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2500
2000
1500
1000
500
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8000
6000
4000
2000
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time(sec)
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600
400
200
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time(sec)
0
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time(sec)
1000
800
600
400
200
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time(sec)
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Cart 1 Velocity, x 1 dot
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2500
2000
1500
1000
500
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time(sec)
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time(sec)
3000
2000
1000
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time(sec)
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0
−0.1
0 1 2 3
time(sec)
0.6
0.4
0.2
0
−0.2
0 1 2 3
time(sec)
0.6
0.4
0.2
0
−0.2
0 1 2 3
time(sec)
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Damped−Seesaw Oscillation Mode (λ 4
=−1.6859−1.5444i)
0.02
0
−0.02
−0.04
P
−0.06
P0
−0.08
0 1 2 3
Seesaw Angle, θ (deg)
time(sec)
Seesaw Angle Rate, θ dot
(deg)
0.1
0
−0.1
−0.2
−0.3
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
Cart 1 Position, x 1
(cm)
0.15
0.1
0.05
0
−0.05
0 1 2 3
time(sec)
0.08
0.06
0.04
0.02
0
−0.02
0 1 2 3
time(sec)
0.15
0.1
0.05
0
−0.05
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
Cart 1 Velocity, x 1 dot
(cm)
0.05
0
−0.05
−0.1
−0.15
0 1 2 3
time(sec)
0.4
0.3
0.2
0.1
0
−0.1
0 1 2 3
time(sec)
0.05
0
−0.05
−0.1
−0.15
0 1 2 3
time(sec)
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Cart−Position Equilibrium Mode (λ 5
=0)
P
9
P
9
Seesaw Angle, θ (deg)
4 10−10 2
0
0 1 2 3
x
time(sec)
Seesaw Angle Rate, θ dot
(deg)
2 10−9
1.5
1
0.5
0
0 1 2 3
x
time(sec)
Cart 2 Position, x 2
(cm)
−0.7748
−0.7748
−0.7748
−0.7748
−0.7748
0 1 2 3
time(sec)
Pendulum Angle, α (deg)
0 10−8
−0.5
−1
−1.5
−2
−2.5
0 1 2 3
x
time(sec)
Pendulum Angle Rate, α dot
(deg)
Cart 2 Velocity, x 2 dot
(cm)
8 10−9 6
4
2
0
0 1 2 3
x
time(sec)
0 10−7
−0.5
−1
−1.5
0 1 2 3
x
time(sec)
Cart 1 Position, x 1
(cm)
0.6322
0.6322
0.6322
0.6322
0.6322
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
2.5 10−10 2
1.5
1
0.5
0
0 1 2 3
x
time(sec)
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Cart−Speed Damping Mode (λ 6
=−9.434)
P Y P
0
0 1 2 3
Seesaw Angle, θ (deg)
1.5
1
0.5
2 x 10−3 time(sec)
Seesaw Angle Rate, θ dot
(deg)
5 x 10−3 0
−5
−10
−15
−20
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
5 x 10−5 0
−5
−10
−15
−20
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
2 x 10−3
1.5
1
0.5
0
0 1 2 3
time(sec)
Pendulum Angle, α (deg)
0 10−3
−1
−2
−3
0 1 2 3
x
time(sec)
Pendulum Angle Rate, α dot
(deg)
0.03
0.02
0.01
0
−0.01
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
0.05
0
−0.05
−0.1
−0.15
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
1
0.8
0.6
0.4
0.2
0
0 1 2 3
time(sec)
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Pendulum Damping Mode (λ 7
=−17.8801)
0P −8
0 1 2 3
Seesaw Angle, θ (deg)
−2
−4
−6
0 x 10−4 time(sec)
Seesaw Angle Rate, θ dot
(deg)
15 x 10−3
10
5
0
−5
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
0.03
0.02
0.01
0
−0.01
0 1 2 3
time(sec)
0.02
0
−0.02
−0.04
−0.06
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
0
−0.1
−0.2
−0.3
−0.4
−0.5
0 1 2 3
time(sec)
1
0.8
0.6
0.4
0.2
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
3 x 10−4 2
1
0
−1
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
0 x 10−3
−1
−2
−3
−4
−5
0 1 2 3
time(sec)
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Seesaw Damping Mode (λ 8
=−5.0763)
5 10−4
P
0
−5
−10
0 1 2 3
x
time(sec)
Seesaw Angle, θ (deg)
Seesaw Angle Rate, θ dot
(deg)
5 x 10−3 4
3
2
1
0
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
0
−0.01
−0.02
−0.03
0 1 2 3
time(sec)
0
−0.05
−0.1
−0.15
−0.2
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
0.2
0.15
0.1
0.05
0.8
0.6
0.4
0.2
0
0 1 2 3
time(sec)
1
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
4 x 10−4 3
2
1
0
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
