Control and Fbw

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CHAPTER 12

CONTROL AND FLY-BY-WIRE


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Control and FBW

TABLE OF CONTENTS

12.1. INTRODUCTION.........................................................................3

12.2. CONCEPTS AND DEFINITIONS.......................................................412.2.1. Systems.................................................................................4

12.2.2. Models..................................................................................5

12.2.3. Control..................................................................................5

12.3. MATEMATICAL TOOLS...............................................................

12.3.1. D!""erent!#l E$%#t!ons................................................................

12.3.2. L#&l#'e Tr#ns"orms...................................................................!

12.3.3. Com&le( N%m)ers..................................................................1212.*. ANAL+SIS OF S+STEMS AND CONTROL.........................................12

12.*.1. Tr#ns"er F%n't!ons..................................................................13

12.*.2. Blo', D!#-r#m Al-e)r#.............................................................14

12.*.3. St#)!l!ty #nd Per"orm#n'e.........................................................1

12.. CONTROL S+STEMS APPLICATIONS.............................................2"

12..1. Fl!-/t Control Systems.............................................................3#

12..2. Fly0)y0!re 'on'e&ts...............................................................3112..3. Ot/er #&&l!'#t!ons...................................................................32

12.. TESTS AND CERTIFICATION........................................................34

12..1. ro%nd #nd Fl!-/t tests............................................................34

12..2. Cert!"!'#t!on #s&e'ts................................................................35

12.4. REFERENCES.........................................................................35

APPENDI$ 12A - E$ERCI%E%

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12.1. INTRODUCTION

The fight testing activity demands a constant contact with complex systems. Inact, a complete aircrat can be considered a system o systems, according the

concepts presented in this text.

An auto-throttle, a hydraulic system operating landing gear or bra!es", thefight control system ex# using fy-by-wire concepts", auto-pilots, or a $A%&' toengine control, to all o them, the system theory and control must be applied.

A control system consisting o interconnected parts is designed to achieve adesired purpose(ob)ective rom the controlled system. To understand thepurpose o a control system, it is useul to examine examples o controlsystems through the course o history. These early systems incorporated many

o the same ideas o eedbac! that are in use today.

*odern control engineering practice includes the use o control designstrategies or improving manuacturing processes, the e+ciency o energy use,advanced space vehicles control, including weapons, among others.

e also emphasie the notion o a design gap. The gap exists between the

complex physical system under investigation and the model used in the controlsystem synthesis.

18th Century James Watts centrifugal governor for the speed control of asteam engine.

1920s Minorsky worked on automatic controllers for steering ships.

1930sNyquist developed a method for analyzing the stability of controlled systems

1940s requency response methods made it possible to design linear closed!loop controlsystems

1950s "oot!locus method due to #vans was fully developed

1960s $tate space methods% optimal control% adaptive control and

1980s &earning controls are begun to investigated and developed.

Present and on!going research fields. "ecent application of modern control theory includes such

non!engineering systems such as biological% biomedical% economic and socio!economic systems.

or this wide range of applications% there have been developed new techniques and theories such

as adaptative% robust% predictive controls% etc.


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The iterative nature o design allows us to handle the design gap e/ectivelywhile accomplishing necessary tradeo/s in complexity, perormance, and costin order to meet the design speci0cations.

This course will be restricted to urnish the general idea how to analye the

systems and how to apply linear control to them. *ore advanced applicationsre1uires courses that are more sophisticated.

The inear 'ontrol Theory deals in modelling physical systems, describing themwith bloc! diagrams and dynamic e1uations that de0ne their behavior. Thecontrol system is designed to obtain responses o a general system withdetermined characteristics o perormance and stability.

$or urther and more advanced inormation, a specialied bibliography is listedat the end o the chapter. Also a list o exercises should orient the student to

the exam.

12.2. CONCEPTS AND DEFINITIONS

3eore we begin the study o analysis and synthesis o control systems, there isthe need or an ob)ective concept and clearly de0ne the terms relating to thesystems and other related terms.

%espite restricted the theory herein, the presented principles and

undamentals remain the same and are the basis or the study o complexsystem.

