bai 3 - chuong 3 - dklt mien t - thiet ke bdk
TRANSCRIPT
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8/10/2019 Bai 3 - Chuong 3 - DKLT Mien t - Thiet Ke Bdk
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III. !I"U KHI#N LIN T$CTRONG MI"N TH%I GIAN
BM!i"u Khi#n T$!%ngTh.S.!&ng V'n M(
3.4 THI&T K&B'!I"U KHI#N
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III. !I"U KHI#N LIN T$C TRONG MI"N TH%I GIAN
3.4 THI&T K&B'!I"U KHI#N
Ph!n h"i tr#ng thi Ph!n h"i $%u ra&x = Ax + Bu
= Ax + B w ! Rx( )
= A!BR( )x + Bw
&x(t) =Ax +Bu
=Ax +B w !Ry( ) = Ax + B w ! RCx( )
= A!BRC( )x(t)+ Bw
det sI! A+ BR( ) = (s ! s1)(s ! s2 )K det sI! A+ BRC( ) = (s ! s1)(s ! s2 )K
C%n xc $&nh ma tr'n R th(a mn:
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3.4 THI&T K&B'!I"U KHI#NPH()NG PHP ACKERMANN
B*+c 2:)*a MHTT v+d#ng chu,n $i+u khi-n
sT= (0,K,0,1)(B,AB,K,A
n!1B)
!1
"sT(B,AB,K,A
n!1B) = (0,K,0,1)
S =
sT
sTA
M
sTA
n!1
"
#
$$$$
%
&
''''
(SB =
sTB
sTAB
M
sTA
n!1B
!
"
####
$
%
&&&&
=
0
0
M
1
!
"
##
##
$
%
&&
&&
SA =
sTA
sTA
2
M
sTA
n
!
"
####
$
%
&&&&
=
sTA
sTA
2
M
!a0sT! a
1sTA !K! a
n!1sTA
n!1
"
#
$$$$
%
&
''''
0 1 0 K 0
0 0 1 K 0
M M M O 0
0 0 0 K 1
!a0 !a
1 !a
2 K !a
n!1
"
#
$$$$$
%
&
'''''
S =
0 1 0 K 0
0 0 1 K 0
M M M O 0
0 0 0 K 1
!a0 !a
1 !a
2 K !a
n!1
"
#
$$$$$
%
&
'''''
sTA
sTA
2
M
sTA
n
!
"
####
$
%
&&&&
=
sTA
sTA
2
M
!a0sT! a
1sTA!K! a
n!1sTA
n!1
"
#
$$$
$
%
&
'''
'
=SA
z = Sx! &x =S!1
&z
&x = Ax +Bu! &z = SAS!1
x+ SBu =
0 1 0 K 0
0 0 1 K 0
M M M O 0
0 0 0 K 1
!a0 !a
1 !a
2 K !a
n!1
"
#
$$$$$
%
&
'''''
x+
0
0
M
1
!
"
####
$
%
&&&&
u
)4t
)4t ma tr'n
Ta c
)5i bi6n
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III. !I"U KHI#N LIN T$C TRONG MI"N TH%I GIAN
Hy tm ma tr!n ph"n h#i tr$ng thi K sao cho h%kn c &'(c cc &i)mc*c mong mu+n l
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3.4 THI&T K&B'!I"U KHI#N
Dnh cho -1i t*2ng MIMO
PH()NG PHP ROPPENECKER
B'!I"U KHI#N PH4N H5I TR6NG THI GN !I#M C7C
(Tham kh8o)
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3.4 THI&T K&B'!I"U KHI#N
PH()NG PHP MODAL
&x = Ax +Bu
y = Cx + Du!"#
B*+c 1:Xc $&nh ma tr'n ModalM $-$*a ma tr'nAv+d#ng $*8ng cho
B'!I"U KHI#N PH4N H5I TR6NG THI GN !I#M C7C
)1i t*3ng MIMO c m hnh:
M!1AM=
!1 0 L 0
0 !2 L 0
M M O M
0 0 L !n
"
#
$$$$
%
&
''''
=diag(!i )
V9i l cc gi tr&ring c7aA!i
M = a1 K a
n( )!
i
I! A
( )a
i
= 0
V d9:Bi6n $5i ma tr'n A thnh d#ng $*8ng cho:
A=1 2
3 2
!
"#$
%&
l cc vec t.bn ph!i c7aAa
i
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3.4 THI&T K&B'!I"U KHI#N
PH()NG PHP MODAL
B*+c 2:)5i bi6n $-thu $*3c MHTT t*.ng $*.ng
G = M!1
AM=
!1
0 L 0
0 !2
L 0
M M O M
0 0 L !n
!
"
####
$
%
&&&&
=diag(!i )
x = Mz ! z = M"1x
! &z = M!1AMz + M
!1Bu = Gz + M
!1Bu
S=
s1 0 L 0
0 s1 L 0
M M O M
0 0 L sn
!
"
####
$
%
&&&&
=diag(si )
B*+c 3:Xc $&nh ma tr'n $*8ng cho S ch:a t;t c!$i-m c0c mong mu1n c7a h/
& & " #
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3.4 THI&T K&B'!I"U KHI#NPH()NG PHP MODAL
T = M!1
B( )!1
= B!1
M
" R = !T S!G( )M!1 B2$i+u khi-n ph!n h"i m
B*+c 4:Xc $&nh b2$i+u khi-n
& & " #
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3.4 THI&T K&B'!I"U KHI#NPH()NG PHP MODAL
Tr*:ng h2p ma tr;n B suy bi
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3.4 THI&T K&B'!I"U KHI#N
Tnh ton b2)K ph!n h"i $%u ra dnh cho $1i t*3ng MIMO
PH()NG PHP MODALB'!I"U KHI#N PH4N H5I !=U RA GN !I#M C7C
& & ' " #
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3.4 THI&T K&B'!I"U KHI#N
T=m hnh )K ph!n h"i tr#ng thi v9iRxl b2)K, c%n tm m2tma tr'n Q$-c th-chuy-n $i-m tr#ng thixv+y, ngh?a l:
PH()NG PHP MODALB'!I"U KHI#N PH4N H5I !=U RA
QC = I
!Q = C"1
Tuy nhin khng ph!i lc no c@ngtm $*3c Qdo ma tr'n Csuy bi6n.Do $, ta tnh nghi/m Q theo ph*.ngphp sau:
QC =I
!CQC = C
!Q = CT(CC
T)"1
& & ' " #
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3.4 THI&T K&B'!I"U KHI#N
Cc b*9c thi6t k6b2)K R ph!n h"i $%u ra theo ph*.ng php Modal:
PH()NG PHP MODALB'!I"U KHI#N PH4N H5I !=U RA
Q = CT(CC
T)!1
B*+c 1:Thi6t k6B)K ph!n h"i tr#ng thi ModalRx
B*+c 2:Xc $&nh ma tr'n Q
B*+c 3:Tnh B)KR R =RxQ
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