1 x 10−3 0
−1
−2
−3
0 1 2 3
time(sec)
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Pendulum Toppling Mode (λ 1
=−6.9121)
3 x 10−3 2
1
0
time(sec)
0P −1
0 1 2 3
Seesaw Angle, θ (deg)
Seesaw Angle Rate, θ dot
(deg)
0
−0.005
−0.01
−0.015
−0.02
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
0.03
0.02
0.01
0
−0.01
0 1 2 3
time(sec)
0.05
0
−0.05
−0.1
−0.15
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
0
−0.05
−0.1
−0.15
Pendulum Angle Rate, α dot
(deg)
−0.2
0 1 2 3
time(sec)
1
0.8
0.6
0.4
0.2
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
3 x 10−4 2
1
0
−1
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
0 x 10−3
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
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Seesaw Toppling Mode (λ 2
=−3.6615)
0
0P 0 1 2 3
Seesaw Angle, θ (deg)
0.2
0.15
0.1
0.05
time(sec)
Seesaw Angle Rate, θ dot
(deg)
0
−0.2
−0.4
−0.6
−0.8
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
Cart 1 Position, x 1
(cm)
0.2
0.15
0.1
0.05
0.08
0.06
0.04
0.02
0.2
0.15
0.1
0.05
0
0 1 2 3
time(sec)
0
0 1 2 3
time(sec)
0
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
Cart 1 Velocity, x 1 dot
(cm)
0
−0.1
−0.2
−0.3
−0.4
−0.5
0 1 2 3
time(sec)
0
−0.05
−0.1
−0.15
−0.2
−0.25
0 1 2 3
time(sec)
0
−0.2
−0.4
−0.6
−0.8
0 1 2 3
time(sec)
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Seesaw Oscillation Mode (λ 3
=0+3.4932i)
0
0 P
−0.2
0 1 2 3
time(sec)
0.2
0.1
0
−0.1
−0.2
0 1 2 3
time(sec)
0.04
0.02
0
−0.02
−0.04
0 1 2 3
time(sec)
P
0.2
Seesaw Angle, θ (deg)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
Cart 1 Position, x 1
(cm)
0.2
0.1
0
−0.1
0.1
0
−0.1
−0.2
0 1 2 3
time(sec)
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Seesaw Angle Rate, θ dot
(deg)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
Cart 1 Velocity, x 1 dot
(cm)
0.4
0.2
0
−0.2
−0.4
0 1 2 3
time(sec)
1
0.5
0
−0.5
−0.05
−1
0 1 2 3
time(sec)
0.1
0.05
0
−0.1
0 1 2 3
time(sec)
1
0.5
0
−0.5
−1
0 1 2 3
time(sec)
5H[
Seesaw Oscillation Mode (λ 4
=0−3.4932i)
0
P
−0.2
0 1 2 3
0P
Seesaw Angle, θ (deg)
0.2
0.1
0
−0.1
time(sec)
Seesaw Angle Rate, θ dot
(deg)
0.4
0.2
0
−0.2
−0.4
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
Cart 1 Position, x 1
(cm)
0.2
0.1
0
−0.1
−0.2
0 1 2 3
time(sec)
0.04
0.02
0
−0.02
−0.04
0 1 2 3
time(sec)
0.2
0.1
0
−0.1
−0.2
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
Cart 1 Velocity, x 1 dot
(cm)
1
0.5
0
−0.5
−0.05
−1
0 1 2 3
time(sec)
0.1
0.05
0
−0.1
0 1 2 3
time(sec)
1
0.5
0
−0.5
−1
0 1 2 3
time(sec)
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Cart−Position Equilibrium Mode (λ 5
=0)
P
9 P 9
Seesaw Angle, θ (deg)
2 10−10 0
−2
0 1 2 3
x
time(sec)
Seesaw Angle Rate, θ dot
(deg)
5 x 10−10 0
−5
−10
−15
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
0.7748
0.7748
0.7748
0.7748
0.7748
0.7748
0 1 2 3
time(sec)
Pendulum Angle, α (deg)
2 x 10−8
1.5
1
0.5
0
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
Pendulum Angle Rate, α dot
(deg)
0 x 10−8
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
1 x 10−7
0.8
0.6
0.4
0.2
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
−0.6322
−0.6322
−0.6322
−0.6322
−0.6322
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
5 x 10−11 0
−5
−10
−15
−20
0 1 2 3
time(sec)
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Cart−Speed Equilibrium Mode (λ 6
=0)
0 10−9
Y
−0.5
−1
0 P
Y
−1.5
0 1 2 3
x
time(sec)
Seesaw Angle, θ (deg)
Seesaw Angle Rate, θ dot
(deg)
0 x 10−9
−2
−4
−6
−8
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
2.5
2
1.5
1
0.5
0
0 1 2 3
time(sec)
8 x 10−8 6
4
2
0
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
0.7748
0.7748
0.7748
0.7748
0.7748
0.7748
0 1 2 3
time(sec)
Pendulum Angle Rate, α dot
(deg)
5 x 10−7 4
3
2
1
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
0
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
−0.6322
−0.6322
−0.6322
−0.6322
−0.6322
0 1 2 3
time(sec)
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Pendulum Damping Mode (λ 7
=6.9121)
0P −2.5
0 1 2 3
Seesaw Angle, θ (deg)
−0.5
−1
−1.5
−2
0 x 106 time(sec)
Seesaw Angle Rate, θ dot
(deg)
0 x 107
