effects of the qutm olmd8 upon splrtr 

8tabUty. Thir ia daw h the saae mmer as war doae pmowly vith 

8hplIfi.d msot Th. -st tmbmpad natuxul frequan~~ ia appmximtoly 

htth& 811 88-8 negligible pr~port- tho 

qpotiamt fly44 : 

(48) ziresl 

C 

AA-6 

=, 

I 

and uhm Ms >> MC 

d'% 

(Uh) 4j2= 

/ 1: 

= - 

uhora Jr is tho eerlea epivalant spring constant as eoea 

faae MM, MS . 

tho em-

Tha ga~alal equatlo~ should also be used in flutter talculationr, 

Tho tnrsl.ior function F/%= is sasily foxmad, sad uad to rophco the 

awtauy Inertla, damp-, atmi spring looking into tho &ace. Tho 

kcit armmpth nrtrlcting this umgo is tht boding ad torsiosr do 

not eouplo with tho ~ mulic stro Beforring again to oquatiasu (40) 

throrrgh (45) it is apparart tbpt tho ruriaco motion may ba apmrrd 

Since tha overall wet- is now being vietrd illor a flutter standpoint, 

I,.,, looking fllor the &ace into tha apt-, tho hydlaulic 

apt- ingat, %, , is marely a distprbsnca ami my ba eonoidored 5.m. 

Tha 

- 

cbpracteriotia doteminant may also be axpressad, 

4 -.( A?,+ f (4S'f 43 +4 + 

Then tha capplote transfer function ralating rurfaaa load ami 

mrfaae nation (with e ) is:

It w ill now be shrnm that the quadrai;ic tern of equation (49) 

includes the only dyneaaical parameters considerd in the mlaal flutter 

-08, where as the first tern, 4, 4+/4++ , cdpreaents 

the correction that must be added to take into account the heretoion 

dirregarded chanrcteristics'of the hydnrulic-flutter sprta. 

In oldiaary flutter calculations it is the practice to nae 

Theodorean~s differential equations of motion, The equation coq,nssing 

the .qrrillbrlum of the mcm~ents on a movable &ace is given by: 

when 

oc = angle of attack 

/B - marface angular deflection 

X = vertical coordinate of ads of rotation of air~oh 

j; = mmt of inertia per unit length of ~uriace (aht hinge 

- 

me) 

static mat of surface (in slugs-feet) 

per unit length (about hfnge fie) 

5 = torsional stiffness of eurface per uait lcmgth (about hinge 

-1 

Mp = total aezwlynamic manmt on sariace per unit length 

(about hfnge line) 

IL = coordinate of ads of rotation of airfoil (percent of 

airfoil half chord length) 

A = hlf dmrd length of airfoil 

c = coordinate of surface hfnge lfne (percent of airfoil 

half cord length) 

Fig. l4 UlstMtaa &tr,wg.o~etrical pamet era of the girfoil-surfaoe 

eabinatimo

Of especid concern is that portion of the total aelPdyrremic 

nent wbich is related to ,9 and its derivatives alane. Designating 

this narmt oaapoor-t by 

yF , 

The above equation, obriowly, does not include the dynamical chsmcteristicr 

of the hydraulic eystsm, but, rather, represeats a ourface inertla 

tied to a -ring, as illustrated belaw, 

F1 

Since MF s - 

4

tp = 4 1' ( 4 include. aU flaxibillty I- the 

a! hydraulic cylinder to the effective mass 

cmter of the surface) 

A' = surface horn radius 

d = surface span 

then in meal terms, equation (51) becomes: 

Caparison of equation (52) with (49) clearly sbua that the camplete 

apresrion for the hgdraulic-flutter sfst- is far more oarpl~x than 

the rimple situation shown in Pig, l4. 

The above ca~~ponant of the total aerodyneaic =ant nlatsd to 

and its derivatives ahe now replaces the orfginal incamplets tern 

in equation (50); thenfore the differential equation of motion ir more 

precisely ~3q)ressed, 

p diagraa~at$c reprermtath of the corrdcted capansnt ir ram . 

in Fig. 16.

A desirable faatan of any well designed hydraulic aatrretor 

installation is that the piston and mounting structure are a8 righi a8 

porsible. Normally, then, the piston spring constant 18 large acupared 

to all other spring aonstants, including that of the hydraulia fluld. 

With this important asmnnption, the quadratic (;*G sa 44 ++Js 

+S] 

becanes an appmxbate factor of the numerator and denaninator of the 

4+ 

portion of oquation (55), reducing it to: 

/A+ + 

Vary little more can be done to slnpUfy the above arprersion; 

actual values of the constants mast be substituted and the s3q,resrion 

nmuerically factored, Experience with typical Uorthmp-typo WrauUc 

sptans, howover, bas shoun that the den-tor cubic has gn appnudYte 

quadratic factor, 

(4sa+4sf 4 +I) j ; this im lies that 

the constant , is rn). large (1.e.. G ia very -7, uuch 18 

the case for valve positions near neutral. Thus, 

The term in the braces, to reiterate, is the cornctive tea uhiah 

must be added to (or mubtracted inn) the quadratic, f#= sa+4 s 

the ae-c 

+AG) , to obtain the proper transfer function bet- 

force, F , and the corresponding surface deflection, Xs . Thir 

corrective tern is of the form,

Frequancy Response of 

Another prorequisite of a f~-powend bgdraulia rena is teot it 

must be capable of resisting lar~e hinge manartm with relatively a m l l 

valve displaemmtr. It follars that the slop of the prosmum tr valve 

error cun. must be rather rteep, or that the value of the rpriry constant 

(=&+/+ rim 

) is hi . On the other M, the oil spring 

eonstant 4 (= A?/*' nstrietd by the eyUPder dse 

tht can be installact a thin airfoil reetim. SO, in gmenl, 4 

will be greater than 4 ; thus

Aldo, since the off sofive damp- constant 4r ia very largo (or 6 

very aa~) 

cappared to tb+ ~ U enurse r #, , 

Fig, 18 reflects tho above older8 of magnitude of the froquanalu inmlnd. 

In the regions marked A) and A2, the comctive tonu contain eurnthIJy 

sero phase angle modification to be applied to the -la roetor 

(M,s2+4s+4) , and, hence, ray be eonslderd g ~n 

spring corrections, The rmgh marked B ir a transitIan msqp batman 

4, and dt ; its upper Wt is detemhd px-harLQ by the value of tho 

sem gain tern, ce , whlch is Inherent in the spring dj . (Tho 

larger the value of At , the higher beaxnos the froqutmcy 

; the 

range B temlnates Ughtly beyond that froquonq.) In the ruy C 

the correction factor is camposed of all three mecbanieal' elqants, i,e., 

marses and dampers as well as spring capblnations, The n-t pwk, 

4" (4 +-.6 /~c) f , fortunately occurs at a verg Mgh fn~amq, 

uld gonerally rill not affect the flutter analysis, 

dficimtly low f~um~ies, ire,, approaching static or 

rtady-state load conditions, the aerodynamic loiPd transfer funotioa 

becanes a pure spring conatant fonned by the eerier lishgo of the 

8pmr , d the effective m d c 

80Z'VO 4 

The spr- 4 , is effective over the f uemcy~ga A$ and its m1U 

Is derirable fmn q one of tho -tion755), (56), or (57). 

Sinoe flutter itself implies a dynamical condition, tho uJor 

of interest lies above the range A/ In fact, the tnsnsition ngioa 

B also includes fmquentios wwch are still well bolw those of the 

nost camonly enccmntered flutter dee. The range A' , thedore, 

ir the one most pertinent to the apalysis, The oxact tmfer hctlon 

/ cannot be obtained merely by adding a corrective spAq tern to 

the quadmtlc (~,s'f~s*-*(C) ; harover nunorim1 =loll.- 

tions for typical systans have shown that the oqairalent spring ia tho 

dynamical range Az is essemtially the series -ring cambination that 

would be obtained if the Wmullc systa were dared es a passim potwork. 

Sn othor ~rords, at sufficiently Mgh fmquson:ies $@ 8.1~00 action 

of the syatm is graatb auppresaed, axxi the effectivr in the 

v 4 is

or, ii the pinton s p w A, in f ~ t e , 

Mod static tent8 (ioeo, loading the surface and remuring itr dafleatione) 

vill not pmvlde a natinfacto~ nrann for obthhgj tho aborr 

spring conetento 

To numnarise,the following concluniosu ngardbg Horthrpp typo 

b@raulic-flutter nptan may be made: 

lo A Wraulic npt comctian factor r~rt bo added routerbllq 

to the no& A c e quadratic ( w,s'+ 4 s t4) 

to obtain the proper load trrranfer function, 

2. Only the range AI of Figo l8 is of intenst in tho prob1 

since the regions A, and 8 ark wll blow atrl tho mnge 

c in far above the normaw encomterod fluttu fnquacioa. 

3, In the nmg. of interest, Aa , the hydraulic vtr mar k 

viawed ensantially an a pan npring, an far an tho abnaae of 

phase lag t am in the correction factor in coacemed. 

The magnitude of this spring mmntant in apprwdrate tht of 

the nerles caabinatian of (1) the spring co~pUq,the hydraulic ~ W e r 

and the surface, (2) the hydmul3c oil wring, and (3) tho pinton rod 

nprln$ (ii finite).

A - cylinder am. 

a - coordinate of axis of rotailon of airfoil. 

% - orifice area 

- a< angle of attack. 

Be .- cylinder-piston damping coef ficiart . 

- 8; input damping 

piston-st ructure damping coef f iciont . 

4 - 

4,- 

- 

aynthatic damping coeff icimt 

Bs surface-structun damping coafficiart . 

b - half chord length of airfoil. 

8, - valve-cylinder damping coefficient , 

p - surface angular deflection. 

a - orifice coefficient. 

Cp - 

torsional stiffness of surface pr anit length 

- 

(about hinge me). 

slope of the fh-valve displacaart curve. 

(Zen, Dim.) 

R;$ 

rn-IT 

la-* 

no* 

(zero Dim.) 

Cp - slope of the fh-pressure differential cum. 

C, - cylinder-piston coulomb frictional forcer. 

C, - valve-cyljnder coulanb frictional forces. 

c - coordinate of dace hiag. lhe. 

- fi valve di6phc~0nt f- nmtml. 

E*- rteady atate valve displacaent (opomting point). 

L - valve displacament perturbation. 

(Zero Dk.) 

f - 

aerodynamic load at surface. 

P 

- gravitation@ constant,

$ - BZ~W~ 

pfY88WC)* 

- presstam on either side of piston. 

%r 

a 

gw- pertq&ed prumn on either side of pfrta. 

bp- proastam drop acmsa orifice 

& = volr~n.tric flow fran valve or flaw into cyIlador. 

a*= stead7 state mlu&ri!2 nln n~. 

p 

- 

volumetric valve flaw perturbation* 

p fluid density. 

S = Iaplaco operator, 

& = static manant per anit length of airfoil (wlfh 

rwpect to 6ude of rotation of airfoil). 

9 = static manant per rmit length of mrface, (with 

respect to eurface hinge line). 

t = the. 

v; = input vslocitJ.0 

y = input v.locit~. perturbationo 

w = specifia woight of fluid. 

5.. = input velocity portul.bstion (velocity soume). 

X,. = 

input displac.nent nlatin to atmcturo. 

Xi = input diaplacenrnt perturbation. 

& = cyllndor displacmmt relative to structuro. 

X, = cylhder diaplacaaent perturbation. 

XF= 

- 

pl6toa ciisplacemmt relative to structure. 

+ piaton displacmuent perturbation. 

X, - surface dlsplaccment relative to rtmotrur. 

(measured at cylinder horn).

Dirariau 

X, = ourface dirplacaont perturbation. L 

X; valve dirplac~t 

relative to rtructura. 

X,= 

valve displacaent perturbation. 

L 

Y = volrm.. 

8' = effective oil voltme within cy~lnder. 

p= 8 .a~ skate 0fl VOl-8. 

r/,I volrm. on either ride of pistono 

g 

T = time conatant, 

w = angular f nquency. 

w, = natural a&hr f roquetlq. 

J - -ping 

ratio 

IJOTB: 

All dirplacaentr, velocities, acaeleration, mrses, spriq 

canstantp, etc., an effectir. valuer rwrsand aoincidatt with 

or parrsUel to Ilae of aatim of ~Ilnder. 

(1) Feensy, To A., Vayermd Control8 Design Practiw at llorthrop 

Ai~~ftWS NO-+- Aircraft, Inc., 1949. 

(2) Lin, So N., "A Method of Successive Appmxiaetione af Evaluating 

The Real and Camplrr Boots of Cubic and Higher Order EqrrPtianrn, 

Journal of Mathtics and PhJrsics, Voltae XX Uo. 3, Augut 194l. 

