3ª avaliação de identificação_senko
TRANSCRIPT
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UNIVERSIDADE FEDERAL DA PARABA
PROGRAMA DE PS-GRADUAO EM ENGENHARIA MECNICA
CENTRO DE TECNOLOGIA
IDENTIFICAO DE SISTEMAS
(3 Lista de Exerccios)
PROFESSOR: Jos A R!"#
ALUNO: R!$%&'( S)*+o
Jo,o P)sso&
M&'o . /012
1
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1 E3)'$4$!os (o Co)#%o5 A A R6 7Identificao de Sistemas Dinmicos Lineares8
5.2. I()*9!!$&' & "*,o () 9'&*s)';*$!& (!s$')9& () "< ='o$)sso >o?)'*&(o =)#& s)>"!*9)
)@"&,o & (!)')*&:1 0
A B A 1B A 1By t a y t b u t+ =
[ ] 1
0
A B A 1B A 1B Ta
y t y t u tb
= =
"9!#!&*(o o )s9!
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u=[1.197; -1.830;-.420;-.5721;-.287;.435; -1.404;.193; -1.771;.701;
-.389;-1.040; -1.256;.966];
n=length(y);
Y=[];
!=[];
"r#=2$1$n;
Y=[Y;y(#)];
!=[!;-y(#-1) u(#-1)];
en%
theta=(!n&(!'!))!'y(2$14);
a1=theta(1)
0=theta(2)
&1 0112
0 011
Co
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5.3. Co*s!()'&' o ='o$)sso (!s$')9o $&'&$9)'!&(o =)#& )@"&,o:
0 1A B A B A 1By t b u t b u t= +
[ ] 0
1
A B A B A 1B Tby t u t u tb
= =
o*() &s s)>"!*9)s
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theta=(!n&(!'!))!'Y;
0=theta(1)
1=theta(2)
t=[1$11];
!gure(1)
*l"t(t+u)
!gure(2)
*l"t(t+y)
"rt=2$1$n
ye,t=!theta;
en%
t=2$1$n;
!gure(3)
*l"t(t+Y+t+ye,t')
0 01
1 021
Co
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5.5. A(
1
1 1
052 A BA B
A1 052 BA1 052 B A Bp
z Y zG z
z z z
= =
Lo>o
1
1 /
A B 052
A B 1 05 J 05 02
Y z z
z z z
=
+
A B 05 J A 1B 05 02 A /B 052 A 1By ! y ! y ! u != + + Q )@"&,o () (!)')*&s (o ='o$)sso
- U9!#!&*(o o M&9#&
E3)'$4$!o 22 (o #!?'o (o Co)#%o
$#)&' #$#os) #$#$
910:02:1/6"'916 '&'&" (06 '06 s06)*(o':1:/2 "(16 ()>'&" (0(-1-002(-/02"(-16 '0'-1-002'-/02"'-16 s0s-1-002s-/02"s-16)*(9/1:1:/26
F!>"'&s (&s ')s=os9&s & $&(& )*9'&(&!>"')1s"=#o91/16=#o99/5"(69!9#)WD)>'&"Ws"=#o91//6=#o99/5(69!9#)WR)s=os9& ()?!(o &o ()>'&"W!>"')/s"=#o91/16=#o9915"'69!9#)WR&
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o' +:1:/06 X(YX(6(+Z6X'YX'6'+Z6XsYXs6s+Z6 !(Y!(6(+-1 "(+-1Z6!'Y!'6'+-1 "'+-1Z6!sY!s6s+-1 "s+-1Z6)*(9)9&(!*?!(W!(!(WX(69)9&'!*?!'W!'!'WX'69)9&s!*?!sW!s!sWXs6&1[(9)9&(10[(9)9&(/&1['9)9&'10['9)9&'/&1[s9)9&s10[s9)9&s/o' 9/:1:/0 )s9(!(9)9&(6 )s9'!'9)9&'6 )s9s!s9)9&s6)*(
M&9'!)s () $o?&'!*$!&=[(!*?!(W!(=['!*?!'W!'=[s!*?!sW!s
&1[( 2022)-0010[( 21/221)-001&1[' 202010/)-0010['
2//0/2)-001&1[s 2/1220)-0010[s 2/11/0/)-001=[( 010)-001 -2012/)-001 -2012/)-001 //)-001=[' /1//2//)-001 -/210121)-001 -/210121)-001 //2/20/)-001=[s
020022111)-001 -0212010)-001 -0212010)-001 021201)-001
a) O9)' & s&4(& (o ='o$)ssoy"t#=&'& os s)>"!*9)s s!*&!s () )*9'&(&:
! S!* ()>'&": u"t# $ %6
7
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0 10 20 300
0.2
0.4
0.6
0.8
1
1.2
1.4
1.6
1.8
2Degrau
0 10 20 300
0.2
0.4
0.6
0.8
1
1.2
1.4Resposta devido ao degrau
!! S!* '&
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0 5 10 15-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1Sinal senoidal
0 5 10 15-1.5
-1
-0.5
0
0.5
1
1.5Resposta devido ao sinal senoidal
b) U9!#!&*(o $o'&"
1
0
052I0K0521G
d
d
d
a
b
= =
V)9o' () =&'
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05 /JJ 05 /IJA B
05/IJ 05//Er
) t
=
M&9'! () $o?&'!*$!& =&'& o s!* s)*o!(
05 I0F 05 GGFA B
05GGF 05GH0s
) t =
V)'!!$&-s) @") os )#)
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5.6. S)& o s!s9)"!*9) "*(& o'()" & 001N1006)001'&*(*N516
11
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0 10 20 30 40 50 60 70 80 90 100-1.5
-1
-0.5
0
0.5
1
1.5
- R"4(o $o<
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R/ 1 $o)!$!)*9) () $o'')#&,o