12.2.1. Systems

454T&* 6 A set o elements(devices, selected and organied, interconnectedor a desired purpose. &very system is delineated by its spatial and temporalboundaries, surrounded and infuenced by its environment, described by itsstructure and purpose and expressed in its unctioning.

789'&44 6 The device, plant, or system under control. The input and outputrelationship represents the cause-and-e/ect relationship o the process.Another important characteristic is the architecture that de0nes therelationship among the internal parameters.

7A8A*&T&84 6 Important actors used in the model to de0ne the processunder analysis. %e0nes the dynamic between input(output.

:A8IA3&4 I;7


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12.2.2. Models

inear or not-linear ? superposition principle :ariants or not-variants ? time dependent Analogic or digital ? in0nite possible values or variables 'ontinuous or discrete ? time interval ex# sampling"

*athematical, transer unction or bloc!s diagram ? %i/erent types orepresentation o system dynamics and relationship among variables.%ependent o architecture and parameters.

12.2.3. Control

'lassic or *odern

'lassical control theory deals with solving di/erential e1uations in a re1uencydomain aplace($ourier(@-transorm", while in modern control theory, we solvein the state space time-domain". In classical control we can analye 4I49single input, single output" systems while a state space based approach isbetter suited or *I*9 systems and can handle non-linear time invariantsystems as well which is how most practical problems are".

That being said, the state space approach hence modern control theory" is notsomething relatively new, but gained popularity ater the BCDs because itinvolved numerically and computer" riendly matrix operations.

The need to move urther rom simple controllers was 0rst posed by aerospaceresearchers due to the *I*9 systems that they wanted to control, this pavedway or modern control theory.

O&'n loo&

Clo('d loo&

E


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12.3. MATEMATICAL TOOLS

*athematics is playing an increasingly important role in all sciences, not onlyin engineering, inciting clouding boundaries between classical techni1ues andcomputational capabilities. 8emar!able progress has been made in both theoryand applications o all-important areas o control theory, which reaches arbeyond the engineering.

'omplex systems re1uire di/erent approaches or di/erent problems.Thereore, we present here some classical tools that are the basics or 'ontrol

Theory, classic or modern.

12.3.1. D!""erent!#l E$%#t!ons

F%i/erential e1uations are nothing more than a manDs attempt to modelphenomena o the natureG

%i/erential e1uations are e1uations where the un!nownsH parameters areunctions. They are presented in the orm o algebraic e1ualities involving

di/erential or derivatives.

&xample#

This di/erential e1uationx(t) is the unknown function.It represents themovement o the mass shown below when excited by an oscillating orce givenby F = F0cos(t).

$igure 2- ? *A44 ? 478I;J ? %A*7&8 454T&*

B


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Control and FBW

The e1uation o motion governing the mass-spring-damper system is an example olinear ordinary di/erential e1uation with constant coe+cients. 9rdinary di/erentiale1uations have the incognita unction with one ree variable, in this case is variabletime t". 9therwise, it is said partial di/erential e1uation. 4tructural systems sub)ectedto dynamic vibration modes are partial di/erential e1uation time and directions".

4peci0c methods o solution o di/erential e1uations are not on the scope o thiscourse.

12.3.2. L#&l#'e Tr#ns"orms

et t" be a real unction with the real variable t K C. The aplace transorm ot" is de0ned by#

were FsG is a complex variable, named Fcomplex re1uencyG#

s = + i, with real numbers and .

9ne important application to this tool is to solve di/erential e1uations. Inpractice, it is not necessary always to calculate the aplace transorms throughthe de0nition. The transorms are tabulated and with some properties we can

solve most o the problem analysis and synthesis o control systems.

The essential properties and theorems are the ollowing#

*ultiplication by real constant=

Addition and subtraction=

%i/erentiation=

Integration=

L


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Time displacement=

$re1uency displacement=

Initial value theorem=

limt 0

f( t)=lims

sF(s)

$inal value theorem=

limt

f( t)=lims 0

sF(s)

'omplex translation=

e M(-att" 6 $ s -(M a"

'omplex convolution= and

Time convolution.

et $s" and Js" denote the aplace transorms o t" and gt", respectively.Then the product Ns" 6 $s".Js" is the aplace transorm o the convolution ot" and gt" and is denoted by ht" 6 Og" t", and has the integralrepresentation

The opposite way to solve the complete problem can be accomplished usingthe inverse aplace Transorm, de0ned by#

P


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Control

&SA*7& # 4how the aplace transorm as seen on the table.