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
0 x 107
−0.5
−1
−1.5
−2
−2.5
0 1 2 3
time(sec)
Cart 2 Velocity, x 2 dot
(cm)
0 x 108
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
Pendulum Angle, α (deg)
15 107
10
5
0
0 1 2 3
x
time(sec)
Pendulum Angle Rate, α dot
(deg)
10 x 108 8
6
4
2
0
0 1 2 3
time(sec)
Cart 1 Position, x 1
(cm)
0 105
−1
−2
−3
0 1 2 3
x
time(sec)
Cart 1 Velocity, x 1 dot
(cm)
0 x 106
−0.5
−1
−1.5
−2
0 1 2 3
time(sec)
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Seesaw Damping Mode (λ 8
=3.6615)
10000
8000
6000
4000
2000
0
0P 0 1 2 3
Seesaw Angle, θ (deg)
time(sec)
Seesaw Angle Rate, θ dot
(deg)
4 x 104 3
2
1
0
0 1 2 3
time(sec)
Cart 2 Position, x 2
(cm)
Pendulum Angle, α (deg)
Cart 1 Position, x 1
(cm)
8000
6000
4000
2000
4000
3000
2000
1000
10000
8000
6000
4000
2000
0
0 1 2 3
time(sec)
0
0 1 2 3
time(sec)
0
0 1 2 3
time(sec)
Pendulum Angle Rate, α dot
(deg)
Cart 2 Velocity, x 2 dot
(cm)
15000
10000
5000
Cart 1 Velocity, x 1 dot
(cm)
3 104 2
1
0
0 1 2 3
x
time(sec)
0
0 1 2 3
time(sec)
4 x 104 3
2
1
0
0 1 2 3
time(sec)
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Frequency Response
80
60
40
Singular Values (dB)
20
0
−20
−40
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−80
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Frequency (rad/sec)
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u
100
80
60
Singular Values (dB)
40
20
0
−20
−40
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−80
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Frequency (rad/sec)
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T rzp
Frequency Response
T reT
Frequency Response
10
10
0
0
−10
−10
Singular Values (dB)
−20
−30
−40
−50
Singular Values (dB)
−20
−30
−40
−60
−50
−70
−60
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
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T ru
Frequency Response
T ruf
Frequency Response
10
0
0
−10
−50
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−100
−150
−70
−200
−80
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nzp
Frequency Response
T neT
Frequency Response
20
10
0
0
−20
−10
Singular Values (dB)
−40
−60
−80
Singular Values (dB)
−20
−30
−40
−100
−50
−120
−60
−140
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nu
Frequency Response
T nuf
Frequency Response
10
0
0
−10
−50
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−100
−150
−70
−200
−80
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di z p
Frequency Response
T di e T
Frequency Response
40
40
20
20
Singular Values (dB)
0
−20
−40
Singular Values (dB)
0
−20
−40
−60
−60
−80
−80
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di
Frequency Response
u
T di u f
Frequency Response
40
50
20
0
Singular Values (dB)
0
−20
−40
Singular Values (dB)
−50
−100
−150
−60
−200
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T do z p
Frequency Response
T do e T
Frequency Response
10
10
0
0
−10
−10
Singular Values (dB)
−20
−30
−40
Singular Values (dB)
−20
−30
−40
−50
−50
−60
−60
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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do u
T do u f
Frequency Response
10
0
0
−10
−50
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−100
−150
−70
−200
−80
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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1.2
1
Output Response to r=[1 0]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 0]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
−0.2
0 1 2 3 4 5 6
sec
−0.4
0 1 2 3 4 5 6
sec
0.5
0.4
0.3
Actuator Input Response to r=[1 0]
V p1
(volts)
V p2
(volts)
0.15
0.1
Actuator Output Response to r=[1 0]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.2
0.1
0
−0.1
−0.2
−0.3
−0.4
−0.5
0 1 2 3 4 5 6
sec
F 1
(Pounds);F 2
(Pounds);
0.05
0
−0.05
−0.1
−0.15
−0.2
0 1 2 3 4 5 6
sec
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1.2
1
Output Response to r=[0 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[0 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 1 2 3 4 5 6
sec
−0.2
0 1 2 3 4 5 6
sec
0.04
0.03
0.02
Actuator Input Response to r=[0 1]
V p1
(volts)
V p2
(volts)
0.015