(3) Th.old0r8.n~ To, wGmneral Thwm of Aerodyna~Ic In8tabillty and 

the Hecbani~~ of FlutteP, UACA TR 496, 1934. 

(4) Meher, Do To, WAn Aualysis of lorthp Airerait Parerad PU@ 

ContmlsW, lortbp Aircraft, Into 19490 

(5) Ino3Jsis of m e F-5 Autaaatic Pilot Applied to the Type P-89 

Aircnrft and Control Systan - Contract AP 33(038)-6946, llerthrop 

Aircraft, Into, 19500

INTRODUCTION 

PARAMETERS FOR THE DESIGN OF HIGH- SPEED 

HYDRAULIC SERVOMOTORS 

by HAROLD GOLD 

EDWARD W. OTTO 

VICTOR L. RANSOM 


National Advisory Committee for Aeronautics 

Lewis Flight Propulsion Laboratory 

Cleveland, 0. 

The servomotor dealt Kith in this paper is a power amplifying, 

positioning device of the type used in such applicatione as control 

valve positioners, flight controls and power steering devices. The 

hydraulic servomotor as a device has been known for approximately one 

hundred years. Its application to high speed machinery, however, appears 

to be relatively recent. There is consequently very little published 

literature on the dynamics of *is servomotor in spite of its long history. 

Nevertheless, when properly designed, the hydraulic servomotor is 

particularly suited for high speed service because of the extremely high 

force-mass ratios that can be obtained and because the device inherently 

is heavily damped. 

This paper is based on an experimental and analytical study of the 

dynemics of the hydraulic servomotor recently completed by the authors 

at Lewis laboratory and soon to be published by the NACA (reference 1) 

The results of this study have shown that although the response of the 

servomotor is essentially nonlinear and discontinuous, the response may 

be closely approximated with relatively simple linear equations. The 

present paper presents data demonstrating the nonlinear, discontinuous 

nature of the dynamic response of the servomotor and inqludes a derivation 

of the baeic analytical expressions for describing the response. 

The derivations wfiieh are presented in the "Analysis" section of this 

paper are essentially an abstract of the detailed derivations given in 

reference 1. 

The derived analytical expressions are summarized in the form of 

charts. By means of these charts the rational design of the servomotor 

to meet specifications on either the transient or the frequency response 

characteristics is made possible. 

DEFINITIONS AFSD IKMT& ASSUMET'IONS 

Straight line servomotor. - The elements of the straight line 

hydraulic servomotor are shown schematically in f imre 1. In the 

nkutral position, the spool member of the pilot valve closes the paesages

HYDRAULIC SERVOMOTOR 

SUPPLY PRESSURE 

-7 

U 

OUTPUT SHAFT 

ROTARY HYDRAULIC SERVOMETER 

PILOT VALVE e 

INPUT SHAFT 

OUTPUT SHAFT 

-597 

FIGURE 1

to the piston. When the spool member is displaced from the neutral position 

by mvement of the input lever at point (A), the flow of fluid 

through the pilot valve causes the piston to move in the direction which 

returns the spool to the neutral position. It follows from the geometry 

of the linkage that for every position of the linkage point (A) there is 

a corresponding equilibrium position of the piston. The description of 

several other forme of pilot valving and feedback linkage is available 

in the literature. 

Rotary servomotor. - The rotary servomotor is also shown schematically 

in figure 1. Rotation of the pilot valve with respect to the output shaft 

opens a pressure passage to one side of the vane and a drain passage to 

the opposite side of the vane. The vane is thereby caused to rotate in 

the same direction as the pilot valve. In the neutral position 'of the 

valve the passages to either side of the vane are closed. 

Initial assumptions. - The analysis which follows is developed with 

the following initial assumptions t 

1. The area of opening of the pilot valve varies liaearly with the 

motion of the valve. 

2. At fixed input, the ratio of pilot valve mvement'to piston mvemnt 

is constant. 

3. At all positions of the pilot valve the inlet and discharge openings 

are equal. 

4. The supply and drain pressure are constant. 

5. The compreseibi~ty and mass of the hydraulic fluid are negligible. 

6. Structure and mechanical linkage are rigid. 

7. Mechanical fraction is negligible. 

'8. Fluid friction losses in motor passages are negligible. 

9. Leakage is negugible. 

Response to a Step Input 

Baeic dynamic considerations. - Under the condition of no load on the 

output shaft and negligible internal motor mass, the pressure drop across 

the piston will be zero. The fluid flow through the cylinder is therefore

essentially unobstructed. The flow of fluid is then proportional to the 

area of the valve opening and the flow coefficient . At constant flow 

coefficient therefore the piston velocity is directly proportional to 

the valve opening. With rectangular valve ports the open area of the 

valve is directly proportional to the error of the piston position. The 

velocity of the piston is consequently proportional to the error. In 

the no load case therefore, the servomotor will exhibit a traneient 

response that is characterized by a linear first order system. 

The pressure drop across the motor is divided equally between the 

inlet and drain valve ports. 

Based on a constant flow coefficient, the piston velocity may then 

be equated to the flow through the valve ports by the, following relation: 

Equation (1) may be written in the form 

where 

The analysis of the response of the se~omotor under an inertia 

load is considerably more complex than in the no load case. Under an 

inertia load the piston is accelerated from zero velocity. There is 

consequently an initial period in the response during which the flow 

through the- valve ports is laminar, as a result of which the flow coef - 

ficient is subject to large variations. After the piaton hae reached 

the laaximum velocity in the transient, the momentum of the load may 

cause the flow of fluid into the upstream side of the cylinder to cavitate. 

The variation of the pressure drop across the piston is therefore 

not describable by a continuous function and consequently a single differential 

equation cannot be written for the entire traneient. 

In spite of the complex nature of the response there are basically 

only two phaees in the transient: the acceleration phase and the deceleration' 

phase. This conclusion, particularly with reference to a continuous 

deceleration phaee without overshoot or oscillat~oii, is baaed 

on the assumption of rigid oil and structure end zero leakage. Under 

these assuntptions the cylinder pressures during the deceleration phase 

are finite but may exceed physical limits.

Figure 2 shows an oscillographlc record of the response of a servomotor 

to a step input under a relatively heavy inertia load. The traces 

shown are: position responee, timing mark, downstream, cylinder pressure, 

and upstream cylinder pressure. The characteristic acceleration phase 

and dead heat deceleration phase are quite' clearly demonstrated. It will 

be noted that the downstream cylinder pressure exceeds the supply pressure 

in the deceleration phaee and at the same time the upstream cylinder 

pressure is driven to zero (cavitation occurs). 

Linear equation for approximation of the acceleration phase of the 

responee. - It is indicated by the measured reeqonee of hydrdlic servomotors 

under inertia loads that the acceleration phase may be approximated 

by a linear second order systein. The general form of a second order differential 

equation with constant coefficient may be written 

At m load the servomotor responds as a first brder system. Equation 

(4) should therefore reduce to equation (1) for the inertialess 

case. meref ore : 

At the start of the transient (t = + o), the upstream cylinder 

pressure Is equal to the supply pressure and the domtream cylinder 

pressure ia kual to the drain pressure . Hence when 

Substituting these values in equation (4) 

me differential equation that approximates the acceleration phaee is 

then

Equation (5) may be def bed in terms of the no-load time constant T 

and the reciprocal of the damping ratio. This quantity is here designated 

the "inertia index - E." The new term is employed in this paper becauee 

the term "bmging ratiow or other tern sometimes associated vith the 

reciprocal of the damping ratio would have no meaning in the type of 

transient associated vith the hydraulic servomotor. 

Equation (5) expreseed in terme of the parameters T and E 

is 

Equating like coefficients in equatione (5) and (6) 

Substituting equation (3) in equation (7) the general expression 

for E is obtained: 

Linear equation for approximation of the deceleration phase. - In 

the deceleration phase of the transient the pilot valve areas are reduced 

to small values. Consequently the flow rate through the vdves is 

affected to a far greater degree by the reducing value area than by 

variatione in the pressure drop across the valve. For this reason the 

reeponee in the deceleration phase does not deviate si&ficsatly from 

the no-load reeponee. Equation (2) may therefore be used to approdmate 

the deceleration phase. 

Evaluation of coefficient for the rotary. servomotor. - By means of 

a parallel development expressions for T and E can be obtained for 

the rotary motor. These expreesione are given below.

lication of equations. - The method of applying equations (2) 

the calculations of the traneient is presented in figure 3. 

As ahown in figure 3, the end of the acceleration phaee 1; defined by 

the inflection point of the solution of equation (6) for E > 1. For 

E < 1, the second order equation may be used to approximate the entire 

t&mient and therefore the inflection point need not be evaluated. 

Figure 4 is a plot of rise time against no-load time conatant for a 

range of values of inertia index. The chart is computed from the relations 

shown in figure 3. The rise time is defined as the time to reach 

90 percent of the flnal value. 

erinrntal response. - Figure 5 shows the characteristic agreement 

bctwe?calcuiated and meataured responses (reported in reference 1) in 

a series of rune in vhidh the factors that determine the parameters T 

and E have been varied. Ae can be sten, t& calculated rehnsee 

have provided a close agpmdmation of the actual responses over a wide 

range of conditions. It may be of particular interest to note that the 

effect of magnitude of the input step ars predicted by the approximating 

tiquatiom is evident in the measured responses. 

Peak cylinder pressure during a transient. - In a transient under a 

heavy load, the downstream cylinder presaure may exceed the supply pressure. 

For this reason an evaluation of the peak cylinder pressure is 

significant from a structural standpoint . It is shown in reference 1 

that the ratio of the mnxrnnlm cylinder pressure to the supply pressure 

is a function solely of the inertia index. The relation derived in reference 

1 is plotted in figure 6. Also ihom in figure 6 are experimental 

values reported in reference 1. 

Response to a Sinu~oidal Input 

Basic dynsmic considerations. - It has been shown that under an 

inertia load, the trans'ient response of the servomotor is nonlinear, 

The basic character of the transient response has been shown to vary 

with time in the transient. It can therefore be expected that the frequency 

response will also exhibit noanear characterXstics and that the 

basic character of the response will vary with the frequency of the 

input. 

Law frequency amplitude attenuation and phase shiFt. - At low fre- 

",.s..ln4aa +'ha err..-.-., &La& --& ^, &I-^ ^o rL- ---- r-- --- ----a. - 1

CHART FOR DETERMINATION OF TlME TO REACH 

90 PERCENT OF FINAL VALUE. HYDRAULIC SERVOMOTOR 

WITH MECHANICAL FEED BACK 

.NO LOAD TlME CONSTANT (TI SEC 

FIGURE 4 

MEASURED AND CALCULATED TRANSIENT RESPONSES 

OF A HYDRAULIC SERVOMOTOR 

I 

65 

- 0 

EFFECT OF LWD INERTIA 

,-GALCUTLATE! RESTONSE 

FIGURE 5

The solution to equation (11) , is 

iB 

The term Ae is a vector quantity having an' amplitude A and 

a phase angle fd. From equation (12) 

High frequency amgUtude attenuation. - At no-load the piston velocity 

is at all times proportional to the valve opening; therefore in the 

response to a sinusoidal input at no-load the pilot valve area is zero 

at the ends of the output travel (the velocity 'being zero). Under an 

inertia load the piston velocity is not linearly proportional to the 

pilot valve opening and hence in the response to a sinusoidal input the 

valve area is not necessarily zero at the ends of the output travel. If 

at high frequencies, the response of the servomotor is assumed to be 

essentially sinuaoidal, the maximum acceleration can be considered to 

occur at the Limits of the output travel and hence when the piston veloc- 

ity ie zero. Under the condition of negligible mass of the hydraulic 

fluid, the pressure difference across the piston at any instant when the 

piston velocity is zero and the pilot valve area is greater than zero, 

is the pressure difference acrose the servomotor. Above some frequency 

the system may then be approximated by a Unear system wherein the preseure 

difference across the piston varies sinurroidally with an amplitude 

of (P,-P~) and with the frequency of the input. On the baeie of this 

app~oximetion the acceleration of the piston is 

Integrating equation (15) and introducing the condition that x 

varies about zero and neglecting changes in sign

Dividing both sides of equation (16) by the output amplitude at zero 

frequency, the equation relating the amplitude ratio and the frequency la: 

The dimensionless quantity, inertia index, may be defined for the 

frequency response by replacing the magnitude of the step (s) with the 

term amplitude of the output sine wave at zero frequency (s'). Rewriting 

equation (8) and introducing the symbol (s') in place of (s) the expression 

for the inertia index for the frequency response is obtained: 

