FinalPaper 315 Latest

8/10/2019 FinalPaper 315 Latest

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Flight Control Systems and AutopilotsBrian Jewell

Department of Engineering, Calvin College

Engineering 315 Final Paper

Professor Ribeiro

Abstract: Autopilot systems have been crucial to

flight control for decades and have been making

flight easier, safer, and more efficient. However,

these autopilot systems are complex devices that

require precise control and stability. These

systems usually include a form of digital control

systems to allow for easier implementation. One

example, the eaver Autopilot system, uses an

inner, outer loop system to maintain control while

simpler systems often only require something as

simple as a !"# controller to keep the aircraftstable.

1. Introduction

Since te creation of te first aircraft, te

abilit! for people to travel large "istances in

relativel! sort perio"s of time as "rasticall!

increase"# $owever, in te beginning of te

airplane age, traveling on tese craft was "iffic%lt

as tere are man! components of air travel an"

controlling tese components can be an e&tremel!

"iffic%lt tas' for a pilot# (n mo"ern aircraft, tereare simpl! too man! tings for te pilot to control

tem all so some form of a%tomation m%st be

"one# )lso, long air trips can ca%se problems for

te pilots# *ile te plane is traveling along te

same tra+ector!, fl!ing can an" "oes become a

rater monotono%s +ob for te pilot an" te pilot

r%ns a iger ris' of falling asleep or s%ffering

from a re"%ce" response time# For tese reasons,

a%topilot s!stems ave become a blessing to te

aerospace in"%str!#

$owever, tese a%topilot s!stems are not

simple s!stems# e! re-%ire comple& control

s!stems wit rob%st meas%ring e-%ipment# escope of tis paper is to give an overview of

a%topilot s!stems .wit a "escription of "igital

controls/, to e&amine te Beaver )%topilot S!stem,

an" to e&plore a simple fligt control e&ample#

2. History

e earliest form of a%topilots ave been

in e&istence for "eca"es# e first s!stems were

create" an implemente" abo%t ten !ears after te

*rigt Broters flew te ver! first airplane0 te

itt! $aw'# ese earlier s!stems were simpl! a

g!roscope tat gave te plane a smooter fligt

pat# e onl! control tat tese s!stems gave was

in te altit%"e an" pitc# e! 'ept te plane from

fl!ing wit its nose pointe" "own an" from fl!ing

croo'e"#

)ro%n" te time of Secon" *orl" *ar, tever! first f%ll! f%nctional a%topilot s!stems were

"esigne" an" teste"# ese earlier s!stems a" te

capabilit! to 'eep te fligt pat level as well as

la%nc an" lan" te aircraft# is revol%tionar!

s!stem, owever, was not a simple tas' an" it was

prone to fail%re# e s!stems wo%l" often brea'

"own an" cras te plane .b! ma'ing te plane

point straigt "own as oppose" to straigt forwar"#

o 'eep te s!stems operating properl!, te plane

re-%ire" a crew tat was more tan twice as large

as te original a%topilot2less planes# is ca%se"

problems beca%se it too' far more wor' to 'eep tea%topilot wor'ing tan it "i" to act%all! fl! te

plane wito%t s%c a "evice# For tis reason, te

a%topilot was not %se" ver! often for man! !ears#

(t wasnt %ntil te 146s tat te "evice reall!

too' off .to %se an atrocio%s p%n/# )t tis point,

more sopisticate" s!stems were being intro"%ce"

an" a new form of fligt control was in te wor's0

a comp%ter controlle" fligt# is tecni-%e calle"

7fl! b! wire8 "i"nt become a stan"ar" %ntil closer

to te 96s b%t it a" its beginnings in te late 6s#

e basic concept of te 7fl! b! wire8

s!stems is "igital control s!stems# o %n"erstan"

tis form of a%topilot a brief "escription of "igitalcontrol s!stems m%st be "isc%sse"#

3. Digital Control Systems

(n a t!pical control s!stem, te e-%ipment

to meas%re an" control signals can be e&tremel!