0.01
Actuator Output Response to r=[0 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.01
0
−0.01
−0.02
−0.03
−0.04
−0.05
F 1
(Pounds);F 2
(Pounds);
0.005
0
−0.005
−0.01
−0.06
0 1 2 3 4 5 6
sec
−0.015
0 1 2 3 4 5 6
sec
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1.2
1
Output Response to r=[1 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 1 2 3 4 5 6
sec
−0.2
0 1 2 3 4 5 6
sec
0.6
0.4
Actuator Input Response to r=[1 1]
V p1
(volts)
V p2
(volts)
0.15
0.1
Actuator Output Response to r=[1 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.2
0
−0.2
−0.4
F 1
(Pounds);F 2
(Pounds);
0.05
0
−0.05
−0.1
−0.6
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sec
−0.2
0 1 2 3 4 5 6
sec
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1.5
1
Output Response to r=[1 −1]
θ (deg)
x 2
(cm)
1.5
1
Tracking Error Response to r=[1 −1]
e θ
(deg)
e x2
(cm)
θ (deg);x 2
(cm);
0.5
0
−0.5
e θ
(deg);e
x2
(cm);
0.5
0
−0.5
−1
−1
−1.5
0 1 2 3 4 5 6
sec
−1.5
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sec
0.5
0.4
Actuator Input Response to r=[1 −1]
V p1
(volts)
V p2
(volts)
0.15
0.1
Actuator Output Response to r=[1 −1]
F 1
(Pounds)
F 2
(Pounds)
0.3
V
p1
(volts);V
p2
(volts);
0.2
0.1
0
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F 1
(Pounds);F 2
(Pounds);
0.05
0
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0 1 2 3 4 5 6
sec
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0 1 2 3 4 5 6
sec
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L
zp
Frequency Response
10
0
−10
Singular Values (dB)
−20
−30
−40
−50
−60
−70
10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
)LJXUH + 'HVLJQ 2SHQORRS )UHTXHQF\ 5HVSRQVH / ]S
80
L u
Frequency Response
60
40
Singular Values (dB)
20
0
−20
−40
−60
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T rzp
Frequency Response
T reT
Frequency Response
10
10
0
0
Singular Values (dB)
−10
−20
−30
Singular Values (dB)
−10
−20
−30
−40
−40
−50
−50
−60
−60
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
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T ru
Frequency Response
T ruf
Frequency Response
10
50
0
−10
0
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−50
−100
−150
−70
−80
−200
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nzp
Frequency Response
T neT
Frequency Response
0
6
−20
4
2
Singular Values (dB)
−40
−60
−80
−100
Singular Values (dB)
0
−2
−4
−6
−8
−10
−120
−12
−140
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−14
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nu
Frequency Response
T nuf
Frequency Response
10
20
0
0
−10
−20
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−40
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di z p
Frequency Response
T di e T
Frequency Response
40
40
20
20
Singular Values (dB)
0
−20
−40
Singular Values (dB)
0
−20
−40
−60
−60
−80
−80
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di
Frequency Response
u
T di u f
Frequency Response
30
50
20
10
0
Singular Values (dB)
0
−10
−20
−30
−40
Singular Values (dB)
−50
−100
−150
−50
−60
−200
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T do z p
Frequency Response
T do e T
Frequency Response
6
6
4
4
2
2
Singular Values (dB)
0
−2
−4
−6
−8
Singular Values (dB)
0
−2
−4
−6
−8
−10
−10
−12
−12
−14
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−14
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T Frequency Response
do u
T do u f
Frequency Response
10
20
0
0
−10
−20
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−40
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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1.2
1
Output Response to r=[1 0]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 0]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
1.5
1
Actuator Input Response to r=[1 0]
V p1
(volts)
V p2
(volts)
0.5
0.4
0.3
Actuator Output Response to r=[1 0]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.5
0
−0.5
F 1
(Pounds);F 2
(Pounds);
0.2
0.1
0
−0.1
−1
−0.2
−0.3
−1.5
0 0.5 1 1.5 2 2.5 3
sec
−0.4
0 0.5 1 1.5 2 2.5 3
sec
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1.2
1
Output Response to r=[0 1]
θ (deg)
x 2
(cm)