: ~quatio~ (3) and (18) substituted in equation (17) yield the general 

expression for the amplitude attenuation 

High frequency phase shif't. - The derivation of equation (19) does 

not provide relations by which the phase shlft may be computed. The 

amplitude attenuation expressed by equation (19),-is, ho&er, the 

asymptotic relation of a linear second order system. The phase shift in 

the high frequency band may therefore be considered to be described by a 

linear second order system. It can be shown further that equation (6) 

Straight Une representation. - The straight line approximation of 

the frequency response relations is presented in figure 7. In the low 

frequency band the amplitude is expressed by the aaumptotes of equation 

(13)

I 

RATIO OF PEAK TRANSIENT CYLINDER PRESSURE TO 

SUPPLY PRESSdRE AS A FUNCTION OF INERTIA INDEX 

HYDRAULIC SERVOMOTOR WlTH MECHANICAL FEEDBACK 

4' a / 

PZ MAX 

--- - E~ eZ 

Ps 14 77 

WHERE K = f i 

a 

- ANALYTICAL RELATION 

a 0 MEASURED VALUES 

INERTIA INDEX (€1 

v 

FIG~E 6 

SUMMARY OF LINEAR RELATIONS FOR M E 

FREQUENCY RESPONSE OF HYDRAULIC SERVO- 

MOTORS WlTH MECHANICAL FEEDBACK 

= 

APPROXIMATIONS OF ASYMPTOTES 

TO ACTUAL ATTENUATIONS 

",., 

1 

fi 

Lducr: 

, , DE,CAlXS PER DECADE 

e II[--j\l--66 

, , , - 

STRA~HT LINE APPROXIMATIONS OF 

- - ,:[ 1 ACTUAL PHASE SHIFT 

DEG PER DECADE 

DECADE 

STRAIGHT LINE 

SERVOMOTOR 

fpJ- T ApJZ m 

2x7 

-- 

ROTARY 

SERVOMOTOR 

hlL1-L:) 

T, JZC:WCQ 

R C R W 

2' 

-4 

XTE 

E'. 

f3. X+,Z ,, 4 c r ~ W -!w 

(h IL:- LA)* 

FIGURE 7 

I

The high frequency attenuation is expressed by the relation of equation 

(19) . The cross-over frequency is defined by the intersection of 

the low and high frequency asymptotes. 

Phase shift is represented by straight lines on semilogarithmic 

coordinates in figure 7. The slope of the low frequency line is defined 

by the slope of the first order system (equation (14)) at jd = 45O. The 

slope of the high frequency line is defined by the slope of the second order 

system (equation (20)) at $ = 90'. The low frequency phase shift line 

passes through # = 45' at the low frequency band break frequency ( fl) . 

The high frequency phase shift line is oriented by the cross-over frequency. 

In figure 7 the cross-over frequency is shown to occur after 

the low frequency phase shift line has reached the 90° limit. The orientation 

of the high frequency phase shift line for other relative 

locations of the cross-over frequency is shown in connection with the 

experimental responses. 

Experimental responses. - Figure 8 shows the experimentally and analytically 

determined effect on the frequency response of the hydraulic 

servomotor of the parameters: load inertia and input amplitude. 

Figure 8(a) shows the effect of load inertia on the amplitude attenuation 

and on the phase shift. An increase in load inertia results in a 

reduction in the frequency at which the attenuation becomes rapid. In 

the analytical expression developed in this paper (summarized in fig. 7) 

this effect is evident in the increased value of E' with increasing 

load inertia and the consequent reduction in the values of f2 and f3. 

Figure 8(b) shows the effect of input amplitude on the frequency 

response. The increase in input amplitude is seen to have an effect similar 

to that of increasing load inertia. This effect is made evident in 

the analysis by equation (17). 

In both amplitude and phase shift the agreement between the measured 

responses and the analytical straight line approximations is in general 

well within the experimental accuracy. The slopes of the attenuation and 

phase data clearly demonstrate the first order characteristics of the 

response in the low frequency band the the second-order characteristics 

of.the response in the high frequency band. The transition from first 

to second order characteristics at the calculated break frequency is 

quite pronojmced. 

APPLICATION TO DESIGlV 

Design Relations 

From equatiol23 (3) and (8) the following expressions for the piston 

area and the product of the feedback ratio and port xidth of a straight 

line servomotor can be derived:

Equations (21) and (22) are written in terms of transient response parameters 

but apply to frequency redponse parameters by replacing S and E 

with St and El, respectively. The corresponding equations for the 

varioue sizes of a rotary servomotor in terms of the various design 

parameters may be obtained from equations (9) and (10) in a similar 

menner . 

Equation (21) expresses the relation between the motor inertia ( roportional 

to 9) 

I 

and the various response parameters. Equation (22 

expresses the relation between the input inertia (proportional to RW 

and the various response parameters. The motor inertia and the input 

inertia are signif icant factors in the design of high speed servomotors . 

The following paragraphs will diecues methods for aiding in the selection 

of optimum designs to meet specifications on either the transient or 

frequency response characteristics. 

Determination of Design Parameters 

Load mass. - The value of M in the design equations includes the 

mass of the output part of the servomotor as well as the load mass. In 

high-speed applications the motor mass may be a significant percentage 

of the total mass. For this reason the estimated mass of the output part 

of the motor should be added to the known load mass. It is obvious from 

the character of the response of hydraulic servomotors of this type that 

the, responee~,characteristics for a given size are always improved by 

reductions in the load mass. 

Pressure differential across servomotor. - In general the size of a 

servomotor for a given response is reduced by an increase in pressure differential. 

The reduction in weight, however, is modified by the need for 

larger sections to withstand the increased pressure. The determination 

of the optimum pressure' is beyond the scope of this paper. The no-load 

time constant varies' inversely as the square root of the pressure differential'whereaa 

the inertia index is independent of the pressure diff 

erential. Therefore in a given servomotor the break frequencies. (f 

and f3) are proportional to the sqwe root of the pressure differential, 

and the rise time is approximately inversely proportional to the square 

root of the pressure differential.

Magpltude of the desired output. - Because the character of the 

response is determined by the magnitude of the desired output, a value 

of the output magnitude must be selected for design purposes. In general 

this information is obtained from the process which the servomotor is 

varying and consists of an estimation of the maximum percent change in 

the process tht is required to occur in a given traneient or sine wave 

oscillation. This variation should then be translated into the output 

stroke required of the servomotor to produce such a change. The total 

stroke of the servomotor will usually be larger than the design value 

of S or St and corresponds to.the steady state range through which 

the process is carried. If a step change or sine wave oscillation larger 

than S or St is introduced the resulting inertia index will be larger 

than that assumed in the design with the consequent possibility of damage 

from high peak cylinder pressures. Protection against such damage can 

be obtained by restricting the length of the pilot valve lands. 

Selection of no-load time constant and inertia index for frequency 

response requirements. - If the frequency response requirements of, the 

servomotor are known they in general will take the form of the first 

break frequency (f l) and the &oesover frequency (f3). The equations 

for T and E' in term of these two frequencies are as follows: 

As shown in the analysis the response of a servomotor of this type is 

characterized in both attenuation and phase shift by a first order relation 

up to the crossover frequency. The phase shift in this frequency 

band is therefore limited to a maximum value of 90'. The crossover frequency 

f3 can therefore be selected on the basis of sufficient amplitude 

attenuation at 90' phase shift to insure stability in the control loop. 

With fl and fg defined, the dimensions of the servomotor are established. 

Substituting equations (23) and (24) in equation (21) the following 

relation is obtained: 

4MS1p 

2 

flf3 

(251 

From equation (25) it can be seen that at a fixed value of 

fl an increased 

margin for fg can only be obtained by a proportionate increase in piston 

area. 

Selection of no-load time constant and inertia index for transient 

response requirements. - Transient response requirements can be expressed 

in tern of the time to reach 90 percent 'of the final value. The

variation of this rise time with T and E was presented in figure 4. 

It can be seen fmm figure 4 that a given value of rise time can be 

obtained at various combinations of T and E. The relation presented 

graphically in figure 4 may be exptessed approximately by the following 

equation : 

Equation (26) combined with equation (21) yields a general relation for 

the variation of piston area with inertia index. This relation is: 

Equation (26) combined with equation (22) yields a general relation for 

the variation of the product of the feedback ratio and the port width 

with inertia index as follows: 

2 3 

The terms (i + $1 and BG + 

in the above equations are proportional 

to Ap and FW, respectively. Thus the numerical values of these terms 

plotted as a function of E will indicate the variation of the size of 

the servomotor with inertia index. The resulting plot is showq in figure 

9. Ae a further aid in the choice of a value of E the maximum 

cylinder pressure which is a function of E is also shown. 

Figure 9 indicates .that values of E above 6 do not materially 

reduce the size oaf the servomotor and result in large values of msximum 

cylinder pressure. Values of E below 1 result in large servomotors and 

in general would be used only if it is desirable to make the response 

substantially first order. In this respect the above curves indicate 

that it would be very difficult to reduce E to values close to zero 

because the motor size and thus the mass of its parts become large, which 

will tend to increase E. Values of E in the range from 2 .to 4 should 

result in a servomotor that is very eatiefactoryboth from a size standpoint 

@ , from a response standpoint.

EFFECT OF LOAD INERTIA ON THE FREQUENCY RESPONSE 

OF A HYDRAULIC SERVOMOTOR WlTH MECHANICAL FEEDBACK 

:ALCULATED STRAIGHT 

LINE APPROXIMATIONS 

FREQUENCY-CYCLES PER SECOND 

FIGURE 8 

EFFECT OF AMPLITUDE ON THE FREQUENCY RESPONSE 

OFA HYDRAULlC SERVOMOTOR WlTH MECHANICAL FEEDBACK 

CALCULATED STRAIGHT 

UNE APPROXIMATIONS 

FREQUENCY- CYCLES PER SECOND 

FIGURE 9

CHART ILLUSTRATING EFFECT OF INERTIA INDEX E 

ON SERVOMOTOR SIZE 

FIGURE 10 

CONCLUDING l3mARKs 

The discussion has shown that the response characteristics of 

hydraulic servomotors with mechanical feedback may be represented by linear 

equations. These equations are defined in terms of the size of the 

servomotor and the load conditions. From these relations, equations which 

define the dimensions of the servomotor i n terms of the known load, and 

desired response characteristics can be obtained. BY means of these relations 

the rational design of the servomotor to meet specifications on 

either the transient or frequency response characteristics is made 

possible. 

1. W A Report. Dynamics of Mechanical Feedback-Type .Hydraulic Servomotor 

under Inertia Loads, by Harold Gold; Edward W. Otto, and 

Victor L. Ransom (soon to be published) .

APPENDIX - bsYMmLS 

The following symbols are used in this analysis: 

ratio of output amplitude at a given frequency to the output amplitude 

at zero frequency 

piston area, sq in. 

constant 

constant 

inertia index (transient response) 

inertia index (frequency response) 

low frequency band break frequency, cycles/sec 

high frequency band break frequency, cycles/sec 

cross-over frequency, cycle~/sec 

width of vane, rotary servomotor, in. 

polar moment of inertia, lb-in. sec2/rad 

inner radius, rotary servomotor vane, in. 

outer radius, rotary servomotor vane, in. 

lomi mass, lb sec2/in. 

upstream cylinder pressure, lb/sq in. abs 

downstream cylinder pressure, lb/sq in. abs 

drain pressure, lb/sq in. abs 

supply pressure, lb/sq in. abs 

ratio of valve travel to piston travel at fixed input 

ratio of valve travel to vane shaft rotation at fixed input, in./rd 

magnitude of step (measured at output), in. 

amplitude of output sine wave at zero frequency, in.

pa lo=$ $8 uoy$eyQd moy pamwam $ndqno JO uoy$yeOCI moa~[~$uw$euy 

pw;r 'Xmanbazj oaan $8 a ~ arqe a $nd$no JO apn$-mBm 

pw;r '(qndqno $8 pamwam) da$e JO. apn$m 

*ny 'pq $8 uoy$yeod m ay pammam $nd$no JO uoy$yeod moaae$m$euy 

3ae '$uayew;r$ JO may amy$

IMPROVEMENT OF POWER SURFACE CONTROL SYSTEMS 

BY STRUCTURAL DEFLECTION COMPENSATION 

JAMES J. RAHN 

EVERETT W. KANGAS 

Boeing Aircraft Corporation 

Seattle, Washington 

This paper is based on original work done by Mr. Howard Carson of 

the Boeing Airplane Company. The authors gratefully aoknowledg 

the cooperation and assistance of their Engineering colleagues 

at Boeing Airplane Company in preparation of this paper.

IMPROVEMENT OF POWER SURFACE CONTROL SYSTEMS 

BY STRUCTURAL DEFLECTION COMPENSATION 

Power controls for operation of aircraft control surfaces have 

become a necessity as a result of increased airplane sise, speed, 

range and control requirements. The direct feedback linkage type 

of powered surface controls presents the problem of stability 

versus respome. Thie is especially true when a large surface 

inertia ie coupled vith a relatively law structural spring rate. 