complicate" an" can re-%ire enormo%s levels of

sopistication# $owever, if it were possible to %se


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a comp%ter to control te s!stems, a simple 7off

te co%nter8 processor co%l" be able to an"le

comple& control s!stems# For e&ample, a s!stem

tat re-%ires complicate" matematical algoritms

for control co%l" simpl! "igiti:e te signal an"

sen" it to a processor to ta'e care of te

calc%lations# e processor .%s%all! calle" a7minicomp%ter8/ is %s%all! ine&pensive an"

relativel! eas! to implement# e control s!stem

%sing tese sorts of "evices is sown below in

Fig%re 10 Digital Control S!stem Bloc' Diagram#

$igure %& #igital 'ontrol (ystem lock #iagram

(n tis s!stem, te "igital comp%ter rea"s in te

"igital signals from te fee"bac' loop an" te

inp%t an" it sen"s tem to te D;) converter# is

converter ta'es te "igital val%es from te

comp%ter an" converts te signals into a %sable

val%e for te act%ator an" process# e signals are

ten sent via te fee"bac' loop tro%g te

meas%rement sensors %ntil it reaces te analog to

"igital convert# is portion ta'es te meas%re"

val%e an" converts it into a binar! "igital signal

tat can be rea" b! te comp%ter#

is "igiti:ing is were te real callenge

enters into te pict%re# Since comp%ters cannot

rea" te same 'in" of signals tat an analog "evice

can, some meto" of transforming te analog "ata

to rea"able "igital "ata m%st be intro"%ce"# is is

"one tro%g a meto" calle" sampling# ) simple

circ%it is set %p wit a switc .sown below in

Fig%re


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)s can be seen b! te above plot, te "igital signal

is no longer a smoot c%rve# Depen"ing on te

sampling rate .in tis case, once ever! secon"/ te

val%e is meas%re" an" ten el" constant %ntil te

ne&t val%e is meas%re"# For a "igital control

s!stem, tis val%e is converte" into a binar!

n%mber tat is ten fe" into te minicomp%ter foranal!sis#

is sort of s!stem is e&tremel! beneficial

to te aviation in"%str!# *it a "igital control

s!stem, te a%topilots can ave a m%c more

precise control of te fligt pat of te aircraft#

Rater tan fee" te controlle" signal .s%c as

altit%"e or !aw/ tro%g a comple& process .wic

wo%l" be e&tremel! "iffic%lt to "esign/, te signal

can be converte" to a "igital signal an" sent to te

minicomp%ter# (n te minicomp%ter, te signal can

be operate" on wit a iger level of ease beca%se

te comp%ter can "irectl! r%n te algoritms on te

"igital n%mbers# is meto" can !iel" a iger-%alit! control s!stem for te aircraft# )lto%g it

"oes re-%ire more circ%itr! .te minicomp%ter/ it is

%s%all! smaller an" easier to implement bac'%p

s!stems#

*it tis general %n"erstan"ing of "igital

control s!stems, te Beaver )%topilot S!stem is

te foc%s of te rest of tis paper# is "igital

control s!stem overview will elp %n"erstan"

some of te m!ster! of te proprietar! .an"

terefore %n"isclose"/ portions of te Beaver

s!stem#

4. Beaer Autopilot System

e Beaver a%topilot "oc%ment tat is

%se" for tis report entitle" 7) Sim%lin' oolbo&

for Fligt D!namics an" Control )nal!sis8 an" is

written b! @arc Ra%w# is "oc%ment "escribes

te Beaver s!stem in great "etail an" "isc%sses its

implementation in te Fligt D!namic Control

toolbo& for S(@G=(H# $owever, since tis

toolbo& was not written b! te S(@G=(H people,

te stan"ar" S(@G=(H pac'age "oes not contain

tis toolbo erefore, for an! attempte"

sim%lations, reg%lar S(@G=(H will be %tili:e"an" an! %n'nown f%nctions will be estimate" as

best as is capable b! tis a%tor#

4.1 Functions

e f%nctions of an a%topilot s!stem can

be bro'en "own into two ma+or categories0

g%i"ance an" control# e g%i"ance f%nction of an

a%to2pilot "etermines te spee" an" te co%rse to

be followe" b! te craft# is is "one b!

