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Ficha catalográfica Universidade Estadual de Campinas Biblioteca da Área de Engenharia e Arquitetura Elizangela Aparecida dos Santos Souza - CRB 8/8098
Martínez Arias, Ronald Ricardo,
M366m MarModelagem de um dirigível robótico com propulsão elétrica de quatro motores. / Ronald Ricardo Martínez Arias. Campinas, SP : [s.n.], 2014.
MarOrientador: Ely Carneiro de Paiva.
MarDissertação (mestrado) Universidade Estadual de Campinas, Faculdade de Engenharia Mecânica.
Mar1. Veículos autônomos. 2. Aerodinâmica. 3. Motores elétricos. I. Paiva, Ely Carneiro de,1965-. II. Universidade Estadual de Campinas. Faculdade de Engenharia Mecânica. III. Título.
Informações para Biblioteca Digital
Título em outro idioma: Modeling of a robotic airship with four electric engines as thrusters Palavras-chave em inglês:
Autonomous vehicles Aerodynamics Electric motors
Área de concentração: Mecânica dos Sólidos e Projeto Mecânico Titulação: Mestre em Engenharia Mecânica
Banca examinadora:
Ely Carneiro de Paiva [Orientador] André Ricardo Fioravanti Paulo Augusto Valente Ferreira Data de defesa: 22-12-2014
Programa de Pós-Graduação: Engenharia Mecânica
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Dedicatória
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Lista de Ilustrações
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w0 M*$>6 .#8O-#.6 F Kw0 M*$>6 6($*7#8S5#.6 F Aw0 M*$>6 7( 1$*1:<)=* F P w0 6-:687* 86 7#$(>=* 7* (#P* X ( 1$*1:<)*$() 1*)#.#N *867*) 6+6#P* 76 <#8C6 7* (F:67*$ 7* 7#$#%&'(< ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! D3 P'!" #$%&'($ )*+,-(+.-$'+/ MGq0 #$%&'($ .-'1(-.$ MKq0 #$%&'($ +&*$2-'34 %-.$ MAq0 #$%&'($ 2& 5*$56/78$ MP q0 +(6+'2$ &% ($*'$ 2$ &-9$ : & & 5*$56/7$*&7 5$7-.-$'+2$7 +;+-9$ 2+ /-'<+ 2$ &=6+2$* 2$ 2-*-)>,&/ ! ! ! ! ! ! ! ?@ !A B$*C+ )&*+2+ 5&/$7 5*$56/7$*&7 D & E '+ 2-*&C8$ 2$ &-9$ F & '+ 2-*&C8$ 2$ &-9$ G ?H !I B$*C+ )&*+2+ 5&/$7 5*$56/7$*&7 D & E '+ 2-*&C8$ 2$ &-9$ F & '+ 2-*&C8$ 2$ &-9$ G ? !@J #$%&'($7 )&*+2$7 5&/$7 5*$56/7$*&7 +(6+'2$ 7$;*& $ 2-*-)>,&/ &% ($*'$ 2$
&-9$ : & .$% 5*$56/7$*&7 5$7-.-$'+2$7 '+ /-'<+ 2$ &=6+2$* ! ! ! ! ! ! ! ! ! ! ?? !@@ K$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ K+-9+ 2& ;+-9+7 ,&/$.-2+2&7 ?" !@D K$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ ,&/$.-2+2& 2$7 3, 5 [m/s] ?" !@E K$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ ,&/$.-2+2& 2$7 10 [m/s] ?A !@H B$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ K+-9+ 2& ;+-9+7 ,&/$.-2+2&7 ?I !@ B$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ ,&/$.-2+2& 2$7 4 [m/s] "J !@? B$*C+7 & %$%&'($7 *&76/(+'(&7 +(6+'2$ '$ 2-*-)>,&/ '+ ,&/$.-2+2& 2$7 14 [m/s] "@ !@" L')6/$ 2& ,&($*-M+C8$ 2$7 5*$56/7$*&7 5$7-.-$'+2$7 '+ /-'<+ 2$ &=6+2$* ! ! ! "D !@A L')6/$ !"#$ 2$ 2-*-)>,&/ .$% 5*$56/7$*&7 5$7-.-$'+2$7 '+ /-'<+ 2$ &=6+2$* "E !@I L')6/$ 2$ /&%& &/&,+2$* 2$ 2-*-)>,&/ .$% 5*$56/7$*&7 5$7-.-$'+2$7 '+ /-'<+