Although these systems nrny be eatisfactory for manual operation, 

they msy prove marginal or u~atisfactory when used with automatic 

flight control equipment. 

A moans for improving the performance of a mechanical-Wdraulic 

control syrtm hoving high surface inertia aad low structural 

spring rate8 has been dweloped and has proven quite ~uccessful 

on an airplane installation. In this discuseion we will first 

cover a basic type powered surface control system; Them it will 

be shm how a rtructural deflection feedback linkage can be added 

to the cystom to imprwe performance. 

A BASIC TTPE PCMER OPERATED CONTROL mTEn 

A powered surface control system operating a high inertia surface 

which had a low reaction spring rate me~y be limited in performance. 

To retain stability of the system the gain must be kept low, resulting 

in slow response which my make the system Inadequate for 

8atisfactoi.g airplane control. This problem was encountered in 

the dwelopment of a rudder control system which is described belaw 

and shm In figure 1. operation of the pilot~s pedals rotatee 

the torque tube Xi by means of cables. A differential linkage ie 

l0~8ted at the upper en3 of the torque tube. Since the surface ie 

initially stationary, the movement of the torque tube causes movement 

of the error link X, which is connected to the Wraulic control 

valve. Displacement of the control valve admits pressure to one 

side of the piston ecld opens the other side to return. The resulting 

pressure differential supplies the force to mom the ndder 

against inertia, friction, damping and air load. The follou-up or 

feedbncK link connected to the rudder and to the differential 

then moves the 3 ifferential to reduce the error to a minimum and 

closes the tgdraulic control valve. When the CIVW is a dniru, tb. 

valve ie in neutral and the fluid trapped on both side8 of the 

pieton holds the rudder in one position against variable loads. 

This eystem as first installed in the airplane, fignre 2, prwed 

to be unstable. Any disturbance to the control surface or to the 

pilot input resulted in a continuous oscillation of the eystem. 

To overcome this instability the system was slowed d m by reducing 

control valve gain. The net result wae a deterioration in 

performance and excessive phase lag. The combined lag of the

s u p p L y ' ~ ~ T ~ H y DTo RCYLINDER 

A uLINES 

L l c 

G. I - DIAGRAMATIC - TYPICAL POWER OPERATED RUDDER CONTROL SYSTEM 

RUDDER RUDDER HINGE 

FIN POWER CYLINDER 

CONTROL VALVE 

(ENLARGED)

FIG. 2 

INSTALLATION - POWER OPERATED 

RUDDER CONTROL SYSTEM 

WITHOUT COYPENSAT ION

power operated syetem and that of the airplane made pilot operation 

difficult and operation with the automatic pilot unsatiefactoxy. 

An analyeis of the problem indicated that the difficulty could be 

attributed primarily to the reaction epring rates of the sgsten. 

The structure of the reaction vetem had been deaignqd for strength 

in accordance wlth anticipated loads and not for rigidity and thus 

accounted for a large portion of the elasticity. The compressibility 

of the oil along with mansion of the power cylinder, 

I~~Iraulic tubing ard other components also contributed to the 

low overall spring rate of the qstem. Bending of a m and linkage8 

in the feedback system ad entrained air in hydraulic oil 

were recognised as other factors involved. 

1t was also found that the original ralw, although providing 

required gain at higher amplitudes, caused too high gain at low 

amplitudes resulting in instability. Other probleuw included 

backlaeh uxl play in the system which was attributed primarily to 

bearings and the movenent of the power cylillder piston "0" ring 

In its Nstardardm groove. 

Various changes to the syetem were made in an effort to improve 

performance. These included the design of a control valve whose 

gain varied as the square of valve displacement, use of close 

tolerance bearings ad bolte throughout, and use of more rigid 

feedback ad control linkages. The reaction structure was also 

etrengthened locally, but it was found that a large portion of 

the fin contributed to the spring rate. 

Althaugh some improvement was realited from this effort, it was 

apparent tMt the performance was still less than desired. Figura 

3 shows the frequency response curves of amplitude ratio ad 

phaee of the sgstem with these inprovements. 

The natural frequency of the airplane upon which this control 

system was being used is shown by the dashed vertical line on 

figure 3. .It can be eeen that the pawered surface control eyetam 

phse lag wae 70° for 11/4 degree eurface amplitude. For 

smaller surface amplitude8 the phase lag increased rapidly. In 

this rmga of unplitndes the combined phaee lag of the control 

syetsm and tht of the airplane approached a value so high that 

mfflcient phaee lead could not be realised from m automatic 

pilot to keep the closed loop sgstem stable. 

To be on the safe 

side the powered control system should ham less than kS degrees 

phase lag, for q amplitude at which the rudder is effectiw, 

at a frequency 5 times that of the airplane natural frequency.

AMPLITUDE RATIO- DB 

I 

0 

I 

0 I 

cn 0 cn 0 

E l I 0 

(0 

O G 

0 0 

0 0 

PHASE ANGLE 

0

~dditional means were tried in laboratory tests to improve performance. 

Damping in the feedback loop was tried, although better results 

were obtained, the installation complications did not warrant 

its use. The use of a double om rlng piston also helped to reduce 

phase lag by reducing backlash of the system. Although the improvement 

did not reach the magnitude desired, the double ROW ring piston 

was installed since bacldash uill deterlorate aw system. 

The main problem, that of low spring rates of the system, still 

remained, and prevented necessary increase in system gain to obtain 

better response. This problem can be illustrated by referring to 

a basic type power operated control system using a direct feedback 

linkage as shown schematically in figure 4. It can be seen that 

external disturbance to the control surface or mass results in 

deflection of the reaction structure. If the input system is held 

fixed while the reaction structure is deflected, the followup linkage 

opens the control valve in a direction to oppose this disturbance. 

~f the system has high gain, the control 'valve may admit 

enough energy to cruse the system to over correct the surface position. 

Due to the inertia of the surface the over correction causes 

a deflection of the structure In the opposite direction which in 

turn again opens the valve and again excess energy is admlttecl ad 

the cycle is repeated. If the energy admltted per cycle is equal 

to or greater than that extracted by aerodynamic damping and friction 

of the system, the surface will continue to oscillate. The 

amount of energy that is added to the gystem is prinudly detelc 

mined by the flow characteristics of the mstering vahe and mry be 

kept small if the flow per unit deflection is emall. Stability 

mey, therefore, be achieved by ube of a law gain valve. This 

improvement in stabil%ty of the system is obtained at the expense 

of speed of response. 

As very little can be done about the hydraulic spring rate and as 

the structure stiffness can be increased only to a limited degree, 

it was evident that some other means should be coxwidered to compensate 

for all of the system spring rates. 

ADDITION OF STRUCTURAL COMPE2SATION TO THE BASIC TYPE SISTBl 

High performance of a servomechanism cannot be obtained if lack of 

stability lindts the allowable gain. Therefore, the stability of 

the system is the gwerning factor. Improvement can be obtained by 

increasing either spring rate or damping or by reducing the mass. 

For this system the mass could not be reduced and adding damping to 

the output was not considered practical or desirable, leaving the 

reaction spring rate as the factor to be considered in order to 

Improve stability.

The overall reaotien rpring rate ir due to a rerier of rpringr. In 

tho sohematio. figure 4, they were grouped into 2 min rpringr, K8 

rtruotural rpring rate and Kh hpdraulio and other spring rater. The 

firrt problem ir to find a rsnr for Garuring tho rpring deflmotion 

thon seeond to find a ma- of uring this rgring defleotien to rtabiliw 

the rymtem. 

The rtruotural defleotion ir a oonvmiently rarurable quantity* It 

om be ured to represent the -tire rpring ryrtem defbotim if the 

propor ratio ir applied. Hw thir defleotim ir ured will be 8h.m 

analytioally. However, in order to provide the baris for the 

analytioal treatment of the subjeot, the rystem and it8 speratiaa will 

be explained first. Roof for thir explanation will then be given. 

In thir ryrter a mohanieal linkage is used te modify the ryrtem error 

in aooordanoe rith the defleotien of the reaotien rtruoture. Tha 

bario system of figure 4 rlth the addition of rtru0tur.l defl~~tion 

oempensatirn ir rhcnn in figure 5. AU external dirturban00 to 

the oontrol surfaoe or maor rill defleot the reaotien rtruoture* 

The follarr-up linkage rlll mols the oontrol valve to oppore th. 

disturbanoe in the same manner a8 illurtratad for the unoampenrated 

syrtem. The ooqtonratian linkage, horswp new alre add8 te the 

valve rignal. The direotion of the valve movemnt due to the 

oompenratiag linkage in opporite to tha valve movement introduoed 

through the follm-up linkage. By the proper urangsmsnt of the 

ratio between the reaotien oompenrating linkage and the follsr-up 

linkage the direotien and mmitude ef oontrol valm rovemont 01~) 

be varied. Tho mwemsnt of the oontrol valw ar a rerult of' an 

external dirturbanoe oan be aade to reduoe tb amount of energy 

added to the syltem or to extraot energy From the ryetom. For a 

rpoial linkage arrangemnt, energy rlll be neither added to or 

extraoted from the ryrtem. The added linkage oarr be mde to 

rtabilire the ryrtem regardlerr of the mpitude, dlreotion or 

origin sf the dirturbing foroe. Thir pormitr m inoreare in 

system gain te obtain improved porfo~oe. 

An malyrir of the ryrtem rhuur that the ryrtem atability ir dependent 

on a derived term whioh rlll be referred te a8 the 'Coqtonratien 

Faotor ."

FIG. 4 - SCHEMATIC - BASIC TYPE POWER OPERATED d 

m 

CONTROL SYSTEM - WITHOUT COMPENSATION 

3 RUDDER -

FIG.5 - SCHEMATIC -- BASIC TYPE POWER OPERATED 

CONTROL SYSTEM -REACTION COMPENSATED

In general, the value of Ks and Kf remain constant for a given 

system. The value of c ad d are usually defined by the geametzy 

of the mechanical input system and cannot be changed. By combining 

these tema the Compensation Factor reduces to a conetu~times 

the reaction compensation linkage ratio. 

To obtain a stable system the value of Cf must be equal to ar 

greater than 1. Actually the system becomes less unstable a d 

inrprovement is obtained even for values of Cf less than ond 

approaching 1. 

The above derived term for the Compensation Factor and the 

criteria for stability can be arrived at mathematically as is 

ehm by the following analysis. The symbol deflnitioars are 

included on page 12 and, refer to figure 5. 

The differential and algebraic equations for %he sgstsm are written 

as follaws: 

Summation of forces on the output member 

Sumfnation of forces on the reaction spstm 

From the geametq of the linkage system 

From the equation of continuity of hydraulic flew 

- Yv K.4 A, (x, + x 'h) 

Substituting equation (3) into equation (4)

With theae substitutions into equation (7) the dlffemntial equation8 

for the systaa becorn, 

Tho solution of these equrtions provldes the transfer -tion 

the syrtm in operator fonn 


An examhatian of this characteristic equation by mane of Routb 

crit8rion, and by assuming tint aerodJmrwic damping is saw 

although it t.ds to etabflise th syrtenn, it can be sham thnt 

the stability of th system ia depedent upon the 'Chponhation 

FautoP. The factor ia defined as 

for the eystem being analysed. For the systcrar to be stable the 

value of Cf muet be greater than 1, Neutral stability is obtained 

when Cf equal 1, 

By proper selection of linkage ratio8 the valw of Cf can, of course, 

be varied. For the epecial case of Cf equal to 1 tbm wlll be sero 

deflection of control valve slide mlativm to the slem for any 

dieturbance of the eystem. If Cf is leer thn 1, the control mlva 

slide movement vill be in the direction to oppore the oxt.mrl 

dieturbance, adding energy to the system ond tending to destabilise 

the -ah. This approaches the uncompensated -tan Mch hrs Cf 

eqd to tern. A linkage ratio resulting in Cf baing greator thn 1 

rill cause the control valve to mon in a direction not opposing 

the disturbance. This ixxlicater a 1088 of onrrgy fian the ayetom and

will result in a damping effect on the power control 678b. 

Obviously, where the rtabillty of the 6yrtQl ir of importame, oaly 

values of the capenution factor Cf equal to or gnator than 1 

are of intereat. 

To illuotrate the .application of the Colap~lsation Faator to oba 

linkage ratio for a stable rystem having Cf equal b 1, 

arauas tho follouing valwr: 

Tbontically u tho ratio of b to a bocorur largor, tb syrtr 

damping becomer gmakr, md u tho ratio get8 W e r it kdr 

to dertabilise the syrtem. 