meas%ring te c%rrent act%al val%es an" comparing

tem to some reference s!stem# e control

f%nction is te f%nction tat ta'es te "ata from te

g%i"ance s!stem an" applies te propercorrections# For e&ample, if te g%i"ance sa!s tat

te altit%"e of te aircraft is


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Figure 6: Block Diagram of Longitudinal Mode

4.1.1 !ongitudinal "ode #erie$

is portion of te a%to2pilot controls te

pitc angle an" te altit%"e of te aircraft# e

complete bloc' "iagram for tis portion of te

a%topilot is sown above in Fig%re 0 Bloc'

Diagram of =ongit%"inal @o"e# )s can be seen b!

te above "iagram, tere are several components

tat ma'e %p tis portion# e main tree bloc's

of te s!stem are te controllers of tis f%nction#

e! ta'e te val%es from te o%ter loops wic

pass tro%g constants an" integrators an" o%tp%t

te appropriate controls for te aircraft# e inp%tsignal $ref is te c%rrent altit%"e as meas%re" from

te g%i"ance s!stems# is val%e ten is ta'en

wit te controls new altit%"e as well as te pitc

angle .I/ an" fe" into te control bloc's of te

"iagram# (t so%l" be note" tat te gains sown

in te fee"bac' loops of te s!stem are all variable

an" "epen" on te velocit! of te aircraft# is

appens beca%se te control to te aircraft will

cange as te spee" "oes# *in" resistance an"

oter factors contrib%te to tis#

e final portion of te longit%"inal mo"e

of te aircraft is te )pproac mo"e# (t so%l" be

note" tat te li"eslope "evice is a %ni-%e "eviceto te Beaver a%topilot mo"e# is portion of te

control s!stem is a fee"bac' loop from te $"ot

o%tp%t .from Fig%re / to te inp%t $"otrefsignal#

e gli"eslope receiver is an on2boar"

meas%rement "evice tat interacts wit a

transmitter on te airport r%nwa!# is s!stem is

an e&tra fee"bac' loop tat as more control over

te "escent of te aircraft# o properl! operate, te

"istance to te r%nwa! is calc%late" %sing Distance

@eas%rement E-%ipment .D@E/# $owever, tis

e-%ipment "oesnt often wor' well wit a%topilot

mo"%les beca%se of ar"ware limitations#

erefore, a "ifferent approac m%st be %se"# e

tree "imensional "istance to te r%nwa! is

calc%late" %sing te following e-%ation#

(n tis e-%ation, R is te tree "imensional

"istance to te r%nwa!, $ref is te eigt above te

r%nwa!, an" Kgs is te reference fligt pat angle

or, te angle te plane ma'es wen fl!ing along

te nominal pat# enerall!, a ra"io altimeter is

%se" to "etermine te val%e of $ref#

D%ring a gli"eslope approac, tere are

two "ifferent mo"es of operation# e first is te

7gli"eslope arme" mo"e# )s te a%tors of te

Beaver "oc%ment sa!0 7is pase is engage" as

te approac mo"e is selecte" b! te pilot# e

longit%"inal a%topilot mo"e in wic te aircraft

flew before selecting te approac mo"e, %s%all!

)=$, will be maintaine" %ntil te aircraft as

reace" te gli"eslope reference plane8 .Ra%w,

1LL/# is mo"e simpl! tells te aircraft tat it isgoing to be lan"ing soon an" tat it nee"s to get

rea"! for lan"ing# (t "oes not affect an! of te

c%rrent fligt pats#

e secon" mo"e is te gli"eslope

co%ple" mo"e# e a%tor "escribes tis mo"e b!

sa!ing tat 7is pase is initiate" as soon as te

aircraft passes te gli"eslope reference plane for

te first time# (n tis pase te control laws of te


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S mo"e ta'e over te longit%"inal g%i"ance tas'

of te a%topilot8 .Ra%w, 1LL/# (n tis mo"e, te

S act%all! ta'es over te rest of te a%topilot# (t

"oes tis b! a""ing its own signals wit te $"ot refinp%t signal# *en te S is not engage", te

signal tat is te o%tp%t of te S is :ero allowing

te aircraft to operate as it normall! wo%l"# etiming of te co%pling of te S is e&tremel!