1.4
1.2
Tracking Error Response to r=[0 1]
e θ
(deg)
e x2
(cm)
0.8
1
θ (deg);x 2
(cm);
0.6
0.4
0.2
e θ
(deg);e
x2
(cm);
0.8
0.6
0.4
0
0.2
−0.2
0
−0.4
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.2
0.15
Actuator Input Response to r=[0 1]
V p1
(volts)
V p2
(volts)
0.05
0.04
Actuator Output Response to r=[0 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.1
0.05
0
−0.05
−0.1
F 1
(Pounds);F 2
(Pounds);
0.03
0.02
0.01
0
−0.01
−0.02
−0.03
−0.15
−0.04
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.05
0 0.5 1 1.5 2 2.5 3
sec
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1.2
1
Output Response to r=[1 1]
θ (deg)
x 2
(cm)
1.4
1.2
Tracking Error Response to r=[1 1]
e θ
(deg)
e x2
(cm)
0.8
1
θ (deg);x 2
(cm);
0.6
0.4
0.2
e θ
(deg);e
x2
(cm);
0.8
0.6
0.4
0
0.2
−0.2
0
−0.4
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
2
1.5
Actuator Input Response to r=[1 1]
V p1
(volts)
V p2
(volts)
0.5
0.4
Actuator Output Response to r=[1 1]
F 1
(Pounds)
F 2
(Pounds)
0.3
V
p1
(volts);V
p2
(volts);
1
0.5
0
−0.5
F 1
(Pounds);F 2
(Pounds);
0.2
0.1
0
−0.1
−0.2
−1
−0.3
−1.5
0 0.5 1 1.5 2 2.5 3
sec
−0.4
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.5
1
Output Response to r=[1 −1]
θ (deg)
x 2
(cm)
1.5
1
Tracking Error Response to r=[1 −1]
e θ
(deg)
e x2
(cm)
θ (deg);x 2
(cm);
0.5
0
−0.5
e θ
(deg);e
x2
(cm);
0.5
0
−0.5
−1
−1
−1.5
0 0.5 1 1.5 2 2.5 3
sec
−1.5
0 0.5 1 1.5 2 2.5 3
sec
1.5
Actuator Input Response to r=[1 −1]
V p1
(volts)
V p2
(volts)
0.4
0.3
Actuator Output Response to r=[1 −1]
F 1
(Pounds)
F 2
(Pounds)
1
0.2
V
p1
(volts);V
p2
(volts);
0.5
0
−0.5
F 1
(Pounds);F 2
(Pounds);
0.1
0
−0.1
−0.2
−0.3
−1
0 0.5 1 1.5 2 2.5 3
sec
−0.4
0 0.5 1 1.5 2 2.5 3
sec
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L
zp
Frequency Response
20
0
Singular Values (dB)
−20
−40
−60
−80
−100
10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
150
)LJXUH + 'HVLJQ 2SHQORRS )UHTXHQF\ 5HVSRQVH / ]S
L u
Frequency Response
100
Singular Values (dB)
50
0
−50
−100
−150
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T rzp
Frequency Response
T reT
Frequency Response
20
10
0
0
−10
Singular Values (dB)
−20
−40
−60
Singular Values (dB)
−20
−30
−40
−50
−80
−60
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP U WR ] S DQG H 7
T ru
Frequency Response
T ruf
Frequency Response
0
0
−10
−20
−20
−40
Singular Values (dB)
−30
−40
−50
−60
Singular Values (dB)
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T nzp
Frequency Response
T neT
Frequency Response
0
5
−20
−40
0
Singular Values (dB)
−60
−80
−100
−120
Singular Values (dB)
−5
−10
−140
−15
−160
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−20
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP Q WR ] S DQG H 7
T nu
Frequency Response
T nuf
Frequency Response
0
0
−10
−20
−20
−40
Singular Values (dB)
−30
−40
−50
−60
Singular Values (dB)
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T di z p
Frequency Response
T di e T
Frequency Response
40
40
20
20
Singular Values (dB)
0
−20
−40
Singular Values (dB)
0
−20
−40
−60
−60
−80
−80
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP G L WR ] S DQG H 7
T di
Frequency Response
u
T di u f
Frequency Response
40
50
20
0
0
Singular Values (dB)
−20
−40
−60
Singular Values (dB)
−50
−100
−150
−80
−100
−200
−120
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T do z p
Frequency Response
T do e T
Frequency Response
5
5
0
0
Singular Values (dB)
−5
−10
Singular Values (dB)
−5
−10
−15
−15
−20
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−20
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP G R WR ] S DQG H 7
T Frequency Response
do u
T do u f
Frequency Response
0
0
−10
−20
−20
−40
Singular Values (dB)
−30
−40
−50
−60
Singular Values (dB)
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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1.2
1
Output Response to r=[1 0]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 0]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.3
0.2
Actuator Input Response to r=[1 0]
V p1
(volts)
V p2
(volts)
0.08
0.06
Actuator Output Response to r=[1 0]
F 1
(Pounds)
F 2
(Pounds)
0.04
V
p1
(volts);V