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0 50 100-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0a1
amostras
0 50 1000
0.2
0.4
0.6
0.8
1
1.2
1.4b0
amostras
0 50 1000
0.1
0.2
0.3
0.4
0.5
0.6
0.7
0.8b1
amostras
SE 51112/ so'&
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- %aro caso (nanb)!(21)
1 / 1 1A1 152 05 F B A B A1 152 B A B A Bz z y t z z u t e t + = +
A B 15 2 A 1B 05 F A /B A 1B 05 2 A /B A By ! y ! y ! u ! u ! e ! = + + +
O ='o>'&
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5.*
i) G)'&*(o ) s?&*(o o s!* () )*9'&(& PRBS \1 ) o '"4(o " & 001N1006)001'&*(*N516
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0 10 20 30 40 50 60 70 80 90 100
-1
-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6
0.8
1
- R"4(o
0 10 20 30 40 50 60 70 80 90 100-0.03
-0.02
-0.01
0
0.01
0.02
0.03
- P'o>'&
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91:1:N6!>"')1=#o995"6&3!sY0 N -1/ 1/Z!>"')/=#o9)
=&'
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SEs"
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0 20 40 60 80 100-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0a1
amostras
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3b0
amostras
SE /2//01)001
R/ 201)-001
P&'& o $&so $o*s!()'&*(o &9o' () )s@")$!" & 05 & so
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)*()*(911:1:1006!>"')=#o99150'5&3!sY0 100 1 /Z
MR*=/6 *"
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0 20 40 60 80 100-0.9
-0.8
-0.7
-0.6
-0.5
-0.4
-0.3
-0.2
-0.1
0a1
amostras
0 20 40 60 80 1000
0.5
1
1.5
2
2.5
3b0
amostras
SE 1111)001
R/ /012)-001
Us&*(o o '&*(o< e+
='o$)sso () )s9!
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5. G)'&*(o ) s?&*(o o s!* () )*9'&(& PRBS \1 ) o '"4(o " & 1N10006)1'&*(*N516
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- R"4(o
0 100 200 300 400 500 600 700 800 900 1000-4
-3
-2
-1
0
1
2
3
- Es9!
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)''o99-!W9)9&6 )''o () )s9!o'!9
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$#os) #o' )$#$
#o&( s!*&!s2(&9"s!*&!s2:516)s!*&!s2:5/6N#)*>9%"691:1:N6
A#>o'!9&*%o 9)9&9)9&>&
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- Para (/0)!(".11)
P&'
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0 200 400 600 800 1000-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2a1
amostras
0 200 400 600 800 1000-0.25
-0.2
-0.15
-0.1
-0.05
0
0.05
0.1a2
amostras
SE 1//)00R/ /112110)-001
Coo'!9
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0 200 400 600 800 1000-1.6
-1.4
-1.2
-1
-0.8
-0.6
-0.4
-0.2
0
0.2a1
amostras
0 200 400 600 800 1000-0.8
-0.6
-0.4
-0.2
0
0.2
0.4
0.6a2
amostras
SE 1/100//)00
R/ /1100/0)-001
- Para !""1
P&'
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R/ 02)-001
Coo'!9"')1=#o995"6&3!sY0 N -1/ 1/Z!>"')/=#o9)
1:/06o' 9:N 9129-1-029-/)96)*(
A#>o'!9
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)''o@99)''o@9-1)''o@96 &''&
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2. I()*9!!$&' os =&'
l"a% r""2g%l.%at
u=r""2g%l($+1);
y=r""2g%l($+2);
n=length(y);
/
Y=[];
!=[];
"r#=3$1$n;
Y=[Y;y(#)];
!=[!;-y(#-1) -y(#-2) u(#-1)];
en%
teta=!n&(!'!)!'Y; &et"r %e *aretr", e,t!a%"
a1=teta(1)
a2=teta(2)
0=teta(3)
ye,t=!teta; ,a%a e,t!a%a
t=3$1$n;
!gure(1)
*l"t(t+Y+''+t+ye,t+'g')
- P&'
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- U9!#!&*(o o >o'!9
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rue1(#)=u(#)err"(#);
en%
>/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
- Co
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- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") 0002
-Co)!$!)*9) () $o'')#&,o