&1uating real and imaginary parts,

&SA*7& 2# $ind the inverse transorm o#

F( s)= 2

s3+4 s2+3 s

The denominator is sM >s2M s" 6 s.sM".sM"

Then $s" 6 A(s M 3(sM" M '(sM"

ith# A 6 2(

3 6 (

' 6 -

$inally, t" 6 2(.ut" M (.e-t

? e-t

The 0nal observation about the solution o a di/erential e1uation is made byloo!ing the answer t". The solution o the homogeneous e1uation is called)r'' r'(&on('dynamic o the system without external excitation". 9n theother hand, there is aparticularsolution, corresponding to the )or*'dr'(&on('o the system. Thus, the total solution is given by#

+,t )r'' r'(&on(' / )or*'d r'(&on('.

C


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Another way to interpret the total dynamic response o a system is to divide asollow#

+,t tran(0'nt r'(&on(' / (t'ad+ (tat' r'(&on('

12.3.3. Co&l' N'r(

A complex number is a number with the ollowing orm#

a M b) , where ) 6 imaginary number 1 ", named 'A;9;I'A $98*, or in

the &


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Control

$igure 2- ? 454T&* %&4'8I7TI9; %I$$&8&;TIA &


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$igure 2-> ? T8A;4$&8 $


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Control

&s" 6 error signal

3s" 6 eedbac! signal

;ormally, bloc! diagrams are not present in simple shapes shown. 'omplex

systems have di/erent unctions and thereore a diagram with variousinterrelationships between signals and variables occur. 4everal WsummationpointsW and bloc!s in WcascadeW are the rule rather than the exception.Nowever, it is possible to reduce them to simple shapes, which are e1uivalentand condensed through algebraic manipulation o transer unctions. Thismethod is called block diagram algebra.

To simpliy our wor!, some orms have already been calculated and tabulated.

$igure 2-B ? 8


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Control and FBW

$igure 2-L ? &SA*7& 9$ 7A8TIA 39'V %IAJ8A* rom F;onlinear %ynamicInversion 3aseline 'ontrol aw# Architecture and 7erormance 7redictionsG -'hristopher Q. *iller ? AIAA paper"

12.*.3. St#)!l!ty #nd Per"orm#n'e

The general procedure in the analysis o a control system is as ollows#

- %etermine the transer unction o each system component=

2 - *ount bloc! diagram=

- %etermine the main characteristics o the system.

The main items that eature a control system#

4TA3IIT5

T8A;4I&;T 8&479;4&

4T&A%5 - 4TAT& &8898

$8&


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Control

The tendency o a system to develop restoring orces e1ual to or greater than thedisturbing orces to maintain the state o e1uilibrium is !nown as (ta0l0t+.

A system is said to be stablei the output ollows the input in a 0nite time. 9nthe other hand, it is considered unstablei the output does not ollow the

input oscillating continuously or diverging to in0nity, out o control. 4tabilitycan be analyed according to two aspects# absoluteor relativestability.

$igure 2-P ? 454T&* 3&NA:I9


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$igure 2-R ? JAI; *A8JI; A;% 7NA4& *A8JI; ? 39%& 79T

FIRST AND SECOND ORDER S+STEMS

$irst order systems has a simple behavior, shown in 0gure below. The

perormance characteristics will be analyed later. In time domain is a simpleexponential unction.

$igure 2-C ? $I84T 98%&8 8&479;4& T9 4T&7 I;7


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Control

$or second order, the response to step input is dependent o the poles location.In other words, the parameter Z. &S&8'I4 Analye the possibilitiesor 7 and stability.

;ow let us ma!e some considerations on the complex roots o characteristic

2nd degree e1uation rom the system and the shape o the resulting response.Assuming the roots in the orm a M b), the response-unction ta!es the orm#

y t" 6 ceaMb)"tM c2ea-b)"t

It is to show that that the above expression may be written#

y t" 6 VM V2eatsinbt" Vand V2are constants

&S&8'I4 Analye the possible cases and responses ormats. remembersymmetry".