2$ &=6+2$* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "H !DJ N$'76%$ 2& .$**&'(& &/1(*-.+ 5&/$7 5*$56/7$*&7 5$7-.-$'+2$7 '+ /-'<+ 2$ &=6+2$* " !D@ B$*C+ )*+,-(+.-$'+/ F Gw0 B$*C+ .-'1(-.+ F Kw0 B$*C+ +&*$2-'3%-.+ F Aw0
B$*C+ 2& 5*$56/78$ F P w0 +(6+'2$ '+ 2-*&C8$ 2$ &-9$ G & 5*$56/7$*&7 5$7-.-4 $'+2$7 '+ /-'<+ 2$ &=6+2$* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "" !DD #$%&'($ )*+,-(+.-$'+/ MGq0 #$%&'($ .-'1(-.$ MKq0 #$%&'($ +&*$2-'34
%-.$ MAq0 #$%&'($ 2& 5*$56/78$ MP q0 +(6+'2$ &% ($*'$ 2$ &-9$ : & 5*$4 56/7$*&7 5$7-.-$'+2$7 '+ /-'<+ 2$ &=6+2$* ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "A ?!@ N6*,+ 2& ,&($*-M+C8$ '&.&77O*-+ 5+*+ .+2+ +-*75&&2 P+;7.-77+ &% %Q7R! S .6*,+
2$ %&-$ .$**&75$'2& T &7(*+(1)-+ 2& $(-%-M+C8$ 2+ *$(-'+ U2-V;%?HDU0 =6& 5*$5W& 6% .$%5*$%-77$ &'(*& + ,+*-+C8$ +;*65(+ 2$ .+7$ 7&% XYBZ & $ .$'76%$ 2& &'&*)-+ &9.&77-,$ 2$ .+7$ .$% XYBZ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! AD ?!D N6*,+ 2& ,&($*-M+C8$ '&.&77O*-+ 5+*+ .+2+ +-*75&&2 P+;7.-77+ &% %Q7R! S .6*,+
2$ %&-$ .$**&75$'2& T &7(*+(1)-+ 2& $(-%-M+C8$ 2+ *$(-'+ U2-V;%?HDU0 =6& 5*$5W& 6% .$%5*$%-77$ &'(*& + ,+*-+C8$ +;*65(+ 2$ .+7$ 7&% XYBZ & $ .$'76%$ 2& &'&*)-+ &9.&77-,$ 2$ .+7$ .$% XYBZ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! AD ?!E S/)$*-(%$ 2+ *$6(-'+ %!&'()*+ ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! AE
9,-Lista de Tabelas
!" #$%&'()*+,-. /$. 0)$0(1.$)-. 0*)* *. .23(1*+,-. 0)$0$.4*. ! ! ! ! ! ! ! ! ! ! 56 7!" #$%.(3$ /* 8$))-%4- -194)28* 0-1$. 0)$0(1.$)-. :(*%/$ -.4-. -.4;$ 0$.282$%*< /$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! BC 7!D #$%.(3$ /* 8$))-%4- -194)28* 0-1$. 0)$0(1.$)-. :(*%/$ -.4-. -.4;$ 0$.282$%*< /$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! B7 7!E F%'(1$ /- A-4$)2G*+;$ /$. 0)$0(1.$)-. :(*%/$ -.4-. -.4;$ 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! B6 7!5 F%'(1$ !"#$ %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! BB 7! F%'(1$ /$ 1-3- -1-A*/$) %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "HH 7!C I$)+*. *4(*%/$ %$ /2)2'@A-1 %* /2)-+;$ Z %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "H" 7!7 I$)+*. *4(*%/$ %$ /2)2'@A-1 %* /2)-+;$ Z %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! ! "HD 7!6 J$3-%4$. *4(*%/$ %$ /2)2'@A-1 -3 4$)%$ /$ -2>$ Y %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! "HE 7!B J$3-%4$. *4(*%/$ %$ /2)2'@A-1 -3 4$)%$ /$ -2>$ Y %$ 8*.$ /$. 0)$0(1.$)-. 0$.282$%*/$. *=*2>$ /* 12%?* /$ -:(*/$) /$ /2)2'@A-1 ! ! ! ! ! ! ! ! ! ! ! ! ! ! "H5 >A22Lista de Algoritmos
!" #$%&'&(&)*+ ,+-+ + $.%*/+%*0+ *1*2*+( '&. 0+(&-$. '$ δv $ XT ! ! ! ! ! ! ! ! !