Tho unc0mpamat.d sgrtom thmomtically ir armmod to bd inunrsible. 

Reverribillty here ir referred to ar dirp&comnt of the mtpt 

d e r d bear8 no relatiomhip to tho proportional pilot feel of 

control marface lod conaaonly refomad to in boort ryrtans. 

Act- it is rrverrible a8 tho valve deadspot .ad leakage -0% 

be reducod to sero, backlarh emmot be ontirely olblnakd, .ad 

thom will alwsgrr be a finik e&rticiQ In the sgrtm linkage. 

The companeated syrta ir tboretically rwaruible. The degree 

of revarribility d e r rtatic cditionr will be equal to Cf 

timer tho rmrritdlity of th. roaction sy&sm. 'For imtance, 

C equal to 1 the memibility of tho syrb king 

dlrcurrd I r approdnrtely .9 degne for. muhum load, Under 

n o d conditions with tho surface at or now rtrermlill. porition, 

the rurface lord8 will actually tm a null porcent of the .urilmma 

load ad the rsverribility willtm proportionally mallor.

Although only one type of power oontrol syrtem has been dieoussed 

here, it should be pointed out that the theory of structural 

defleotim oompensation applies equally -11 to ans basio 

poe itioning sys tom. 

Analpis of the system has ahm that the stability of the syrtem 

is primarily dependent upon linkage ratios . An evaluatim of a 

system for a desired oompensation faotor rill provide an approxiap.ta 

value for the required linkage ratio. In an aotual installation, 

it may be diffioult to aocurately determine the spring rates of 

the system, and tests mry be required to obtain the best liPkopp 

ratio as governed by desired symtem perf onmnoe. This prooedure 

was used in arriving at the optimum linkage ratio for the installation 

disoussed in this paper. 

A diagrwtio sketoh of the basio pwer control system with tho 

addition of the oanpensated linkage ie ahom in Figure 6. In tb 

aotual inrtallation as rhom in figure 7 it was neoessary to add 

five links to the original eystem. The nwnber of links required 

is prila~rily omtrolled by the physioal location of oaapmenta in 

the system. The applicati~n of this type linkage into a.sy8t.m 

already designed may be mere difficult than for a new system whioh 

oan be designed to inolude the simplest and most effeotive 

arrangemnt. 

The improvement in st+bility of this system rith ths addition of 

tho ompensating linkage permitted use of a higher gain valve with 

a nearly linear flow versus diaplaoement oharaoteristio. This 

resulted .in a higher performance system for all amplituder. The 

value of the canpensation faotor for this system as installed in 

the airplane was approdmately 1.1. 

The degree of imprmmnt of the actual airplane installation is 

shm in figure 8. This is a representation of the power oontrol 

syatem performance'. It can be seen that the phase ohraoterirtior 

of the rptem have been improved oonsiderab2y war the uuo0mpenaat.d 

syrtem as shown in figure 3. For better oomparison, figures 3 md 

8 are both shom in figure 9. It rhould be noted that the 

amplitude at whioh the oolapensated system was tarted 1.8 only 

fl/L degree as oompand te tl-l/LO for the morpluated ry.tem. 

This to ahow e m more the degree of imprmunt whish 

ma obtained, a8 the reapse of a system pnemlly beeomor 

poorer rith a deorease in amplitude.

& 

" A-. 

'9. TAB 

10. ,ROD Jd 

I 

2- - 

RUDDER-BOOST VALVE 

CONTROL ARM 

r 3. FIN 

1. RUDDER 

r23.1 

ACTUATOR ARM 

BY-PASS 

VALVE 

1 

SHUTOFF 

VALVE- I 

C Y 1 Jl2 TAB-LOCK ARM 

(V- I B . 1 3 . TURNDUCKES 

d"!? 11 

INSTALLATION 

FIG. POWER 7 OPERATE1 

RUDDER CONTROL SYSTEM 

4. HYDRAULICALLY-OPERATED 

I, ann=n n.4 I A-u RFACTlnhI r.numcucarcn 

3 

17. TURNBUCKLE ACCUMuLATOR ROD

0 

AMPLITUDE RATIO- D8 

I I 

I I 

rU rU 0 

I + - + 

UI 0 UI 0 UI 0 UI 0 

I I 

AIRPLANE NATURAL FREQUENCY - ------- -- 

---- 

-- 

UI 

I 

I 

I 

/ 1 

/ I 

A 1(. 

- 

I I I I 

0 

1 I I I 

I 

0 l 

0 

cP 

0 

a0 0 

0 

0 

0 

PHASE ANGLE

IMPRESSED FREQUENCY - RAD/SEC. -L 

FIG 9 - FREQUENCY RESPONSE - WITH a WITHOUT COMPENSATION 

N) 

w

In the range ai airplane natural frequenoy, the phre lag of tho 

pmred rurfaoe oontrol ryrtem h r been nduoed to 20'. m n though 

tb airplane phare lag (rudder ncnenmnt to ow) ir approrirkly 

90' in thir Srequmoy range, tb total kg ir ruduoed to a value 

ruoh that the moerrary phare lead om be realired in m automatie 

pilot in 0rd.r to athim ratimfactoq overrtl porforrurrre. 

The final mluatien of the ryrtem, of oourre, depend8 on performmoe 

on a flight tort airplum. The ryrtem whioh h r been dirourred 

here proved suooesrful in eliminating steady rtak oroillatianr and 

improving maneumrability and perfomoe for automat10 pilct 

operation. 

1. The perfornnoa of a mohanioal-hydraulio rervo ryrtem ir 

liaikd by the reaotien rpring rate. 

2. This limitation om be emroom by utiliting rtruotural 

defleoti on feedbaok* 

3. The rtruotural defleotisn feedbaok linkage om be desipud 

to aompensate for a11 defbotions of the ryrtm. 

4. Capensation rerultr in a rererribb ryrtem proportional 

te elartioity of maotion struoture. 

5. Higher responre of the ryrtem can be realired with 

rtruotural defleotian feedbaok rerulting in isprored parform- 

.no.

A SURVEY OF SUGGESTED MATHEMATICAL METHODS 

FOR THE STUDY OF HUMAN PIWT'S RESPONSES 

by EZRA S. KRENDEL 

The Franklin Institute 

Laboratories for Research and Development 

Philadelphia, Pennsylvania 

During the last decade considerable effort has been directed by 

several laboratories, both in this country and in England, toward the 

solution of the problem of rationally characterising the human operator 

of various type8 of control equipment. The goal of this research has 

been the determination of what might be called humen "transfer functions," 

where the term transfer function is used in a loose 8ense. In general, 

the work has dealt with problems arising in gun directing situetione. 

Although relatively little effort has been concetned with the study of 

the guidance problems arising in the control of aircraft, the display and 

aontrol problems for sighting system and aircraft have sufficient similarity 

to make the suggested methods of study applicable to both problem. 

The purpose of this paper is to state some of the pst suggestions for 

appropriate ma thematical models to describe human operator performance, 

and to present some of the current thinking at The rh-anklin Institute on 

the problem. 

The problem under discussion arises from the control situation 

wherein an operator is attempting to orient a device so that a visually 

perceived error may be minimized. Figure one represents this situation in 

a simple tracking task which was Fnvestigated at The Franklin Institute. 

The specification of the transfer functions in this figure is only for 

explanatory effect. The humen element in this control system consiets of 

the eye, which is the primary error sensing mechanism; the nerves, which 

are the data transmission system; and the arm muscles which are the motor 

system. It is, however, necessary to specify more about the situation. 

Since the operator is largely non-linear, the stimulus must be carefully 

- 

specified. The visual signal can be characterized by the degree to which 

the operator is able to predikt the stimulus. Close to perfect prediction 

can be achieved either by having the future behavior of the signal disclosed 

to the operator over a length of time greater than his reaction tlme plus - 

movement time, or by conveying very little infomation in the visual stimulus 

by presenting the useful past history of a signal the future of which 

is determined simply from its past. ' Ekamples of the first type of easily 

anticipated signal arise in the driving of an automobile; whereas an exemple 

of the second type of predictable signal would be the tracking of a siapple 

sine wave. The display which a gunner sees in his sights or which a pilot 

sees when getting on target differs from the foregoing in thet the possible

Figure 1. 

anticipation of the target's motion is limited by the narrow field of view 

as well as by the conditions generating the motion, such as evasive maneuvers 

and unforeseen random dls turbances due to gust6 . It can be seen f'rom the 

foregoing examples that any study of human responses must carefully consider 

the nature of the visual Input because of thia anticipation characteristic 

of the operator. 

Another well-Imom characteristic of the human operator is the ability 

to adjust to and compeneate for specific tracking problems and specific 

equipment. For example the operator is able to adjust his response to take 

into account friction, different control ratios and other aspects of 'the 

equipment. Similarly the operator is able to adjust his response with regard 

to instructions such as "track accurately,""track rapidlyn or in the case of 

aircraft flight to meintain a smooth course through a series of gusts instead 

of attempting to compensate for each one. In addition the operator's behavior 

is capable of changing as a function of bxperience and training in any particular 

tracking task. 

The foregoing characteristice point up the difficulties in attempting to 

arrive at a linear, time invarlnt, description of human operator behavior. 

In addition 'this non-linear nature of the human operator makes any character-

imation of the humrn mom or lur prtioulrr to the oiroume tama under 

which the mwsuromentr were mde. Thum, If a tramfor or, mom pporly, 

desoriptiw funotion oan bo determined for the. operator, it aan only bo 

epeolfled for a given olasr of input sigpala, for a given pieoe of applrat-, 

a d for givon Inetruotiona and degree of praotioe. In additlimp 

thb function will exhibit variations arising from the Individual diifbrencee 

in the sampled population of subjeotr. If a Uneer operator 

description is to be attempted, thia Idnear operator expression will Mve 

valldity only in discussing behavior with input8 roughly similar .to the 

inputa wed in the measuring experimsnts. Conaequantly, a statistical type 

of input f'unotion seeme appropriate. 

The following la of neoeasity a vary brief intqodwtion to some of the 

attempt8 to deal with the foregoing problem. Among the earlieat attem~ptr 

to charaoterise the human operator's operation were thoee by R. 5. Phi Ups 

a d A. ~obcayk;' and R. H. Randall, F. A. Rumrell and 5. R. Raprrini. 4 

The ,Phillips equation for dbscriblng handuhwl oontrol which uns developed 

for a study of aided traoking assumed that the operator generated a 

velooity proportional to the valw of the error a d to the rate of chbnge 

of the error all delayed by a time lag, L. Thuo the handwheel velocity , 

pH(t) oould be mittan In tm of the eqmr signal Input ~ (t) aa followrc 

Both b and c are parameters, and p is the uowl diifemnti.1 oprator. 

Rendall a@ his coworkers evolved an expression for dmoribing human 

operator behavlor which add8 derivative control to the farogoing caprersiqn 

so that we have; 

The coefficient of the additional tom ia a pramkr, a. 

~ w ts tudied d the problan #omowhat more elaboretoly by aruting a 

rigM1 oompored of three harda and det.rmining an appxiPute linear . 

law by meens of harmonio analysis of these throe oomponsntr. Trurtln considered 

the bandwheel diaplaoement and ermr sip1 to bo oompored of 

components dssorihble by this linear law a d a rammnt dw to nonlinearitiw 

and noiso. TwtIn arrived at an equrtion of tho folhuing 

form;

The constant k helped to improve the fit at low frequenciee. Using tuo 

cam apeeda Tuatin studied eight frequencies from .018 to204 cp. 

L. ~uesell~ in a recent MIT meatarts thesis conducted an eate~ive 

series of experiments in a stdy of linear approximatione to human tracking 

behavior. He used a beet linear model plue noise approach and 

employed a signal of four harmonica whioh odd be presented at three 

speeds. He thus had a range of from .Q442 to 1.43 cp in the input 

signal. Russell evolved an eqmtion similar to the Phillip equation. 

Russell indicated that the husrpn appears to adjust hia response parameters 

in order to minimiru, the meen square error in tracking a signal of given 

power epectrwn. In addition the humen appeera to set hla gain at a value 

yielding a reasonable margin of stability. It is well to point out that 

the parameters found for the four preceding operationel ~preseiona were 

all different. The fact that a, b, and c differed indicates thet the 

human's response ia peculiar to given apparatus and display problem. 

The variation in L from .3 eeconda to .5 seconds is probebly a function 

of the training of the operators and the predictability of the signal. 

North? in a reoent paper on the humen transfer Function, he8 developed 

a sophisticated framework for the study of human transfer functions. 

A mean linear operator of simple form is postulated and in addition the 

cbracteristice of a superimpdeed stochastic distribution are discussed. 