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"r#=1$2
y(#)=0;
ye,t(#)=0;
err"(#)=0.0;
err"(#)=0.0;
err"1(#)=0.0;
err"(#)=0.0; rue1(#)=0;
en%
"r#=3$1$n
!=[-y(#-1);u(#)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") 001
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-Co)!$!)*9) () $o'')#&,o rr" %e e,t!a"')
38
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- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") -000
-Co)!$!)*9) () $o'')#&,o
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!=[-y(#-1);-y(#-2);-y(#-3);u(#);u(#-1)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") -0000
-Co)!$!)*9) () $o'')#&,o
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- o&e7o &e ;8 or&em 1 :ero
cl",e all
clear all
clc
l"a% r""2g%l.%at
u=r""2g%l($+1);
y=r""2g%l($+2);
n=length(y);
/
n*=6; nuer" %e *araetr",
*=1000eye(n*+n*); c"n%!e, !n!c!a!,
teta=er",(n*+1);
la=1; at"r %e e,uec!ent"
"r#=1$4
y(#)=0;
ye,t(#)=0;
err"(#)=0.0;
err"(#)=0.0; err"1(#)=0.0;
err"(#)=0.0;
rue1(#)=0;
en%
"r#=5$1$n
!=[-y(#-1);-y(#-2);-y(#-3);-y(#-4);u(#);u(#-1)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
41
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- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") -000/
-Co)!$!)*9) () $o'')#&,o
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"r#=6$1$n
!=[-y(#-1);-y(#-2);-y(#-3);-y(#-4);-y(#-5);u(#);u(#-1)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") -000/
-Co)!$!)*9) () $o'')#&,o
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- o&e7o &e 68 or&em 1 :ero
cl",e all
clear all
clc
l"a% r""2g%l.%at
u=r""2g%l($+1);
y=r""2g%l($+2);
n=length(y);
/
n*=8; nuer" %e *araetr",
*=1000eye(n*+n*); c"n%!e, !n!c!a!,
teta=er",(n*+1);
la=1; at"r %e e,uec!ent"
"r#=1$6
y(#)=0;
ye,t(#)=0;
err"(#)=0.0;
err"(#)=0.0; err"1(#)=0.0;
err"(#)=0.0;
rue1(#)=0;
en%
"r#=7$1$n
!=[-y(#-1);-y(#-2);-y(#-3);-y(#-4);-y(#-5);-y(#-6);u(#);u(#-1)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
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- Co'')#&,o $'"&(& )*9') o s!* () )*9'&(& ) o )''o () =')?!s,o:
R") -0000
-Co)!$!)*9) () $o'')#&,o
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a2(#)=0;
0(#)=0;
1(#)=0;
err"(#)=0.0;
err"(#)=0.0;
err"1(#)=0.0;
err"(#)=0.0; rue1(#)=0;
en%
"r#=3$1$n
!=[-y(#-1);-y(#-2);u(#-1);u(#-2)];
err"(#)=y(#)-!'teta; err" %e e,t!a"
:=*!(la/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
!gure(3)
,u*l"t(221)+*l"t(t+a1(t))+t!tle('a1')+Clael('a",tra,');
,u*l"t(222)+*l"t(t+a2(t))+t!tle('a2')+Clael('a",tra,');
,u*l"t(223)+*l"t(t+a1(t))+t!tle('0')+Clael('a",tra,');
,u*l"t(224)+*l"t(t+a2(t))+t!tle('1')+Clael('a",tra,');
- Co
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7/23/2019 3 Avaliao de Identificao_Senko
47/50
- C"'?&s (os )''os () )s9!
-
7/23/2019 3 Avaliao de Identificao_Senko
48/50
- U9!#!&*(o &s ("&s "#9!
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7/23/2019 3 Avaliao de Identificao_Senko
49/50
err"(#)=err"(#)err"(#);
err"t(#)=err"(#-1)/=,u(err") ,"at?r!" %" err" ua%r@t!c"
2=1-(>/,u(err")) c"e!c!ente %e c"rrela"
Alt!*la
rue=(1n),u(rue1) c"rrela" crua%a entre ",
,!na!, %e entra%a e err" %e *re&!,"
t=1$1$n;
!gure(1)
*l"t(t+y(t)+t+ye,t(t))+t!tle('B"*ara" %a ,a%a real e a e,t!a%a')
!gure(2)
*l"t(t+err"(t))+t!tle('>rr" %e e,t!a"')
!gure(3)
,u*l"t(221)+*l"t(t+a1(t))+t!tle('a1')+Clael('a",tra,');
,u*l"t(222)+*l"t(t+a2(t))+t!tle('a2')+Clael('a",tra,');
,u*l"t(223)+*l"t(t+a1(t))+t!tle('0')+Clael('a",tra,');
,u*l"t(224)+*l"t(t+a2(t))+t!tle('1')+Clael('a",tra,');
- Co
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7/23/2019 3 Avaliao de Identificao_Senko
50/50
- C"'?&s (os )''os () )s9!