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Lista de Abreviaturas e Siglas
SISO !"#$%&'()* !'"#$%+)*()* V AN T s !"#$%&'( )*+"'( ,-' .+/0%&12'( ABC 3/(4"51 2" $''+2"6121( &'$1&7 $"64+12' "5 O = CV N ED 3/(4"51 2" +"8"+96$/1 21 4"++1 :,'+4"7 &"(4"7 ;1/<'= DY L 3/(4"51 2" +"8"+96$/1 2' >"64' :1++1(4'7 8'+?1 &14"+1&7 "&">12'+= C = CG @"64+' 2" 51((1 2' 2/+/A#>"& O, CV, CB B+/A"5 2' (/(4"51 2" $''+2"6121( &'$1&7 $"64+' 2" >'&%5" " $"64+' 2" C%4%1;/&/212" 2' 2/+/A#>"&! D [ax, 0, az]T !"4'+ 2' @! 01+1 ' @E !T R7 !T L !"4'+ 2' @! 01+1 2/+"/41 " "(F%"+21 2' $"64+' 2' 0+'0%&('+ !tail !"4'+ 2"(2" @! 14* G*&/$" 21 $1%21 " .+16(8'+51?-' 21 514+/H 2' F%12+' ,IJ 01+1 F%1K 2+' )L@ "a .+16(8'+51?-' 21 514+/H 2" ' (/(4"51 2" $''+2"6121( 2' >"64' 01+1 ' (/(4"51 2" $''+2"6121( 2" )L@ φ7θ7ψ M'&&7N/4$G7O1P Q6A%&'( 2" I%A&"+ 1(('$/12'( $'5 1
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&'$/212" 2" B "5 (/(4"51 2" $''+2"6121( ,IJ= " ("%( $'50'6"64"( 6' (/(4"51 2" $''+2"6121( )L@ ω = [p, q, r]T !"&'$/212" 16A%&1+ 2' F%12+' )L@ 6' (/(4"51 2" $'K
'+2"6121( ,IJ " (%1( $'50'6"64"( 6' (/(4"51 2" $''+2"6121( )L@
$ = [#, ω]T !"&'$/212" /6"+$/1&7 >"&'$/212" 2" ('&'T>"&'$/212" 16K
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δ N+"U<' /62/$162' %51 0"F%"61 0"+4%+;1?-' 2" %51 >1+/V>"& 2121 "5 4'+6' 2' ("% >1&'+ 6'5/61&
δxv= [δu, δω, δq, δθ]T ∈ <4×1 !"4'+ 2" "(412' 2' 5'2"&' &'6A/4%2/61& &/6"1+/H12'
δxh= [δv, δp, δr, δφ]T ∈ <4×1 !"#$ %! !&"'%# %# (#%!)# )'"!$') )*+!'$*,'%#-v∈ <4×3. !v∈ <4×3 /'"$*,!& %'& !01'23!& %*+4(*5' )*+!'$*,'%'& )#+6*"17
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(!+"!-"g= [ug, vg, ωg, pg, qg, rg]T !)#5*%'%! %! '"'01! ! 5#(8#+!+"!& +# &*&"!(' %!