In simple position treickfng North postulates a relation of the form 

as the mean steady state operator; and, in addition, he posits a treneient 

which is kept in a state of continuoue excitation by the stochastic 

elements. This problem is studied by a epstem of finite difference 

equations as well as by differential equations in vim of the evidence 

for discontinuity of human operator tracking responses. The discontinuity 

arises from the fact that there ia a refractory per,iod in tracking since 

the human appears to prseet reaponsee in accordance with his beet esthate 

fro@ available data, and that these responses, once initiated, can not be 

cksnged continuously. The stochastic process arises from two sources8 

one, is inaccurate eathatid of the input signal, and two, is the inability 

of the operator to perform the appropriate response.

There has been some work done at. The F'ranklin Institute on the 

problem of studying human frequency response with the view in mind of 

obtaining "transfer functions ,It on a project sponsored by the United 

States Air ~orce.6,7,8 The method which this project has selected for 

studying the human operatorts frequency response is the comparison of 

the output spectral density to the spectral density of the visual input 

using a random signal as the input. Such a comparison yields utleFul 

informetion whether or not the human operator behaves in a lineer 

fashion. Were a linear aystem under study, it can be ehom that the 

amplitude part of the systemle frequency response is equal to the square 

root of the ratio of the speotral density of the output to the spectral 

density of the input. A complete description of the linear eyatem would 

reqnlre the cross spectral density of the output and input so that 

phase as well as amplitude characterietics could be specified. Since 

the computation of the cross spectral density would have required twlce 

as much work as the computation of spectral densities, it was decided 

that only the amplitude response would be computed in the preliminary 

experiments. The main purpoee of the preliminary experimente, the 

apparatus for which was a simple compensatory position tracking device, 

was to determine whether the foregoing input-output analysis was a 

suitable method for analyzing the data of more ambitious experimente using 

a dynamic flight simulator for a high speed jet fighter built by The 

Franklin Institute Leboratories. The random input function was obtained 

by constraining a pip on an oscilloscope to take positions on a horizontal 

axis alternatively to the left and to the right of a vertical 

fiducial line so that the number of zero crossings were described by a 

Poisson distribution. In order to make the display somewhat less 

predictable the amplitudes to the left and to the right were rtandamly 

selected from a Gaussian population of the same mean and standard 

deviation for amplitudes to the left and to the right. One of the underlying 

reasons for selecting a random time series input was the belief 

that the human operator is largely non-linear. This particuhr random 

time series had a specitrum which was similar to the spectrum of atmoepheric 

turbulence. 

In order. to add psychological interkt to the investigation of the 

applicability of the analytical procedures, three questions were examined. 

Does the operator track the random input in a linear fashion? How does 

his behavior change as a function of practice? How do different instructions 

affect his response patterns? The question of linearity was 

examined by comparing the amplitude frequency response for two subjects 

when tracking a distribution whose mean absolute amplitude was one 

centimeter and when tracking a distribution of mean absolute amplitude 

equal to two centimeters. The effect of practice, i.e., time variation 

of the system, was exambed by comparing the output of the two subjects 

when naive and when hi.ghly trained in following a certain random input 

signal. The effects of instructions to track for accuracy and of 

instructions to track for speed were compared for two subjects in order

to determine if there was behavioral evidence in the output spectra 

for two different sets to respond. 

An example of the we of spectral densities for examining behavioral 

characteristics can be seen in figures 2 and 3 which illustrate a comparieon 

of smoothed spectral densities for'two different instructions 

for one highly trained subject. It rill be noted that Inatrbtione for 

accuracy resulted in a considerably smoothed output. The fiducial lines 

represent 2 t confidence bands arising from instrument errors in the 

computations of the spectrum. 

In general, the experiments were not of sufficient magnitude for an 

adequate test of the psychological questions raised. On the other hand, 

the form of the results indicates the fruitfulness of this method of 

analysis and its logical extension to the interpretation of tracking 

dat'e from the dynamic simulator. 

At present the dynamic simulator has been used for a small experiment 

utilizing three trained jet pilots. The data obtained, which is 

in the form of responses to gust inputs, will be used to obtain certain 

order of magnitude approximetions to "humen transfer functions" using The 

Frenklin Institute Advanced Time Scale Analog Computer. The general 

research program for the study of the human operator envisione the use 

of special data reduction equipment to be constructed at The Franklin 

Institute for the determination of the pertinent spectral densities and 

cross spectral densities.

7 

135 

REE-CES 

James, Nichols, Phillip : Theory of Servomechanisms. 

Laboratory Series, Vol. 24, 1947, pp. 360-368. 

Radiation 

Randall, R. H., Russell, F. A., and Rsgassini, J. R.8 Engineering 

Aepecte of the Humen Being ae a Servomechaniem. Unpubliehed 

mimeographed no tee, 1947. 

Tuatin, A.: The Nature of the Operator's Reeponse in llanuel Control 

and its Implications for Controller Design. Journal Institution 

of Electrical Engineem, Pert 11 A, No. 2, Niay 1947. 

Russell, L. : Characterietics of the Human a8 a Linear Servo-Element. 

Sc.M. Thesis, Mass. Inst. Tech., Cambridge, Mass., May 1951. 

North, J. D.: The Human Transfer Function in Servo Systems. 

Minis try of Supply, Report No. ~iRD/6/50, November 1950. 

Krendel, E. S.: A Preliminery Study of the Power Spectrum Approach 

to the Analysis of Perceptual Motor Performance. UW1, Vright- 

Patterson Air Force Base, Dayton, Ohio, AFTR 6723, Oct. 1951. 

Krendel, E. S. : A Spectral Density Study of Tracking Performance, 

The Effect of Instructions. Uw, Wright-Patterson Air Force Base, 

Dayton, Ohio, !uADC TR 52-ll Part 1, Jan. 1952. 

Krendel, E. S. : A Spectral Density Study of Tracking Performance, 

The Effects of Input Amplitude and-Practice. U W , Wright- 

Patterson Air Force Base, Dayton, Ohio, TR 52-11 Part 2, 

Jan. 1952.

SYNTHESIS OF FLIGHT CONTROL SYSTEMS 

by DR. JOHN G. TRUXAL 


Purdue University 

Lafayetfe, Indiana 

During the past year Purdue University has been privileged to have 

a contract from the Office of liaval Research to investigate design techniques 

for power boost systems for aircraft control. We at Purdue feel 

that the university research groups can not, and should not, be in direct 

or indirect competition with industrial research. Rather we feel that the 

primary job of university research should be the development of basic 

synthesis techniques. 

In line with these aims, our prima~g interest has been in the investigation 

of the basic general problem of the stabilization and design of power 

boost qystems. He have attempted to clarify and delineate the problems 

involved in this design and to develop and determine those design technique8 

which will be generally applicable in this problem. We have not worried 

particularly about specialized methods of stabilization which might be 

applicable to one aircraft, not to another. Rather, our main concern has 

been with methods which we hope will be generally: applicable; in the absence 

of any one specific problem, we leave the more specialized techniques to the 

industrial research groups. 

What is the fundamental problem? As we see it, the problem arises from 

a basic conflict between speed of response and stability. On the one nand, 

we have the speed of response of our control system; on the other, the 

stability of the overall aircraft. The relative location of these two 

conflicting requirements depends on a number of factors--e.g., the aircraft 

speed. As long as we are dealing with low-speed aircraft, there is essentially 

no problem. At low-speeds, a relatively sluggish aircraft response is permissible. 

In addition, the aerodynanlical characteristics of the plane itself 

may be relatively stable. however, as the required aircraft speed increases, 

two things start to happen: the speed of response must be increased; the 

relative stability of the aircraft decreases. Inevitably, as we demand better 

and better perforlance frdm our aircraft, the problems involved in realizing 

a system which is sufficiently stable and at the same time responds with 

adequate spee4 becomes more difficult . 'tie feel that we are now at the point 

where design has become difficult, particularu in those cases in which we 

deal with the aircraft as a gun platform. Essentially, the situation here 

is no different t t u that in ~nany fields of engineering. TPis is a universal 

phenoniena--this development of tauter and tauter specifications, as the years 

go by; this demand, as these specifications become more taut, for a more 

complete understanding of the basic system--and in particukr a fuller understanding 

of what factors influence the system performance. 

Chw first concern then has been with a deten~unation of those factors 

which do determine the stability and the speed of response of the aircrafts

with a control system actuated by a poner boost system. The syatsan we have 

considered is shown in Pig. 1. Our cgr6tam consi8ts basicaUy of five parts. 

Working from the stick to the control surface, from lef't to right on the 

diagram, we have first a mechanical coupling system, between the stick and 

the hydraulic power qystem. k here represents the compliance of the push 

rod. or control cable from the stick to the input to the Wdraulic gyetm. 

The damper fp aad lnrrsr % represent the impedance seen looking into the 

input to the-bdraulic Getem from the output d of the control cable. In 

our initial &udy of the qystm, ws have a 8 d that these parameters are 

irdqandent of the gain of the Wdraulic system. I will have &re to say 

ooneerning these oimplifying arsumptionr later. 

The inprt to the hydraulic system is the displacsmsnt xp. 

We consider 

a singlbstage maulic system, with an output displacement + actuating 

the bell crnk to give a deflaation of the control surface & . The normal, 

or vertical aeceletration of the airplane, n, is detarmined by this deflection 

through the aermcsl characteristics of the aircraft. The artificial 

fael ~8'km Vb is the 8-108t po88ibh8 COM~S~* OW of the 

bobweight of mas8 rmnll n. We do nat Imply that this is at all typical of 

general artificial feel ayrtaw. Certainly our system probably should 

include at least a spring. Howwer, we feel very strongly, as I shall txy 

to point out later, that the desis of a witable artificial feel qpstsm 

depends on consIdaration8 of dynamic &ability (and when I speak of stability, 

I refer to dpadc stability) and the nature and characteristics of the pilot 

in the closed loop system. We feel, and perhaps you will agree as wd continue, 

that this simple bobweight system suffices as an emample of the general 

prooeduree and ideas I hope to present to you. The introduction of a spring 

does not, for e~mple, materially change our development. 

Figures 2, 3, and 4 show the basic components of our syetem in more 

detail. Figure 2 shows the aerodynamic axes a& basic equations, Plg. 3 

the stick dynamics and Fig. 4 the hydraulic qystem. The pertinent equations 

accontparUr the figures. A considerable portion of the &fort of the Purdue 

group over the past year haa been spent in the aualyds of the bdraulic 

system, the development of measuring techniques and the correlation of valve 

configuration with static and dynamic characteristics. Homera today I would 

like to consider the hydraulic valve as described simply by the flav-proportionalto-displacement 

equation, which is an adequate deecription over the frequency 

range of interest to usa and oadt any detailed disoussion of other possible 

linear and nonlhear analytical descriptions of the system. 

Referring again to figure 1, ue see that there are basically two feedback 

eystcms to be designed-the &draulic system, ach is a closed-loop, positional 

feedback ggstem, and the overall airplane control system which contains 

the 4ydrauU.c loop ao one co~lponent. OPT initial interest at Purdue was 

concentrated on the waulic system, but it rapidly became apparent that 

this one component could not be intelligently designed or andlysed without 

c~neideration of the overall qyatem. I mid like to speak briefly about the 

stabilization of the maulic system and then consider in more detail the 

desi- of the overall loop.

The hydraulic system itself is a high-gain feedback ayetern. The 

load parameters of the hydraulic qystem are the effective mass of' the 

elevators, the aerodynamic spring rate and the damping, both the aeromeal 

damping and that associated with the =in power piston, In 

addition, the compressibility of the oil acts essentiallg in shunt with 

the main load, since the flow of oil can go either into compression of 

the oil or into motion of the main piston and control surface. Up to 

reasonably high frequencies, typically in the order of magnitude of 15 

cps or above, the open-loop hydraulic system integrates, or, if we look 

at it from the frequencp-response standpoint, the gain drops off inversely 

proportional to frequancy, Aa we reach the frequency at which resonance 

oocure between the oil compressibiUty and the load, the output tando to 

inorease. In other words, in this b a of frequencies the aofnpre5aibUty 

effeat is such that it tends to increase the motion of the main piaton. 

When the main piston is moving to the right, for example, the oil in the 

left cylinder is expanding, tending to give the piston motion an extra push. 

This resonance phenomena is very lightly damped due to the low frictional 

losses in the systam. When the hydraulic loop is closed, through the 

input -age, the system will ordinarily oscUte with an amplitude 

driving the system into the nonlinear region of oscillation. In certain 

cases, these nonlinearities, inherently preaeat in the system, or the 

frictional losses which we have neglected tend to stabilize the wetem, 

but the relative stability is poor. 