p2
(volts);
0.1
0
−0.1
−0.2
F 1
(Pounds);F 2
(Pounds);
0.02
0
−0.02
−0.04
−0.06
−0.3
−0.08
−0.4
0 0.5 1 1.5 2 2.5 3
sec
−0.1
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.2
1
Output Response to r=[0 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[0 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.15
Actuator Input Response to r=[0 1]
V p1
(volts)
V p2
(volts)
0.025
0.02
Actuator Output Response to r=[0 1]
F 1
(Pounds)
F 2
(Pounds)
0.1
0.015
V
p1
(volts);V
p2
(volts);
0.05
0
F 1
(Pounds);F 2
(Pounds);
0.01
0.005
0
−0.005
−0.05
−0.01
−0.015
−0.1
0 0.5 1 1.5 2 2.5 3
sec
−0.02
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.2
1
Output Response to r=[1 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.4
0.3
Actuator Input Response to r=[1 1]
V p1
(volts)
V p2
(volts)
0.08
0.06
Actuator Output Response to r=[1 1]
F 1
(Pounds)
F 2
(Pounds)
0.2
0.04
V
p1
(volts);V
p2
(volts);
0.1
0
−0.1
−0.2
F 1
(Pounds);F 2
(Pounds);
0.02
0
−0.02
−0.04
−0.3
−0.06
−0.4
−0.08
−0.5
0 0.5 1 1.5 2 2.5 3
sec
−0.1
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.5
1
Output Response to r=[1 −1]
θ (deg)
x 2
(cm)
1.5
1
Tracking Error Response to r=[1 −1]
e θ
(deg)
e x2
(cm)
θ (deg);x 2
(cm);
0.5
0
−0.5
e θ
(deg);e
x2
(cm);
0.5
0
−0.5
−1
−1
−1.5
0 0.5 1 1.5 2 2.5 3
sec
−1.5
0 0.5 1 1.5 2 2.5 3
sec
0.3
0.2
Actuator Input Response to r=[1 −1]
V p1
(volts)
V p2
(volts)
0.08
0.06
Actuator Output Response to r=[1 −1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.1
0
−0.1
−0.2
F 1
(Pounds);F 2
(Pounds);
0.04
0.02
0
−0.02
−0.04
−0.3
−0.06
−0.4
0 0.5 1 1.5 2 2.5 3
sec
−0.08
0 0.5 1 1.5 2 2.5 3
sec
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DUH VKRZQ LQ )LJXUH
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L
zp
Frequency Response
60
40
Singular Values (dB)
20
0
−20
−40
−60
10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
)LJXUH + 'HVLJQ 2SHQORRS )UHTXHQF\ 5HVSRQVH / ]S
L Frequency Response
u
140
120
100
Singular Values (dB)
80
60
40
20
0
−20
−40
−60
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
'HVLJQ 2SHQORRS )UHTXHQF\ 5HVSRQVH / X

T rzp
Frequency Response
T reT
Frequency Response
20
10
0
0
−10
Singular Values (dB)
−20
−40
−60
Singular Values (dB)
−20
−30
−40
−50
−80
−60
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
−70
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP U WR ] S DQG H 7
T ru
Frequency Response
T ruf
Frequency Response
0
0
−10
−20
−50
Singular Values (dB)
−30
−40
−50
−60
Singular Values (dB)
−100
−150
−70
−200
−80
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP U WR FRQWUROV X DQG X I
T nzp
Frequency Response
T neT
Frequency Response
20
10
0
0
−10
Singular Values (dB)
−20
−40
−60
−80
Singular Values (dB)
−20
−30
−40
−50
−60
−100
−70
−120
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP Q WR ] S DQG H 7
T nu
Frequency Response
T nuf
Frequency Response
20
50
0
0
Singular Values (dB)
−20
−40
−60
Singular Values (dB)
−50
−100
−150
−80
−200
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T di z p
Frequency Response
T di e T
Frequency Response
40
40
20
20
Singular Values (dB)
0
−20
−40
Singular Values (dB)
0
−20
−40
−60
−60
−80
−80
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP G L WR ] S DQG H 7
T di
Frequency Response
u
T di u f
Frequency Response
40
50
30
20
0
Singular Values (dB)
10
0
−10
−20
−30
Singular Values (dB)
−50
−100
−150
−40
−50
−200
−60
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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T do z p
Frequency Response
T do e T
Frequency Response
10
10
0
0
−10
−10
Singular Values (dB)
−20
−30
−40
−50
Singular Values (dB)
−20
−30
−40
−50
−60
−60
−70
−70
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−80
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH + 'HVLJQ )UHTXHQF\ 5HVSRQVHV IURP G R WR ] S DQG H 7
T Frequency Response
do u
T do u f
Frequency Response
20
50
0
0
Singular Values (dB)
−20
−40
−60
Singular Values (dB)
−50
−100
−150
−80
−200
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
)LJXUH +
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1.2
1