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"!(' %! 5##$%!+'%'& =>?-"ω ="cω+"g = [#ω, ωω] !"#$ %! <!)#5*%'%! %# <!+"#. *61') @ 5#+&"'+"! %! <!+"# ('*& # '"'01!-#a =# − #ω !"#$ %' <!)#5*%'%! %# '$ )*+!'$-ωa = ω − ωω !"#$ %' <!)#5*%'%! %# '$ '+61)'$-"a= [#a, ωa]T =" − "ω !"#$ %' <!)#5*%'%! %# '$-α A+61)# *+5*%!+"! %' '!$#%*+4(*5' )#+6*"1%*+') B4+7 61)# %! '"'01!C β A+61)# *+5*%!+"! %' '!$#%*+4(*5' )'"!$') B%!$$'8'7 6!( %# 4+61)#C ρ ?!+&*%'%! %# '$ Pd= 1/2ρVt2 D$!&&E# %*+4(*5' Vt=pu2a+ va2+ ω2a <!$%'%!*$' <!)#5*%'%! %# '$ F G9H $ = [N, E, D]T D#&*2E# %# ; !( 01'%$# =>?
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+'%'& =>? ¯
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¯g !"#$ %! &#$'() ! *#*!+"#) %! ,$(-.%(%! ¯p !"#$ %! &#$'() ! *#*!+"#) %! /$#/01)2# ¯k !"#$ %! &#$'() ! *#*!+"#) 3.+4".3# ¯ω !"#$ %! &#$'() ! "#$50! %! -!+"# .+%06.%# clp, cmq, cnr 7#!83.!+"!) (!$#%.+9*.3#) %! (*#$"!3.*!+"# $#11: /."3; ! <(=> Cd, CY, Cl ?$$()"#: &#$'( 1("!$(1 ! 3#!83.!+"!) %! !1!-('2# +# ).)@ "!*( %! 3##$%!+(%() %# -!+"#> CL, CM, CN 7#!83.!+"!) %! *#*!+"# $#11: /."3; ! <(= +# ).)"!*( %! 3##$%!+(%() %# -!+"# Cdi, CY β, Clα &#$'( (!$#%.+9*.3( %!$.-(%#) %! 3#!83.!+"!) CLβ, CM α, CM αβ, CM βα, CM β, CN β A#$50! (!$#%.+9*.3# %!$.-(%# %! 3#!83.!+"!)> Clδe, CY δr, CLδa, CM δe, CN δr B+"$(%( (!$#%.+9*.3( %!$.-(%# %! 3#!83.!+"!)> ! C#*!+"0* 1.+!($ " C#*!+"0* (+,01($ W B+!$,.( 3.+4".3( W D!)# B E#$'( %! F0"0(G.1.%(%! m C())( !)3(1($ %# %.$.,H-!1 mB C())( %! F0"0(G.1.%(%! # = m$3 C("$.6 %! *())( %# %.$.,H-!1> #v C("$.6 %! *())( -.$"0(1> #a= m$3+#v C("$.6 %! *())( (/($!+"!> #Ba= mB$3+#v C("$.6 %! *())( (/($!+"! %# ($ F0"0(+"!> % C("$.6 %! .+!$3.( %# %.$.,H-!1 I-!H301#J> %v C("$.6 %! .+!$3.( -.$"0(1> %B C("$.6 %! .+!$3.( %# ($ F0"0(+"!> %a=% + %v C("$.6 %! .+!$3.( (/($!+"! %# %.$.,H-!1> %Ba=%B+%v C("$.6 %! .+!$3.( (/($!+"! %# ($ F0"0(+"!> ¯ #v C("$.6 %! *())( -.$"0(1 "#"(1 3#* *())() ! .+!$3.()> ¯ #a C("$.6 %! *())( (/($!+"! "#"(1 %# %.$.,H-!1 3#* *()@ )() ! .+!$3.()> KK...
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FFH-1 Introdução
1.1 Motivações
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1.3 Estado da arte em modelagem e controle de dirigíveis
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2 Modelo matemático do dirigível
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