important# (f te S is co%ple" too earlier, te

aircraft will follow te pat as sown below in

Fig%re L0 Res%lt of Earl! S Co%pling

$igure & -esult of arly /( 'oupling

)s can be seen b! te above fig%re, te timing is

important beca%se, if te S is co%ple" too earl!,

te aircraft tries to approac te reference line .te

slante" "otte" line in te fig%re/ before it is

s%ppose" to# e res%lt of tis is tat te plane

will rise to te reference line an" ten ave to

s%""enl! sift "own after te line is crosse"# o

properl! co%ple te S, te mo"e controller is

constantl! e&amining te state of te aircraft#

*en te aircraft reaces te correct point, te

mo"e controller imme"iatel! switces to co%ple"mo"e an" te aircraft can lan"# is s!stem is not

perfect an" it "oes !iel" a sligt oversoot b%t te

res%lting oversoot is far more "esirable tan te

oversoot sown in Fig%re L#

4.1.2 !ongitudinal "ode Simulation

o get a better pict%re of ow e&actl! tis

a%topilot s!stem wor's, it became "esirable to

sim%late te s!stem in @)=)B# )ll of te

val%es .as seen in Fig%re / are given in te Beaver

"oc%ment an" can be constr%cte" in Sim%lin'#

$owever, tere are still a few "ifferent bloc's tatare not e&plaine" in te Beaver "oc%ment# is is

"%e to te fact tat te a%topilot s!stem is

proprietar! information .or if it isnt, te a%tors of

te "oc%ment "ont "isclose te information/#

Beca%se of tis, te following ass%mptions are

ma"e# e first is in te Comp%tational Dela!

bloc'# is bloc' is ass%me" to be a simple signal

"ela! an" is set to "ela! te signal b! one secon"#

e ne&t bloc' is te )ct%ator an" Cable

D!namics bloc'# is bloc', for te sa'e of te

sim%lation is ass%me" to be a simple transfer

f%nction .a secon" or"er is %se"/# )t te eart of

te bloc' "iagram is te Beaver D!namics# is

bloc' is te portion of te control s!stem tat rea"s

in te meas%re" val%es an" operates on tem# Forte sa'e of sim%lation, te bloc' was ass%me" to

be tree transfer f%nctions0 one of wic is a

simple constant val%e, te secon" is an integrator

f%nction, an" te tir" is a "erivative f%nction#

)fter te s!stem was constr%cte", te o%tp%ts were

e&amine"# e I plot is sown below in Fig%re 90

I Sim%lin' Plot#

$igure 0& 1 (imulink !lot

)s can be seen, tis is invali" "ata# e plot

sows noting an" ever! one of te o%tp%ts loo's

abo%t te same# Canges ma"e in te f%nctions of

te control s!stem !iel"e" no res%lts eiter# e

s!stem wo%l" eiter be :ero an" ten "rop off to

negative infinit! or te signal wo%l" be :ero an"

rise to positive infinit!# e s!stem "i" notcompensate for an!ting# e reason tat tese

sim%lations "i" not !iel" vali" res%lts is beca%se of

te fact tat te set%p of te Beaver D!namics is

%navailable for researc# e act%al s!stem for te

Beaver D!namics ( probabl! not act%all! a simple

transfer f%nction# (f it was a simple transfer

f%nction, canges to te sim%late" s!stem wo%l"

ave a" a larger effect# e Beaver D!namics is

probabl! a control s!stem in an" of itself# Since

te s!stem is a mo"eratel! comple& s!stem, it can

probabl! be ass%me" tat te Beaver D!namics is

a "igital control s!stem# ere is probabl! aminicomp%ter .as "isc%sse" earlier/ at te eart of

te s!stem tat "oes all of te act%al control for te

aircraft# For tis reason, it cannot be a"e-%atel!