Thie resonance phenomena, and the consequent instability or poor 

relative stability occurs at such a hi* frequency compared to the siepificant 

frequencies of the remainder of the overall aerodynamical systcrm, 

it doe6 not appear troublesome on the surface. The main difficulties arise 

because these frequencies are, however, of the same order of magnitude as 

the flutter frequencies of the aircraft. The coupling between the flutter 

system and the Wdraulic and control system may cause undesirable amgUfication 

of the flutter amplitudes. 

This coupling between the unstable hydraulic system and the flatter 

system and the resulting tendency to increase flutter troubles can be 

circuw~ted in either of two ways. First, we might simply cut off the 

Wdraulic wstem at a frequency mch lower than the band of frequencies of 

significance 'in flutter phenomena. Seconily, w mi@t try to increase the 

relative stability of the hydraulic system while maintaining the high lowfrequency 

gain. The first solution is certainly the simpler. The principal 

disadvantage of this method of cutting off the wdraulic system at low 

frequencies is the resultant sluggiah response of the overall aircraft 

system, or even of the wstem from the stick to the control cnrrface. This 

relationship betwema the bandwidth and the tims de4 or time of the transient 

response is nothing quantitative, but in general it can be said that, if the 

aystem is suitably damped so that there is not undesirable overshoot in the 

transient response, the time required for the wstem to respond to a step 

function input and essentially reach the steady state is inversely proportid 

to the bandwidth. In particular, if the bandwidth is one cps, as an example, 

the system will respond to a transient input in something like one-half to one

second, at least to the proper order of magnitude. Thus, if we attempt 

to rid ourselves of the trouble with the relative or absolute instability 

of the hydraulic system by cutting down the bandwidth, we soon reach a 

point where the time of response of this part of the overall system becomes 

undesirably long. In one sense, this is indeed an unfortunate circumstance, 

since the bandwidth of this part of the system can simply be reduced by 

cutting down the gain, the bandwidth being r0ughJ.y proportional to the gain 

over the range of frequencies of interest to us. 

The second alternative for eliminating the undesirable effects of 

coupling between two highl~ underdamged system--the flutter system and 

the hydraulic system--involves stabildnation of the hydrado system wNle 

maintaining the hi& gain essential for fast response. The diagram of 

figure 5 indicates the difficulties involved here. As it now stands, the 

hydraulic system is charact eristied by a transfer function-the Laplace 

transform of the ratio of the output over the input-with three polesone 

at the origin, and the other two a conjugate complex pair very close 

to the jw-axis. If we use the root-locus method of analysis we can see 

at once the effect of closing the loop with varying amounts of gain. In 

particular, we study what happens to the poles of the closed-loop transfer 

function of the hydraulic system as the gain is increased. For very low 

values of gain, the poles of the closed-loop system function are identical 

with those of the open-loop transfer function. As the gain is increased, 

the poles of the closed-loop system function move toward infinity, the 

location of all the zeros of the open-loop function. The particular paths 

taken by these poles as the gain is varied are shown in Fig. 6: one moves 

out from the ori- along the negative-real axis, the other two move away 

from the conjugate cornex pair of poles over into the right-half plane. 

For a relatively low value of gain, these poles have crossed into the righthalf 

plane, indicating that the closed-loop system is unstable. 

How CM such a system be stabillzed? There are a variety of nays, im 

terms of the pole-zero loci, and then a number of ways in which these desired 

changes may be instrumented. We consider only one general method in any 

detail. The furdamental difficulty is the proximity of the conjugate poles 

to the jW ds. This arises because of the very sharp resonance betwem 

the compressibility of the ofl and the mechanical and aerodynamical load. 

This resonance can be msde less sharp, and also incidentally moved to a lower 

frequency, if the compressibility of the oil can be effectively isolated from 

the load--in other words, if at the same time the expanding oil is giving the 

piston an extra push, there exists an alternate network which is absorbing 

this extra effective flow. One possible system for doing this is shown in 

fig. 7. 

Hare in Fig. 7 both the hydrauuc-mechanical system and the equivalent ' 

electrical network are shown. In the equivalent circuit, the load corresponds 

to the series resonant circuit made up of LC, Rc, and Cc, repressnting 

respectively the mass, damping, and compUance of the aerodynamical and 

mechanical load. The oil compressibility is represented by the parallcondenser 

C. The resonance phenomena, speaking in electrical terms, ie

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of the stabiUzation systau 

Poles introduced by the load characteristi- 

Poles (at over 1000 rad/aoc) representing 

resonance of stabilization qyetem with 

compressibility and load not shown 

0 Zeros 

x Poles 

Determination of Opem-J.aop Poles with Compmsation 

Fig. 8 

Closed-loop pole 

positions for gv - 80 

'.\ \ 

0' 

. ----- *---/- I"" 

,X 

Open-loop trander function of 

the stabilleed system 

Closed-bop Poles for Compensated @)retm 

Fig. 9

By way of introduction to this problm, I wauld like to revert for 

a momsnt to some of the ideas expressed in the axcellent papr we heard 

on Tuesdey rnornbg by Mr. Andrm of Hughes Aircraft and presmted bgT 

Mr. Turner. In this paper it was rather forcibly pointed out that we 

are rapidly rea- the point where we must design our porn boo& 

control system to meet quantitative speclfioatiom concerning both 

stability and control. I like to think of the situation in something 

like the foIloving light, with a very s-6 analogp. I picture the w 

control system designer in a position somewhat analog~ls to a &ernyew 

old boy in a baseball game. An the game start@, the other bags are 

all under ten years old; the mere presepce of our slxtem-year old is emougb . 

to throw fear into the opposition, Just es in the early years of pmr boost 

system, the mere presence of the control wet= desiepar and a little 

imaginetion on his part solved the problems. As the game plogresses, however, 

older boys arrive. Our aixtegt-year-old has to work to get his base hits. 

He begha to look amuad for a better bat and tools; he starts to consider 

using a little stratem instead of the previous brute-fome tactics. In an 

analogous manner, the control systems engineer starts to adopt same of the 

servomechanism theorg--the use of Nyquist diagrams that have been mentioned 

several times here during the past few days, for axample. BLlt unfortunately, 

the game has not yet stabWed. For, approaching our ballfield are a half 

dozm professioaal ball players, eager to get into the game. Our sMemyear 

old is wing to have to call on all his ability if he is to hold his 

own. In our inmediate problm, we see these professional ball players as 

the problems associated with our planes flying at a Mach number of &5. 

If we are to design successflrl power-boost aystams and tactically-capable 

aircraft operating at these high speeds, it seerme imperative td us at Purdue 

that all available knowledge be brought to bear on the problem. We feel 

that in a few years, when we are confronted 

- 

with the design of the power 

boost systems for these high-speed aircrafb, there will be no accuse for 

us not h a m a understanding of the problem and a general idea of a suitable 

approach to the aolut ions. 

What specifically are the problems associated with the design of a highperformance 

power-boost wstem? Thw are in number. We wish to mention 

only a few of them today in any detail. The problem we have heard most about 

at this meeting is the design of an appropriate artificial feel system. I 

feel, howemr, tinat this is only one of the basic problems. It has received 

considerable attention here during the past few days principally +cause it 

is a problem which is already confronting the engineer. Of a perhaps !laore c 

basic nature, however, are the twin problem of stability and control. Indeed, 

the satisfactory solution of the artificial feel problm can only be arrived 

at in conjunction with at least partial solutions to the stability and control - 

problems, for the artificial feel system is an integral part of the overall 

loop which does determine both the relative stability and the control charact'eristics 

. 

What essentially are the problems associated with control and stability? 

The most pressing problem, it seams to me, is the development of a more

explicit set of specifications-or a more quantitative description of 

the behavior we desire from our system. Some of you ~lvyr say that quantitative 

specificstiona can not be written--instead we nust be satisfied with euch 

specifications as the statement-The airplane mst fJy satisfactorily. 

This field of engineering is not alone in this difficulty of writing a 

cpantitative set of specifications. The seruomechaniem field in general 

is plagued by the same difficulties. I have heard maqy tin108 the et,atemsnt-- 

We want a real fast servo that has practically no aror--or somuthing 

equally vague. If there is to be logic to the eyetom design, the first 

step involves making this specification quantitative. Indeed, when this 

is done, the problem is half solved. 

In particular, what specifications are appropriate to the aircrai"t 

control problem? We consider still, for the sake of explicitness, only 

the longitudinal control system. 1i-1 addition, we consider on. 

the 

performance specifications, taking the word performance in its conmon, 

narrow meaning, and excluding such factors as the maxhm~ allowable 

acceleration, etc. We consider only specifications governing the etabillty 

and dynamic performance in general of the aircraft undsr small daflections 

of the control wface. 

The specifications, it seems to me, should include at least the following 

quantities: the relative damping of the overall aircraft system, the damped 

(or undam~al) natural frequencies af oscillation, the low-frequency gaia of 

the system, and the thm lags in the various parts of the system. The firat 

two quantities, relative damping and oscillation frequency, dot elmine the 

relative stability . The third quantity, the low-f requency gain, datemines, 

essentially, the effectiveness of the feedback, the abillty of the systan to 

continuously calibrate itself, reduce the effect of nonlinearities, aDd control 

the effect of corrupting signals entering the system (for example, wind gusts). 

Thg last quantity, the time lag In the various system components, measures 

the speed of response of our alrcraft. 

Other quantities will of course have to be specified qventuaUy,in the 

complete problem. For example, we are interested not only In the low-frequency 

responee of the system to wind gusts, but also the overshoot and sattlhg timb 

associated with the response to a gust of wind. However, the above four 

parameters will give us a basis for the remainier of this paper. 

Ql the bade of specifications of this sort, at least the prelhhaxy 

design of the syetm can be aarried out on a logical basis. The dismssion 

here is samewhat difficult, because the two aepecte of control and stability 

can not be divorced, but I shall try to indicate the general tra of a 

method which we think is reasonable for design. Mrst, let us consider the 

stability problem. does the system basically tend toward instability? 

And does the stability problem become more difficult as the speed of the 

aircraft increases. In the very simple system we are conaideriag here (shown 

' in Fig. 1) significant phase lags In the system are introduced from two

eutione, the aerodynamics and the contrdl stiok dynamicre If the phugoid 

motion and very low frequency behavior is neglected, the a-cr 

behaver essmtially as a sewnd-order rgrstem, with a tranefer f'unction 

of the form ahom in SQ. 1. The relative damping ratio assoaicrted wlth 

the conJugete pole8 here ir in our arample about 0.4. At'high apwds, 

this relative damping ratio could be axpected to go or low as 0.1 or lesr. 

Additional phaae lag is introduced in the uontrol stick dynamics, the 

medwiaal vtan frm the control otick to the input to the hydraulic 

~grrt-. The ~grutm wr ere oonaidaring here ir ahom in Fig. 3 atxi ha8 

en rppmxbate tranafer funotion af the form: - 

The overall open-loop systsm th& has a transfer function proportional 

to the product of these two individual functions. 

K 

Sfs+8.Z)(sZ+ 7:l.s tC3) 

The corresponding pole configuration for the open-loop wstem is of the 

fom shown in Pigo 10. 

We now consider what happens as we close the loop and bring up the loop 

gain from a very low value. The poles of the closed-loop transfer function 

move in the maaner shown in Fig. U. For relatively low values of loop gain, 

the closed-loop system is unstable. How can this ~syotem be stabillzed? In 

particular, haw can the system be stabilized at a value of loop gain vrNch 

is mfficie~lrtly high to insure that we have adequate control characteristics? 

The first and mgot obvious method is to introduce a device to cut the qotem 

off, at least part way, at very low frequenciee-a device which the electronic 

engineer wuuld term integral control. Such a device necessarily tends, as 

we saw earlier, huuever, to decrease the speed of response of the system. We 

have felt that the primary Job of any stabilization that is introduced should 

be to force the airplane to respond more rapidly than the aerodynamical 

uoefficients would ordinarily allow. Certainly, at least, thq stabilization 

system should not make the system more sluggish. 

Considering this pole configuration, one possibility is irmnediately 

evident. We might attempt to move the pole due to the stick dynamics, wr 

at-8.2, so far out into the l&-half plane that the system essentially 

reduces to a third-order rither than a f ourth-order system. This can be 

readily accomplished as shoun in Fig. U simply by an increase in the value 

of the damping.coeffic5mt fp. There are two difficulties that arise at 

once however, with such a scheme of partial stabilization. Flrst, the force 

- 

required of the pilot to move the stick at a constant velocity, when he is 

moving essentially against this damper, increases intolerably. Secondly, 

the time lag betwleen the stick and the output of the hydraulic ~ s t e ~ 

increases proportional to this damping coefficient. In particular, this 

time lag, assuming the hydraulic system acts instantaneously, is given tgr 

the ratio of the damping coefficient, fp, to the spring constant of the 

push-rod, k, as is shown in appendix A. Thus, about the beet we can do

her@ is to lnake the push-rod as stiff as possible, and increase the 

damping fp as much as pemissible and then live with these components. 