$igure 2- ? 4&'9;% 98%&8 8&479;4& T9 4T&7 I;7


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Are de0ned actors that measure the system 7&8$98*A;'& in transient phase.These parameters depend on the system order and are used, in the design, toprovide the so-called Wspeci0cations in the time domainW.

@&89 98%&8 454T&*4

Y(s)X(s)

6 V constant" 6K thus yt" 6 V ut"

$igure 2-2 ? @&89 98%&8 8&479;4& T9 4T&7 I;7


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$igure 2- ? $I84T 98%&8 8&479;4& T9 4T&7 I;7


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$igure 2-> ? 4&'9;% 98%&8 8&479;4& T9 4T&7 I;7


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Control

T4 3

n

T7 6 d , where [d 6 [n 12

%TEADY-%TATE PERFOR9ANCE

Ater the analysis o the transient system perormance, we access thecharacteristics in steady state. 'onsider the closed loop system shown below.

The error signal &s" acting on this system has its corresponding time domainet". e can show exercise" that & s" can be written as#

E (s )= X(s)

1+G ( s)(s)

$igure 2-E ? 'T$

The error in the steady state is de0ned as#

ess= limt

e (t)

The error in the steady state is resultant rom the interaction o two dynamics#the input type and the actual system dynamics, i.e., the degree o thedenominator o the product Js" Ns". It de0nes the error constants as ollows#

22


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Vpposition error constant" 6 lims0

G (s )(s)

Vvvelocity error constant" 6

lim

s 0

sG ( s )(s)

Vaacceleration error constant" 6 lims0

s2

G ( s)(s)

In summary, we ound that the steady-state error depends on the input typeand the type o system. The table below shows the values o the errorconstants and their corresponding error in steady state.

TYPE OF

%Y%TE9

ERROR CON%TANT% '((FOR TYPE OF INP:T

;& ;< ;a %TEP RA9P PARABO

LA

C V C C (M Vp" ] ]

1 = ; # # 1> ;< =

2 ] ] V C C ( Va

] ] ] C C C

$igure 2-B ? TA3& $98 4T&A%5-4TAT& &8898

Ta!e a type system to exempliy the interpretation o the table above. 4uch asystem is able to ollow a step input with ero steady-state error. ;ow, or theramp input, type system is able to go with it in a stationary operation, butwith a 0nite error given by ( Vv". 9n the other hand, in the case o a parabolicinput, the system type is not able to ollow this dynamic and steady-state

error tends to in0nity over time.

FRE?:ENCY RE%PON%E

The term Wre1uency responseW reers to the steady state response o a systemwith sinusoidal input. 4o, we abandoned the standard inputs o step, ramp etcin order to eed the system with a sinusoidal excitation and we can study now

the response behavior o the system under analysis sub)ect to oscillatoryentries. A scan o various input signal re1uencies is perormed. This type oapproach is very e/ective because o existing acilities and precision omeasurements. 4ome Transer $unctions o complicated components are

2


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Control

determined using this techni1ue. The methodologies and tolls to accomplishedthe analysis o re1uency response are, mainly, 39%& diagrams, ;5


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8esonance pea!

8esonance re1uency

9vershoot

Attenuation slope

Jain and 7hase margin

Today there are sotware to produce these diagrams *ATA3 or instance".Thereore, the design o control systems is much easier.

;5


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Control

$igure 2-R ? ;5


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Control and FBW

$igure 2-2C ? ;I'N94 'NA8T

899T 9'


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Control

$igure 2-2 ? '94&% 997 454T&* ITN NIJNIJNT&% JAI; V"

The method o the locus o the roots was developed by &vans, . 8. andconsists in carrying out a mapping o the poles and eros rom the closed looptranser unction in the 4 plane, the extent to which the system gain variesrom C to M]. The result o this mapping is called F899T 9'


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Control and FBW

12.. CONTROL S+STEMS APPLICATIONS

The increasing complexity o embedded systems and the improvement ocomputational techni1ues have emphasied the importance o control systems theory.

