!
"
#$
% %
) &
, - ( . "/$ 0 1
& "2$
3 & 4 !
& !
5 & & & 6) ( 7 ( & &
5) 5& !
! !
#) ! & & +0 '+-0) "#$ "%$ & ' & )
! & ( ' & () - & & ' ( ) & & & Æ 3 & & &
& %) 8 &
! !
* & + &
*
* ( ! (
6 * & & "9$ ! & & & ' 0& :! ,1 1 ";$7 !
" #
$
"
% &'()* !
" +, -). '/( %' .)'%& 0
1 23
"<$ 6
! = #
6 & > "?$ "@$ A
differentiator
+
low-pass filter
θ
"#B$ "##$ "#%$ ωest
C θest
"#/$ "#2$
integrator
regulator
& & & 4" ( 5
& & - & & & & ! ( &
'
)
3 & & '& ) &
&
8 & & &
& & & '
) & & & & & & & & C & & ( & & & & * & & & & '
) & & ( "
( +-0 & & % & & & & ¬
¬
¬
' ) E
¬
F #
·½½
* &
, %
&
* ¾
E
' F
%)
#
'
%)
& / ( # * & 2 * & 9
- ' )
! & 6 & !
7 (
D D $ & D &
3&
&
& C & &
& &
& & + & & & & '?. -) , 9
& & * 0
& (
& & # & & ! # & ' 3 & & ) & & & 6 & & & & %
ωest
ωslow
Gs(z)
ωfast
K
10
T/2
Angle (rad)
θ
Reference Position
20
Θest
T
0
-10
-20
z-1
-30
-40
0
0.05
0.1
0.15
4" % 0.35
0.4
0.45
0.3
0.35
0.4
0.45
0.35
0.4
0.45
100
Speed (rad/s)
aslow
Gs(z)
0.3
150
ωest
Gs(z)
0.25
Reference Speed
aest
θ
0.2
T/2
50
0
-50
-100
afast
Gr(z)
T
z-1
-150
T(z+1) Θest
2(z-1)
0
0.05
0.1
0.15
0.2
0.25
Reference Acceleration
Acceleration (rad/s2)
0
4" ) & & & -500
-1000
-1500
0
( & 0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
4" & 6
7
- / & ! &
& & &
! & & & & & * & 7
& & ¾ * * & ' ) 5
&G & & & ' )
' )
E
'
F #)
# %'
#)
7 &
' )
E
'
)
+ * & -
& & * /
2 Actual Acceleration & Estimated Acceleration
Actual Speed & Estimated Speed
5000
150
Accel. (rad/s2)
Speed (rad/s)
100
50
0
-50
0
-100
-150
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-5000
0.45
0
0.05
0.1
0.5
50
Accel. (rad/s2)
Speed (rad/s)
100
0
-0.5
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-100
0
0.45
Speed (rad/s)
0.5
Angle (rad)
0.005
0
-0.005
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0.45
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.35
0.4
0.45
0.35
0.4
0.45
Speed Estimation Error
1
0.05
0.3
-50
Position Estimation Error
0
0.25
0
0.01
-0.01
0.2
Acceleration Estimation Error
Speed Estimation Error
1
-1
0.15
0.35
0.4
0
-0.5
-1
0
0.45
0.05
0.1
0.15
0.2
0.25
0.3
Position Estimation Error
4" / 1 0.01
Angle (rad)
0.005
& F#9B
#9B
6 *
#9BB
#B
0
-0.005
-0.01
( &
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
4" * /''' 5 1
2 :! * &
6 9BBB - & %BB *
/ /#2
#B
D ( E
& 2 & & ¾
E B@2
& E ?
E ?##;
#B
E BB2% ( E #;;<
;B & ! & D E
,9 & 6
E #9<
D E
* & E <?92
& :
6 & & (
& 6) & ( & B%%
?
7 5) & ( #;;<
E?
& & & * & % B%<
; 2
Reference Speed & Estimated Speed
150
100
100
Speed (rad/s)
50
0
-50
50
0
-50
-100
-100
-150
-150
0
0.05
0.1
0.15
0.2
0.25
*
0.3
0.35
0.4
0
0.45
0.1
0.15
0.2
0.25
0.3
Speed Error (ω*- ω , ω* ω
est
ω*-ωest (rad/s)
2
0
2
-2
0
ω*-ωbackward (rad/s)
ω*-ωest (rad/s)
0.05
*
Speed Error (ω ω
- est, ω ω
- backward)
0.35
0.4
backward
2
0
2
-2
0
-2
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-2
0
0.45
0.01
0.005
0.005
Angle (rad)
0.01
Angle (rad)
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
0.35
0.4
0.45
0.4
0.45
Position Estimation Error
Position Estimation Error
0
0
-0.005
-0.005
-0.01
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
-0.01
0
0.45
0.05
0.1
0.15
0.2
0.25
0.3
Estimated Acceleration & Reference Acceleration
Estimated Speed, Slow & Fast Components
4000
100
Acceleration (rad/s2)
150
Speed (rad/s)
0.45
)
ω*-ωbackward (rad/s)
Speed (rad/s)
Reference Speed & Estimated Speed
150
ωslow
50
0
ωfast
-50
ωest
-100
2000
0
-2000
-4000
-150
0
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
0.4
0
0.45
0.05
0.1
0.15
0.2
0.25
Time (s)
0.3
0.35
4" : 1 9 4" 8 1 9 6 * & & * & C & & & 5 & 7 ! & ( & &
0 *
< ? * & & ( G* ## 8
#2#B & &
& &! 4 6 &
? & 9
< / Actual Acceleration & Estimated Acceleration
5000
Accel. (rad/s )
- 6 2
& ? - @ &7 0
& +-0 -5000
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
5 Acceleration Estimation Error
100
Accel. (rad/s2)
* H 5 50
& & 0
& -50
-100
0
& & & 0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
;(< $ =" +
6 > ?@
A 0$B
"0
#" +
(..:
0.5
;%< C +
"0#"
! (..*
0
;)< D = 3 @ E
F ! "
( ( /*G*8 (..*
-0.5
;&< H
@ D = , E F ! ! ! (/
-1
/*G*' 43 (../
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
;/< > = @ = #
E$ ?
Position Estimation Error
9
F ! !
0.01
! &( & /('G/(* " (..%
;*< = #
$
@ E$ 0
4$ I
F
0.005
! ! ! &* / (%'%G(%'8
= (..8
0
;8< > = @ # E" 0
1 F ! ! ! &8 /
(%((G(%(8 = (..:
-0.005
;:< 6 $ !J" E
" F ! ! !
-0.01
#! ! ? 4 (..% /:/G/.%
0
0.05
0.1
0.15
0.2
0.25
0.3
0.35
0.4
0.45
;.< >B C " E 9 3
Time (s)
"
F !
! "! & * *%8G*&' ?
(..*
4" . 5
1 ;('< !
$ +
B D C # 6 EA"0
0" F ! $$ %8 & 8'(G8'/ >5" (..(
;((< !
> $ ?
@ E?
& & ! 3 "0
F ! ! &% & ))8G)&) "
! 0
(../
& ;(%< ," D E6
30
F
! $$ )* ( .:G('&
>543 %'''
;()< + E$
3 9 I
" 0
KF )& ) )8.G):& (..:
;(&< H H
" 6
E$
0
7 " , " I
F %&&& $ '&& D H " (...
< & ;(/< $ A !
H " E "
F ! ! ). ( ((G(. 43 (..%
Speed Estimation Error
Angle (rad)
Speed (rad/s)
1
6 ;