Output Response to r=[1 0]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 0]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.25
0.2
0.15
Actuator Input Response to r=[1 0]
V p1
(volts)
V p2
(volts)
0.06
0.04
Actuator Output Response to r=[1 0]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.1
0.05
0
−0.05
−0.1
−0.15
−0.2
F 1
(Pounds);F 2
(Pounds);
0.02
0
−0.02
−0.04
−0.06
−0.25
0 0.5 1 1.5 2 2.5 3
sec
−0.08
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.2
1
Output Response to r=[0 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[0 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.1
0.08
Actuator Input Response to r=[0 1]
V p1
(volts)
V p2
(volts)
0.02
0.015
Actuator Output Response to r=[0 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.06
0.04
0.02
0
−0.02
−0.04
−0.06
F 1
(Pounds);F 2
(Pounds);
0.01
0.005
0
−0.005
−0.01
−0.08
−0.015
−0.1
0 0.5 1 1.5 2 2.5 3
sec
−0.02
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1.2
1
Output Response to r=[1 1]
θ (deg)
x 2
(cm)
1.2
1
Tracking Error Response to r=[1 1]
e θ
(deg)
e x2
(cm)
0.8
0.8
θ (deg);x 2
(cm);
0.6
0.4
e θ
(deg);e
x2
(cm);
0.6
0.4
0.2
0.2
0
0
−0.2
0 0.5 1 1.5 2 2.5 3
sec
−0.2
0 0.5 1 1.5 2 2.5 3
sec
0.3
0.2
Actuator Input Response to r=[1 1]
V p1
(volts)
V p2
(volts)
0.08
0.06
Actuator Output Response to r=[1 1]
F 1
(Pounds)
F 2
(Pounds)
0.04
V
p1
(volts);V
p2
(volts);
0.1
0
−0.1
−0.2
F 1
(Pounds);F 2
(Pounds);
0.02
0
−0.02
−0.04
−0.06
−0.3
−0.08
−0.4
0 0.5 1 1.5 2 2.5 3
sec
−0.1
0 0.5 1 1.5 2 2.5 3
sec
)LJXUH +
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1
0.8
0.6
Output Response to r=[1 −1]
θ (deg)
x 2
(cm)
1.5
1
Tracking Error Response to r=[1 −1]
e θ
(deg)
e x2
(cm)
θ (deg);x 2
(cm);
0.4
0.2
0
−0.2
−0.4
e θ
(deg);e
x2
(cm);
0.5
0
−0.5
−0.6
−1
−0.8
−1
0 0.5 1 1.5 2 2.5 3
sec
−1.5
0 0.5 1 1.5 2 2.5 3
sec
0.2
0.15
Actuator Input Response to r=[1 −1]
V p1
(volts)
V p2
(volts)
0.05
0.04
0.03
Actuator Output Response to r=[1 −1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.1
0.05
0
−0.05
−0.1
F 1
(Pounds);F 2
(Pounds);
0.02
0.01
0
−0.01
−0.02
−0.03
−0.04
−0.15
0 0.5 1 1.5 2 2.5 3
sec
−0.05
0 0.5 1 1.5 2 2.5 3
sec
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FRV]DDGPSP[A]GAFRV]AVLQ] DA PSFRV]]GOSVLQ]DDGP[AFRV]
FRV] DAPSDGKVLQ]]GP[AVLQ]AVLQ] DAPSAOS[AFRV]]GDGVLQ]A
VLQ]DPSFRV]D[GDG- VLQ]AVLQ]DPSFRV]D[GDGP[AVLQ]VLQ]DA
PS[GFRV]]G- PA[A]GAPSKAIFRV]FRV]DPSAVLQ]AOSVLQ]DAK]GA
[FRV]FRV] DPSAJVLQ] D[A FRV]AFRV]DPSVLQ] DK]GA- FRV]A
FRV] DAPSAOS[AVLQ] DDG]G FRV]AFRV] DAPSADG[A]G FRV]A
FRV]DAPSAOS[VLQ]D[GVLQ]DG FRV]FRV] DAPSAOS[VLQ]ADGK]G
FRV]FRV]DPSAOSK]GA[ FRV]AFRV]DAPSAOSK]GA[FRV]AFRV]DPS
]GVLQ]DDGKP[AVLQ]VLQ]DAPSJP[AFRV]AFRV]DAPSAOS[AVLQ]
DG]GFRV]AFRV]DPSAOS[VLQ]DAK]GA FRV]AFRV] DPSAOS[VLQ]DA
[GDGFRV]FRV]DAPSAOS[VLQ]A[GDG PKAIPSKAIPKAII-PSA
[APSA[AVLQ]AVLQ]DA PSA[AFRV]AFRV]DA[AVLQ]AFRV]DAPSA
[AFRV]AVLQ] DAPSAPSP[AVLQ]AVLQ]DAPSP[AFRV]AFRV]DA-
PSPS-VLQ]VLQ] DFRV]FRV] D PS-FRV]AFRV]DAP[APSPSP[A
VLQ]VLQ] DFRV]FRV] D P[APSPS-VLQ]AVLQ]DA PSP[AVLQ]A
VLQ] DA PSP[AFRV]AFRV] DA [AFRV]AVLQ] DAPSP [AVLQ]A
FRV]DAPSPP[AP-PPA[A
[GGRW
FRV]AFRV] DPS[VLQ] DKI FRV]AFRV] DAPS[VLQ]PJ[ FRV]
FRV] DAPS[VLQ ] KP[]GA FRV]FRV] DAPS[VLQ]APZJF FRV]
FRV] DAPS[VLQ]P[]G[GPSAK[FRV]VLQ] DAJFRV]FRV]DAPS[G
VLQ]DG-FRV]FRV]DAPS[GVLQ]DGP[AFRV]AFRV]DPS[GVLQ]D]G-
FRV]FRV] DAPSDGKVLQ]]GP[A FRV]FRV] DPSVLQ]VLQ]DI[A
FRV]AFRV]DAPSDG[]G- FRV]FRV]DPSJVLQ]D-PSAFRV]OSVLQ]DDGA
[AFRV]FRV]DPS]GVLQ] DDG[VLQ]P[AFRV]FRV]DAPSKVLQ]]GA
P[A FRV]FRV] DAPSDGKVLQ]]G-VLQ]VLQ] DAPS[GFRV]]GP[A
VLQ]AVLQ] DPSFRV] DDGK]GP[AVLQ]VLQ]DAPS]GDGKFRV]P[A
VLQ]AVLQ] DPSFRV] D[GDGP[AFRV]FRV] DAPS[GVLQ]]GP[A
FRV]FRV]DPSJVLQ]DP[A FRV]AFRV]DPSAOS[AVLQ]DA]GDGVLQ]

PSA]GA[AFRV]AFRV]DAVLQ]AVLQ]DPS[G]GFRV]D-VLQ]AVLQ]DA
PS]GDG[APVLQ]AVLQ] DAPS]GDG[-VLQ]AVLQ] DPSFRV] DK]GA-
VLQ]VLQ]DAPS]GDGKFRV]- VLQ]VLQ]DPSAOSK]GA[VLQ]VLQ]DAPSJ
P[AVLQ]VLQ]DAPS[GFRV]DGP[A VLQ]VLQ]DAPS]GDGKFRV]P[A
VLQ]VLQ] DAPSKFRV]]GAP[A VLQ]AVLQ] DPSFRV] DK]GAP[A
VLQ]AVLQ] DPSFRV] DDGK]G-VLQ]AVLQ] DPSFRV] DDGK]GP[A
VLQ]AVLQ]DPS[FRV]DKP[]GAVLQ]AVLQ]DPS[FRV]DPZJF VLQ]A
VLQ] DPS[FRV] DKIVLQ]AVLQ]DPSAOS[FRV]DA[GDGVLQ]VLQ]D
PSAFRV]AOSFRV]DAK]GA[ VLQ]AVLQ]DAPSAOS[FRV]FRV]DDGK]G