Topics such as linear control, robust control, adaptive or predictive control have beentarget o new developments and design techni1ues directed to automation ounctions on board, reducing pilot wor!load and increasing the possibilities andperormance o modern aircrat.

12..1. Fl!-/t Control Systems

The fight control systems also progressed rom mechanical to hydraulicpowered to 0nally electronic computers as part o the chain o command ofight. This allowed the introduction o fight monitoring systems, fightenvelope control, and increment o natural stability o the aircrat eg# 4A4 6stability augmentation system". These new eatures allow a saer fight andeven the perormance increase eg# relaxed stability". 9n the other hand, thesepossibilities have increased the wor!load o designers and responsibility ocerti0cation authorities. Testing and re1uirements compliance demonstration

become more complex.

$igure 2-2 ? J&;&8AI@&% $IJNT '9;T89 454T&*

4tability Augmentation 4ystems are automatic control devices that supplementa pilotDs manipulation o the aircrat controls and are used to modiy inherentaircrat handling 1ualities. Abbreviated 4A4, are essentially damping devices.

They have various orms o auxiliary subsystems added to the primary fightcontrol to achieve desired aircrat characteristics by selection o variable gainin eedbac! loops rom aircrat control suraces. These devices oten have

limited authority and do not move the pilotDs controls. In many aircrat, aninoperative 4A4 ma!es the aircrat unairworthy.

2R


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Control

$or illustration, a yaw damper is a device used on many aircrat usually )etsand turboprops" to damp reduce" the rolling and yawing oscillations !nown asthe %utch roll mode. It re1uires yaw rate sensors and a processor that providesa signal to an actuator connected to the rudder.

$igure 2-2> ? 4A4 &SA*7&4

*ore inormation about $light 'ontrol 4ystems, reer to 'hapter ? J&;&8A454T&*.

12.5.2. Fl+-+-0r' *on*'&t(

A fy-by-wire $3", by de0nition, it is a fight control system wherein thetransmission o the control stic! signal to the mechanism, which will actuatethe control surace, is perormed by a transmitted electrical signal thru awiring. Nowever, the fy-by-wire technology, currently implemented incommercial and typical military aircrat, covers much more than )ust thetransmission o command through an electrical signal.

In a conventional aircrat, with a mechanical fight control system or powered,the movement o coc!pit controls control wheel and pedal" are ampli0edmechanically or hydraulically and then applied to the various control suraces.

The orce re1uired to operate the surace is supplied directly by the pilot in thecase o mechanical systems" or ampli0ed by servo-hydraulic mechanisms.Nowever, the responsibility o coordinating the various movements o thecontrol suraces belongs to the pilot.

9n the other hand, an aircrat with fy-by-wire system, sensors in the coc!pitmechanisms stic! and pedal" measure the pilot inputs and send them to one

or more electronic modules dedicated to indicate what the aircrat should do.'omputer systems interpret the signals rom these and several other systemsensors and generates appropriate commands to the various actuators.4ensors on the control suraces continuously eedbac! their signals to the fight

C


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Control and FBW

computers. ith this technology, it reduces pilot wor!load on operation o theaircrat. *oreover, this method allows the implementation o algorithms whichmonitor, process and modiy the original pilotHs re1uest in order to acilitate thepilotage, such as laws to increase control 'ontrol Augmentation 4ystems -

'A4" or increase stability 4tability Augmentation 4ystem - 4A4". As a result, itbecomes possible to perorm a series o improvements in aircrat perormanceand design that without the fy-by-wire would not be possible. $or example, anincrease in cruise speed, increased maneuverability crucial or militaryaircrat", increased saety margin to prevent exceeding the saety limits duringoperation, among other characteristics such as weight reduction andcomplexity o fight control mechanisms, etc.

$igure 2-2E ? $5-35-I8& '9;'&7T


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Control

nonprecision approach. 5ou must accurately determine the installed options,type o installation, and basic and optional unctions available in your speci0caircrat.

*any advanced avionics installations really include two di/erent, but

integrated, systems. 9ne is the autopilot system, which is the set o servoactuators that actually do the control movement and the control circuits toma!e the servo actuators move the correct amount or the selected tas!. Thesecond is the fight director $%" component. The $% is the brain o theautopilot system. *ost autopilots can fy straight and level. hen there areadditional tas!s o 0nding a selected course intercepting", changing altitudes,and trac!ing navigation sources with cross winds, higher level calculations arere1uired.

