Aircraft Pitch Control System

7/26/2019 Aircraft Pitch Control System

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Aircraft Pitch ControlSystem

VIBHOR DABAS ( 2K12/C/1!"#

VIBHOR $%P&A ( 2K12/C/1!!#

VIKAS ( 2K12/C/1!'#

VIKAS ADAV ( 2K12/C/1')#

*o+ellin,



What is Pitch ?

Stability and control arecomplex for an airplanemove freely in three dimfor cars or boats, which two.

Rotation around the sidecalled -itch.

&he le.ator Controls!n the hori"ontal tail suelevator tilts up or downincreasin# lift on the tai

nose of the airplane up

%y movin# the elevator control bac&wards the pilotmoves the elevator up 'a position of ne#ativecamber( and the downwards force on the hori"ontaltail is increased. $he an#le of attac& on the win#s increased so the nose is pitched up and lift is#enerally increased.

http://en.wikipedia.org/wiki/Angle_of_attack

http://en.wikipedia.org/wiki/Wing

http://en.wikipedia.org/wiki/Wing

http://en.wikipedia.org/wiki/Angle_of_attack



%n+erstan+in, the PhysicalSet-

• $he e*uations motion of an aicomplicated secoupled di+ere

• owever, unde

assumptions, tdecoupled and lon#itudinal ane*uations.

• ircraft pitch islon#itudinal dyexample we wiautopilot that c

of an aircraft.

$he basic coordinate axes and forces actin# onan aircraft are shown in the /#ure



nderstandin# the underlyin#mathematics

SS2P$!3S 4 1. ircraft is in steady-cruise at constant altitude and velocitydra#, wei#ht and lift forces balance each other in the x - and y -directions.). 6han#e in pitch an#le will not chan#e the speed of the aircraft under any ci



Symbols sed 4



&ransfer 0nction

%efore /ndin# transfer function ,we need to plu# in some real values .We are ufrom irbus9 commercial aircraft .

$a&in# :aplace transform of the above mentioned e*uations 4



&ransfer 0nction

fter a simple mathematics, We can #et the transfer function for aircraft pcontrol system .



%n+erstan+in, the Desi,nReirements

$o desi#n a feedbac& controller so that in response to a step coman#le the actual pitch an#le overshoots less than 1=>, has a rise tim) seconds, a settlin# time of less than 1= seconds, and a steady-stathan )>. or example, if the reference is =.) radians '11 de#rees(, an#le will not exceed approximately =.)) rad, will rise from =.=) rwithin ) seconds, will settle to within )> of its steady-state vaseconds, and will settle between =.1A; and =.)=7 radians in steady-s

n summary, the desi#n re*uirements are the followin#.

Pea& !vershoot less than 1=>

Rise time less than ) seconds

Settlin# time less than 1= seconds

Steady-state error less than )>



!pen loop 2odellin#

rom the above plot, we see that the open-loop response does not satisfy the desi#ncriteria at all. n fact, the open-loopresponse is unstable.



6lose loop 2odellin#

Bxaminin# the above closed-loop stepresponse, the addition of feedbac& hasstabili"ed the system. n fact, the steady-state error appears to be driven to "ero andthere is no overshoot in the response, thou#hthe settlin#-time re*uirements are not met.



Choosin, the ri,ht Controller

• proportional controller CDpE will have the e+ect of reducin# rise time breduce steady state error.

• n inte#ral control CDiE will eliminate the steady state error for constant or swill ma&e the transient response slower.

• derivative control CDdE will increase the stability of system ,reducin# timprovin# the transient response .



%asic 6ontroller rchitecture

or a step reference of =.) radians, the desi#ncriteria are the followin#.• !vershoot less than 1=>• Rise time less than ) seconds• Settlin# time less than 1= seconds

• Steady-state error less than )>

We will ta&e advantaautomated tunin# cathe SISO Desi,n &o2$:% to desi#n oucontroller. irst, ente

followin# code at theline to de/ne the moplant P's(.

$he SISO Desi,n too

opened by typin# sisotthe command line



Pro-ortional Control

Dp H 1 $he performance is improved with -ro-ortionalcontroller, thou#h the settlin# time is still muchtoo lar#e.



Pro-ortional Inte,ral Controller

Di H =.8;, Dp H 1.==$he addition of inte,ral control helped reducethe avera#e error in the si#nal more *uic&ly.nfortunately, the inte#ral control also made theresponse more oscillatory, therefore, the settletime re*uirement is still not met. urthermore, theovershoot re*uirement is no lon#er met either.



PID Controller

$he response with PID meets all of the #iven

re*uirements as summari"ed below. !vershoot H 8> I 1=> Rise time H 1.) seconds I ) seconds Settlin# time H 8 seconds I 1= seconds Steady-state error H => I )> $herefore, this PID controller will provide thedesired performance of the aircraftJs pitch.



Root ocs Plot

We specifcally need to shit the root locusmore to the let in the complex plane to getit inside our desired region. One way to do

this is to employ a lead compensator.

$ype sisotool'JrlocusJ, PGpitch( in thecommand window. $wo windows willinitially open, one is the SS! Fesi#n $as&which will open with the root locus of theplant with #ain D as shown below, and theother is the 6ontrol and Bstimation $ool

2ana#er which allows you to desi#ncompensators, analy"e plots, and so forth.



Root locus with :ead 6ompensator

$he transfer function of a typical leadcompensator is the followin#, wherethe "ero is smaller than the pole,that is, it is closer to the ima#inaryaxis in the complex plane.

Since the root locus is entirely in thene#ative half of s-plane, the system isstable.



%ode Plot 4 6losed :oop Response



nalysin# the %ode plot

Bxamination of the plots demonstrates that the settle time re*uirementis not close to bein# met. !ne way to address this is to ma&e the systemfaster, but then the overshoot shown above will li&ely become a problemthe overshoot must be reduced in conKunction with ma&in# the system rfaster. We can accomplish these #oals by addin# a compensator to reshplot of the open-loop system.

$wo !bserved %ehaviour• the #ain crossover fre*uency is directly related to the closed-loop sysresponse, and

• the phase mar#in is inversely related to the closed-loop systemJs overshoot. $herefore, we need to add a compensator that will increase the #ain crossoveincrease the phase mar#in as indicated in the %ode plot of the open-loop system



:ead 6ompensator

A type of compensator that can accomplish both of our goals is a lead compensator

lead compensator adds positive phase to the system. dditional positive phase phase mar#in, thus, increasin# the dampin#. $he lead compensator also #enerallyma#nitude of the open-loop fre*uency response at hi#her fre*uencies, thereby, in#ain crossover fre*uency and overall speed of the system. $herefore, the settlin# decrease as a result of the addition of a lead compensator. $he #eneral form of thfunction of a lead compensator is the followin#.



%ode plot with 6ompensator



6losed loop response with lead compensator



nalysin# the Results

Therefore, the following lead compensa

satisfy all of our design requirements.



Conclsions

&he +esi,n reirements are fl3lle+ 4y the PIcontroller +esi,n5

Since the ,ain mar,in( in3nity # an+ -hase mar,i("156 +e,ree# 4oth are -ositi.e 7 the system sta4le5

Aircraft Pitch Control System

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