It appears then that in the absence of the abillty to effect arg 

'remarkable isprovaments in system components, the stabilloation of our 

system with the simultaneous realization of high performance characteristics 4 

demands the introduction of additjanal components. We ask ourselves what 

distortion of the pole confiwation we mw have for the opm-loop system 

would result in desirable characteristics. One particuhrly si@e 

configuration is shown in Fig. 13. We leave the two poles due to the 

- 

stick dynamics at the origin ard -8.2, but move the conjugate compleeg 

poles due to the aerodynamics either onto the negative-real axis or at 

least well out into the left-half plane. Now what happens as we close the 

loop and increase the gain? The poles way out to the left are of little 

interest to us. The imporLant loci are those stemming from the two poles 

on the negative-real axis and close to the origin. At low frequencies, 

these poles move as a function of gain in the manner shown in Fig. U. 

the addition of a zero at -10 and the moving of all other poles way out 

into the left-half plane we have kidded these two poles into thinking we 

have a configuration of the farm shown in Fig. 15. It is not until we 

reach reasonably large values of loop gain and fairly high frequencies, 

that these two poles realize the deception and bend over toward the righthalf 

plane. Then if we keep the gain at a value corresponding to these 

poles located at the points A and 81, we have a closed-loop system, an 

overall aerodynamical system, uhich behaves eesentially as though it had 

this pole-zero configuration. The response is characteristized by one 

pair of conjugate complex poles at a reasonable damping ratio and a dipole 

on the negative real axis. The transient response will be roughly of the 

shorn in Fig. 16. 

dseenthlly the earns results can be achieved by a slightly different, 

and basically more logical approach. Suppose we simply start off by saying 

that we want a transient response of the form shown in Fig. 16. Int us 

write the overall syatm function, the Saplace transform of this transient 

response. We denote this desired closed-loop transfer fundion as ~(8). 

horn this ~ (a) we determine the required open-loop transfer function, which 

we migbt call p/q, the ratio of two polynomials in s. This opan-loop 

tranafer function, ~/q, is related to ~(8) a8 s hom at the bottom of PZig. 17. . 

p and q, the ~xumrator and denominator polynomials of the open-loop tranafer 

function are readily determined from this relationship. p is simply the 

numerator of ~(8). q is simply the denominator of ~(8) minus the numarator, 

and can be determined in factored form by a simple graphical subtractian, 

- 

plotting the polpomials for negative-real values of the variable s. A plot 

of this form is &awn above the equations in Fig. 17. 

Let us review for a moment., We have said that our fundamental 

philosophy in the design of the power boost system' should be something 

like the following: We first decide on suitable specifications for our

91 '))M 

o=oa WTM F' 

om* 03 eeuodra me*&

particular problem. We then choose a transfer f'unction which yields 

these specified characteristics. The last step in the design involves 

the instrumentation of a sgstau which will yield our desired transfer 

function. Several of you w i l l undoubtedly object to this general approach 

which re are postulating. me principal objection possibly wlll be that 

we can not in general force our aerodynamical system to behave in any 

we want. Wa know, for exi%&ple8 that we can not d d an overall widean 

function of unity in practise. That is, we can not expect to realise a 

power-boost control stick aption, with absolutely no time lee. However, 

we are obviously being ridiculous in asking for performance of this qua,lity. 

Clearly, m, are Uted in attainable performance by the saturation of the 

control surface effectiveness. What our stabilisation and' equamtiaa 

sgstau is doing is anticipating the lago axi instability inherent in the 

aerodydos and stick dynamics and attempting to compensate. 

Up to this point the design of the cprotsm is straightforuzmi, follawing 

lines well established in the servomechanism field. (I of course do not 

mean to imply simplicity by the mrd straightfommi). If the control system 

is electrial in nature, or at least contains certain electronic wmponents, 

the compensation can be conveniently and readily introduced. However, if 

the control system is mschanical-hydraulic systa~, the design of suitable 

compensation networks is not as straightforward. The Purdue University group 

is now investigating a &or of lnechanical and hydraulic circuits which look 

promising for the accomplishment of this compensation. The design of 

comgcmsat$oa networks is made diffioult by. several factors which can not 

readily be expressed enalytioallg, but which are of paramount importance 

if the networks are to be of practical value. First, we hew felt that 

comparnsation mst be accamplished simply. We do not feel that rrr, can introduce, 

for exa@e, a large number of nonlinear circuits or complicated circuits. 

Secoadly, the synthesir taf suitable mschanical-k@raullc networks is complicated 

by the requirements on the allowable forces against which the pilot will have 

to work. In other rrords, networks introduced in that wction of the system 

which we kve called the stick dynamics ~ilrst not lead to rmdesirable forces 

referred back to the dick bandle. Thirdly, it is verg difficult, If not' 

hpOSSibl@8 to &idpate diific~lties With distributed fri&i0n8 &C b 

the last aaalysis, the propriety of any system mrst doped upon W a . 1 

tests. At this t-, we have not yet reached the point where we are able to 

present experimental data. 

- The basic type of compomtion which seema to be most dfectirs theoraticalls 

is a lead form of network. A generalized. form of tranafer function 

for th. desbed conrpensation network ;auld of the fomt 

sa+2&d,,a +w, 4 4 b 

sttas +A* 

Ye have spont eorm time investigating ,the poesibility of instnmnanrting 

mechanically and hydraulically a transfer function of this type and feel 

that a twin-T qgetga of the fora shown an Fig. l8 holds eoneiderable prauise. 

The mechanid sohematia ia shown at the top of the page and a &doh of 

the qgsta~ at the battm. Referring to the sketch, the top half of the 

twin-T is realiaed by the center tm springs atxi the orifice, the battau 

U of the twin-T by the tm end orifices and springs and the hydraulic

coupling between the tm ends and through the line shown above the main 

part of the figure. The output spring, shown in. the schematic is not 

shown on the figure at the bottom of the page. 

* 

There are a number of other systems which accomplish essentially the 

same results, but the difficulty of realizing a decent range of element 

values has led us to consider a schane of this sort in s om detail. For 

the stabilization of the control system with the numerical parameter values 

used as an example during this paper, the spring and damper values for the 

twin-T shown here coma out to be of order of magnitude yielding time constants 

of about 1/10 secord. Specific values depd on the location in the ~ystem. 

The element values can be readily determined'using the methods of network 

synthesis well known in electrical engineering. 

Clearly a findamental question is the proper location of thls twin-T or 

any other form of compensation network in the overall loop. The answer to 

thls westion depends on a number of theoretical factors (e.g., the effect 

of loading at either end of the network on its characteristics, the effect 

of the loading on the rest of the gystem produced by the network, etc.) as 

well as such practical factors as space avadlability, effect of failure, etc. 

One possible scheme is shown in Figure 19, where the compensation network 

is inserted at the input to the hydraulic system. 

Two comments are appropriate at this time concerning the stabilization 

and compensation concepts discussed in the past few minutes. Eirst, it is 

clear now, I hope, why we feel that the entire westion of artificial feel 

is one which can not be divorced from the stability and control questions. 

In the airplanes which have been discussed during the past few days, the 

performance characteristics have been sufficiently low, in mimy cases, so 

that the artificial feel system presented a more or less isolated problem. 

However, as the satisfaction of performance specifications becomes more 

difficult (and we do not envision this as being too far in the future) the 

artificial feel system and the characteristics of the pilot (or at least 

some generalized description of these characteristics) must be of basic 

importance in determining system stability and controllability . 

If the stability and controllability problams are to be resolved without 

unnecessary difficulties, the feel system must be designed as part of the 

overall loop. 

The second comment I would like to make at'this time concern8 the effect 

of nanlinearities in the various system components on the stabilization 

procedures we have discussed. ~hese nonlinearities are, as I see it, of two 

general types--the nonlinearities of specific hardware, as the hydraullo 

system. Xe feel that nonlinearities of this type can be controlled and 

kept small enough to make a linear analysis and -thesis at least a good 

first order approximation. In the last analysis', final adjust~nent must of 

couree be done axperbentally. The second type of nonlinearity is perhaps 

more troublesome. I refer to the changing aerodfnamical coefficients Kith

changing flight corditions. Idea-, one would design dynamic compensation 

networks, as suggested in some of the earlier talks--compensation networks 

which would be automatically compensated for c-ng longitudinal velocity, 

eta. If the compensation is effected entirely electricalJy, thle dynamic 

cornpensat ion can be approximated fairly well, although the complexity of the 

instrumentation necessarily is greater than with a linear qystem. If as we 

have tried to suggest in the past fm moments, the campensation is effected 

hydraulically and mechanically, dynamic compensation is a more difficult 

problem. Ae yet we have done nothing along this line. 

I would like to summarize briefly. We feel that the time is rapidly 

approaching when the stability and controllability problems of design will 

be of paramount importance. We feel that it is essential that logical 

design procedures be established in anticipation of these difficulties. 

logical desiep prodwe must proceed from quantitative 8pecifications. 

It must lead to suitable general networks for accomplishing the cornpeneation. 

We feel that conpensation system can be determined which will essentially 

force the airplane to meet the selected performance specifications. The 

realization of these compensation systems can be accoqlished electronically. 

We al8o feel that compensation can be effected hydraulically and mechanically. 

We believe that there is a great deal of work yet to be done in evaluating 

various Q-draulic-mechanical systems for compensation, in studying the 

effects of various locations of these networks in the overall system, in 

considering the poabibillty of using parallel compensation, and in the 

related probldl~lb. 

The system. I have ueed throughout this paper as an ~ l of some e of 

these ideas is about as simple a system as one can devime to scoomplish even 

theoretically the desired control. We feel that it is essential that mare 

complar (and reallatie) system8 be considered from this standpoint of 

stabillaation devices. appreciable complication of the system will 

necessitate going to computer and simulator studies, as the introduction 

of additional degrees of freedom rapidly places the complex it^ of the wstsa 

beyond the bounds of human comprehension. Thus far, we have not done Whlq 

appreciable with d o g computer studies, as we have felt that intelligent us. 

of ccenputer data required a solid understanding and background in the behavior 

of simpler elystams.

Int e~pretat ion of Specificat ions in Tenas of Syat em Parametera 

Specification on low-2requency loop gain: 

At low frequencies, open-loop transfer function behaves as 

$ is directly related to the polee and zeros of the closed-loor, 

transfer function: 

Specification on time lag between stick mtion and nrotion of control -face: 

Denote transfer function from stick motion to control surface as: 

= J(s) 

xsb) 

Then with constant velocity input, time lag (steady-state) is: 

with our unstabilized system 

specification on stability r 

A specification that the short period dynamic oscillation of normil 

acceleration shall be damped to 0.1 amplitude in one cycl* msane that if 

the response is primarily controlled by one pair of condugate complex polee, 

the associated relative damping ratio should be greater than about 0.37. 

4 i) .So Air Force Specification No. 1815-B

A,. Area of bydraullc jack giston. 

c, ceJ cn# &S % 

Parameters In electrical system nrrrlngcrus to bydmullc 

aystsp! vith compensation. 

Damping coefficient of mechanical linkages. 

f~ 

fn ~~mping coefficient of bydrau~c agrstcm canpamator. 

c Damping factor in hydraulic systsla loed. 

pa Bob weight acceleration force. 

8 Aoceleratiata of gravity. 

H(8) Overall system finetion 

h(s) Denanbator polynomial for H.(B) 

J(s) *stem function from stick to control 8uriaee. 

K Gain constant. 

k Spr3.ng constant of prsh rod from stiok to qydrrulla qpd& 

kc A-c force spring rate. 

k e OF1 oompressibility spripg rate. 

KQ Qnirau3.i~ elyatan control valve gain. 

k, Spring constent of wraallc qgstam wmpn88tioa nstworlr. 

=, Velocity constant. 

1 Born we-t mss. 

Msc@anicsl linkage mass. 

Wp 

n, Cantrdl column mass. 

Hc EXfectiw mass of elwator. 

n, kes of 4pdraul.i~ system ampmeation nstmrk. 

n &ad factor. 

P Pressure across hydraulic jack. 

PI, p2,. . Negative of poles of trandar hnctions. 

~[s) Nunrrtrator po- far ~(s). 

s 6) ~emdnator polyr~~ndal fool opgl loop trandor hmcticm. 

fa 

Net rate of flow through bdraulic qpstm aatrol valm. 

8 Isplace transform variable 

t Timb 

Time Lag from stick to cc4rtirol surface. 

Tlag 

U Average f OM airplene velocity. 

5 

Inpllt to hydsaulic Iaystmn 

=c Output displacement of maulic qstm. 

% Valve displaament 

Control coluaP diaplauenmt 

]b Mechanical linkage displaaaernnt.

'b 

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