The $% is designed with the computational power to accomplish these tas!sand usually displays the indications to the pilot or guidance as well. *ost fightdirectors accept data input rom the air data computer A%'", Attitude Neading8eerence 4ystem AN84", navigation sources, the pilotHs control panel, and theautopilot servo eedbac!, to name some examples. The downside is that youmust program the $% to display what you are to do. I you do not preprogramthe $% in time, or correctly, $% guidance may be inaccurate.

In every instance, you must be sure what modes the $%(autopilot is in andinclude that indicator or annunciator in the crosschec!. 5ou must !now what

that particular mode in that speci0c $%(autopilot system is programmed toaccomplish, and what actions will cancel those modes. %ue to numerousavailable options, two otherwise identical aircrat can have very di/erentavionics and autopilot unctional capabilities

$igure 2-2B ? A


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Control and FBW

^ 5ou can control the uel, ; and ;2.

^ 'hec! the engine parameters during the process o Wstarting motorW andprevents the engine Ni &JT that exceeds the limit maximum permissible.

^ 4ystem wor!s in two ways# manual and autothrust.^ 9ptimie the operation o the engine by controlling the fow o aircompressors and the turbines operation parameters.

$igure 2-2L ? $A%&'

AI8 '9;%ITI9;I;J '9;T89 ? Temperature control system.

$IJNT '9;T89 454T&* ? 8ide smoothing turbulence" and 4ingle enginefight optimiation.

12.. TESTS AND CERTIFICATION

12..1. ro%nd #nd Fl!-/t tests

The 0nal proo o design o any control system is the demonstration osuccessul integration o the control system into the total vehicle o which it isa part. 4uch a demonstration o satisactory and thereore sae design must

include an assessment o the behavior o the vehicle and its control systemover the ull range o normal and extreme environmental conditions to which itwill be sub)ect. Thus, in the case o an aircrat fight control system, this canonly be achieved by testing the fight control system $'4" when it is ully


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Control

integrated into the aircrat and assessing it over the ull operating envelope othe aircrat. $light testing thereore represents the ultimate proo that thedesign o the $'4 is 0t or purpose, meets the design re1uirements and veri0esthat the design re1uirements themselves were valid.

Nistorically, the fight test process has been viewed as an independent chec! othe whole aircrat and its systems by the fight test team o pilots andengineers whose tas! was to assess the aircrat behavior and identiy anyproblems with the design. Any problems identi0ed had to be understood andresolved by the designers and the modi0ed aircrat reassessed by the fighttest team.

As the system get more complex, the ground testing becomes morecomplicated and must embrace all aspects. 3ased on the ground results, the

fight testing can be programmed.The !ey steps are#

o/-line design phase=

pilot in the loop simulation=

iron bird tests=

clearance to fight= and

validation thru fight testing.

12..2. Cert!"!'#t!on #s&e'ts

Now did the $AA certiy 7art 2E $ly-3y-ire $3"_

^ 'urrent 8ules do not address modern $3

^ $AA did not FdictateG design

^ $AA accepted 3oeing M Airbus approach

3ut $AA levied 4pecial 'onditions $it into existing regulatory structure

12.4. REFERENCES

9JATA, Vatsuhi!o ? F&ngenharia de 'ontrole *odernoG ? ` &dio

>


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Control and FBW

%HA@@9, Q.%. N9


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Control

APPENDI5 6 12A

E5ERCISES

1 - Explain the cncept!"

3loc! diagram 4teady-state perormance Transient phase parameters perormance Time domain and re1uency domain Transer unction

2 - $ind the Transer $unction o the system below#

- hat !ind o inormation comes rom Froot-locusG and Fbode diagramG thathelps the control system analysis and design_

> - 7rove that the relation below gives the multiplication o complex numbers#

,a / . ,* / d ,a*-d / ,*/ad

E - 4!etch the step response o a system o 0rst order and another o secondorder. 4how the main perormance parameters on the s!etches.

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Control and Fbw