sim%late" for tis paper# For tat to appen, more

information abo%t te Beaver D!namic wo%l" ave

to be available for st%"!# o ma'e %p for tis lac'

of sim%lation, a simple aircraft fligt control


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s!stem is e&amine" in te final portion of tis

paper#

4.2 Beaer Conclusion

e Beaver )%topilot s!stem is a comple&

s!stem tat cannot be rea"il! sim%late" "%e to itscomple&it! an" a lac' of information concerning

its primar! controllers .te Beaver D!namics to be

precise/# $owever, tat asi"e, it is still a

fascinating s!stem# e "oc%ment b! @arc Ra%w

gives a soli" an" "etaile" "escription of te s!stem

an" ma'es it simple for people wit basic

e&perience in control s!stems to %n"erstan" te

periperals# *ile it "oes not go into "etail on te

eart of te s!stem, it at least gives a general

overview of ow te s!stem wor's# e Beaver

a%topilot s!stem is a %ni-%e s!stem tat "oes not

follow all of te same r%les tat its bretren follow#

For e&ample, te S as "isc%sse" is a %ni-%efeat%re to te Beaver )%topilot S!stem in tat it is

not ow te lan"ing mo"e is implemente"# @ost

oter s!stems %se te "istance meas%rement

e-%ipment .D@E/# (t so%l" be note" tat te

"escription given in tis paper onl! gives a brief

overview of te s!stem# @an! of te "etails of te

s!stem .as well as te lateral an" t%rn

compensation mo"es/ were not "isc%sse"# o

better %n"erstan" tose mo"es, or to %n"erstan"

te s!stem in greater "etail, see te paper b! @arc

Ra%w#

%. "A&!AB Simulation

%.1 'urpose

e p%rpose of te following sim%lation is

te better %n"erstan" a partic%lar e&ample of a

fligt control s!stem# Since te Beaver )%topilot

co%l" not be sim%late" in tis paper, a simpler

e&ample is necessar!# e following sections give

a "escription of a partic%lar simple s!stem# e!

ten r%n tro%g some sim%lations to e&amine ow

te s!stem respon"s#

%.2 &he 'ro(lem

is e&ample comes from page


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$igure %6& (teady (tate rror of !ure /ain (ystem

)s can be seen b! te above plots, te s!stem tat

as te faster an" smooter response also as a

completel! %nacceptable stea"! state error# e

s!stem tat as a slower response an" a large

amo%nt of oversoot as a better stea" state error

b%t it is still aro%n" 15M wic is %nacceptable#

(f a better res%lt is to be attaine", a

"ifferent approac becomes necessar!# o

eliminate tis error an" oversoot, implementing

some oter 'in" of controller will be beneficial#

e %s%al approac is to implement a P(D

controller# e components in tis 'in" of

controller can ta'e sensitive control s!stems an"give tem a more stable, smooter, faster, an" less

oscillator! response# ) P(D controller was a""e"

an" te s!stem was teste" in S(@G=(H# e

first step in setting %p a P(D controller is to set all

of te val%es to 1# e res%lts of tis test are

sown below in Fig%re 110 P(D Controlle" S!stem

.P?1, (?1, D?1/#

$igure %%& !"# 'ontrolled (ystem 7!8%, "8%, #8%9

)s can be seen, tis response is alrea"! better tan

an! of te constant gain s!stem responses# e

stea"! state error is eliminate" an" te percent

oversoot is less .alto%g it is still abo%t 36M/#

$owever, as can be seen, te response of te

s!stem is relativel! slow# is wo%l" not be

acceptable for an aircraft as it is imperative tat tes!stem respon" -%ic'l! to canges in its state# o

spee" %p te response time, te proportional

portion of te P(D controller is increase" %ntil te

"esire" response time is met# (f te response time

is "efine" to be te time nee"e" to rise from 16M

to 46M, a goo" response time wo%l" be 6#5

secon"s# is is acieve" wen te proportional

component is set to 5# (t !iel"s te res%lt sown

below in Fig%re 1


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