PAKA]GA[VLQ]AVLQ]DAPSAOSK]GA[ VLQ]AVLQ]DAPSAOS[FRV]
FRV]D[GDGVLQ]VLQ]DAPS[FRV]KP[]GAVLQ]VLQ]DAPS[FRV]P
[]G[G VLQ]VLQ]DAPS[FRV]KIVLQ]VLQ] DAPSAOS[FRV]AK]GA
VLQ]AVLQ]DAPSAOS[AFRV]D]GDG VLQ]AVLQ]DPSAOS[FRV]DAK]GA
VLQ]VLQ] DAPSKFRV]]GA-VLQ]AVLQ]DPSAOS[FRV]DADGK]GVLQ]
VLQ] DAPSAOS[FRV]A[GDG VLQ]VLQ]DAPSAOS[FRV]A]GDGKVLQ]
VLQ]DAPSAJ[AFRV]AFRV]DPSA[AVLQ]DJ FRV]AFRV]DPS]GVLQ]D
DGKP[AFRV]AFRV] DAPSDG[]GP[AFRV]FRV] DAPS[GVLQ]]G-
VLQ]VLQ]DAPSJ- VLQ]AVLQ]DPSAFRV]DDGK]G[AVLQ]AVLQ]DPSA
FRV] D[GDG[AVLQ]VLQ] DAPSA[GFRV]DG[A VLQ]AVLQ] DPS[
FRV]DP[]G[GVLQ]AVLQ]DPS[FRV]DKI VLQ]VLQ]DAPS[FRV]K
IVLQ]AVLQ] DAPSA]GDG[AVLQ]VLQ] DAPSA]GDGKFRV][A VLQ]
VLQ]DPSOSPK]GA[VLQ]VLQ]DAPS[GFRV]DGP[AVLQ]VLQ]DAPS[G
FRV]DG-FRV]AFRV]DPSVLQ] D[GDGP[AFRV]AFRV]DAPSDG[A]GP
VLQ]AVLQ]DAPS]GDG[P[A PSAKVLQ]OSVLQ]DAFRV]AFRV]D[GDG
PSAKVLQ]AOSVLQ] DAFRV] D[GDGPSAKAFRV]]GOSVLQ] DDG FRV]
FRV]DAPS[VLQ]KI FRV]AFRV] DPS[VLQ] DKIFRV]AFRV]DPS[
VLQ] DKP[]GA FRV]AFRV] DPS[AVLQ] DJPJVLQ]PA[A FRV]
FRV]DAPS[VLQ]KI FRV]AFRV]DPS[VLQ]DP[]G[GFRV]AFRV]D
PS[VLQ]DPZJFVLQ]FRV]FRV]DAPS[GVLQ]DGP[A FRV]AFRV] DPS
VLQ]D[GDGP[APSAKVLQ]AOSVLQ]DA]GDG[ PSAKAVLQ]AOSVLQ]DA
]GDGFRV]PSAKAVLQ]AOSVLQ]DAFRV] DDG]GPSAKVLQ]AOSVLQ]DA[G
FRV]DGPSAKFRV]AOSFRV]DA[GVLQ]DGVLQ]AVLQ]DPS[G]GFRV]DP
[APSA]GA[AVLQ]AFRV]DAFRV]FRV]DPSOSPK]GA[FRV]AFRV]DPS
[VLQ] DPJ[ IP[APSPKA[VLQ]AFRV] DADG]G PSPK[FRV]A
VLQ]DFRV] DJVLQ]PSPK]GOSVLQ] DDG[VLQ]PSKP[]G[GVLQ]A
VLQ] DAPSKPZJFVLQ]AVLQ] DFRV]FRV] D PSPK[G]G[PSKAI
VLQ]AVLQ] DAPSKAP[]GAFRV]AFRV]DA PSKAIVLQ]VLQ]DFRV]
FRV]DPSKPZJFVLQ]FRV]AFRV] DAPSKPJ[FRV]AFRV]DAPSKP[
]G[GVLQ]VLQ] DFRV]FRV]D PSKAIVLQ]VLQ]DFRV]FRV]DPSA]GA
[APSKAP[]GAPSKAIVLQ]AVLQ] DA PSKAIFRV]AFRV]DAPSKAI
FRV]AFRV]DA PSPK[VLQ]AFRV]DVLQ]DJPSPK[VLQ]AFRV]DA[G
DGPSPKA[VLQ]AFRV]DA]GA PSPK[VLQ]AFRV]DA[G]GPSI[APS
PKAVLQ]]GOSFRV] DDGPSPK[VLQ]AFRV]DAFRV]JPSPKA[FRV]A
VLQ]DA]GDGPSPKA[FRV]AVLQ]DA]GAPSPK[FRV]AVLQ]DA[GDGPS
PKOSFRV]DDG[FRV]]GPSPKJ[FRV]PSAKA]GA[VLQ]AVLQ]DA PS
PK[VLQ]FRV]DJVLQ]DPSPKAFRV]]GOSVLQ] DDGPSAKOSVLQ]DDGA
[VLQ]PSAKAVLQ]AOSVLQ] DFRV]FRV]DADG]GPSAK[VLQ]FRV]DJ
VLQ]DP[]GAP[A PSAK[VLQ]AFRV]DAVLQ]DOSDGA PSAK[VLQ]A
FRV]DA[GDG FRV]FRV]DPSVLQ]AVLQ]DPJ[AFRV]FRV]DPSJVLQ]D
P[AFRV]AFRV]DAPSAOS[VLQ]DDGKVLQ]]G FRV]FRV]DPSAVLQ]A
VLQ]DJ[A FRV]AFRV] DPSVLQ] DK]GAP[APSAK[VLQ]AFRV] D
VLQ]DJPSAKA[FRV]AVLQ]DA]GDGPSAK[FRV]AVLQ]DA[GDGPSAK[
FRV]AVLQ]DFRV]DJVLQ] PSAKOSFRV]DDGA[FRV]PSPKA]GA[PSA
KA[VLQ]AFRV] DA]GA PSAK[VLQ]AFRV] DA[G]G PSAK[VLQ]A
FRV] DAFRV]J PSAKA[FRV]AVLQ] DA]GAPSAFRV]OSVLQ]D]GA[A
VLQ]AFRV] DAPSAFRV]AOSVLQ]DA]GA[APSAFRV]OSVLQ]DA]GA[A
VLQ]APSAFRV]AOSVLQ]D]GA[AFRV]DAPSJVLQ]P[APSAKVLQ]A
OSVLQ] DFRV]FRV] DA[GDG PSAKOSVLQ] D[GFRV]DGPSAK[FRV]A
VLQ]DAFRV] DOSDGA IP[A PSAKOSVLQ] DADGA[VLQ]A PSAKJ[
FRV]AFRV]DA PSAK[G]G[FRV]AFRV]DAPSAKA]GA[PSAVLQ]A]GA
OSFRV]DA[APSAVLQ]]GAOSFRV] D[AFRV]AVLQ]DA PSAVLQ]]GAOS
FRV]D[APSAVLQ]A]GAOSFRV]D[AVLQ]DAPSA]GA[AVLQ]AVLQ]DA
PSAKFRV]AOSFRV] DADG[]G PSAKA[VLQ]AFRV]DADG]G PSAFRV]OS
VLQ]D]GA[A PSAK[VLQ]AFRV]DAFRV]OSDGAPSAVLQ]]GAOSFRV]DA
[AFRV]APSAVLQ]OSFRV] DDGA[APSAFRV]A]GOSVLQ]DADG[APSA
KA]GA[FRV]AFRV]DAPSAK[G]G[VLQ]AVLQ]DAPKP[]G[GPK
PJ[FRV] PKAP[]GA PSAJVLQ][AFRV]AFRV] DA PSAVLQ ] AOS
FRV]DDGA[AVLQ] DAPSAFRV]AOSVLQ] DDGA[AFRV]DAPSAFRV]OS
VLQ]DDGA[AVLQ]AFRV] DA PSAFRV]OSVLQ] DADGA[AVLQ]A PSA
FRV]AOSVLQ]DADGA[APAKJ[FRV] PKPZJFVLQ]PAK[]G[GPSA
KJ[FRV]PSJVLQ]P[AFRV]FRV] DPS]GVLQ]DDG[AVLQ]PFRV]
FRV]DPS]GVLQ]DDG[VLQ]-FRV]FRV] DAPSKVLQ]]GA-FRV]AFRV]D
PS]GVLQ] DDGK- FRV]AFRV] DPS[GVLQ] D]GP[APSPK[G]G[
VLQ]AVLQ]DAVLQ]AVLQ]DPS[FRV]DPJ[FRV]PSAK[G]G[PSAK
[FRV]VLQ]DFRV]D[GVLQ]DGPSAK[FRV]AVLQ]DFRV]DAVLQ]OSDGA
PSAK[FRV]AVLQ] DAVLQ]OSDGAPSAK[FRV]VLQ]DAVLQ]AOSFRV]D
DGAPSAKFRV]AOSFRV]DAVLQ]D[GDGPSAKAFRV]AOSFRV]DADGVLQ]]G
PSAK[FRV]AVLQ] DA[G]G PSAVLQ]OSFRV]DDGA[AFRV]AVLQ]DA

PSAJVLQ]A[AFRV] DAPSAKAFRV]AOSFRV] DA]GVLQ] DDG PSAKOS
FRV]D[GVLQ]DGPSAK]GOSVLQ] DDG[VLQ] PSAKOSFRV]DDG[FRV]]G
PSA]GA[AFRV]AVLQ]DAPSKPJ[FRV]VLQ]AVLQ]DAPSKPZJFVLQ]A
VLQ]DAPSAKA[FRV]VLQ]DFRV]DDGVLQ]]G PSAFRV]]GOSVLQ]DDG
[APSFRV]]GOSVLQ]DDGP[APSPK[G]G[FRV]AFRV]DAPSKAP[
]GAVLQ]AVLQ]DAPSAVLQ]AOSFRV]DADGA[APSAJVLQ][APS]GA[P
[AFRV]AFRV]DAPS]GA[-VLQ]VLQ]DFRV]FRV] DPS]GA[P[APS
]GA[P[AVLQ]AVLQ] DA PS]GA[-FRV]AFRV] DA PS]GA[P[A
VLQ]VLQ]DFRV]FRV] DPS]GA[-VLQ]AVLQ] DA P[]GA-PSVLQ]OS
FRV]DDGAP[APSVLQ]OSFRV]DDGAP[A PSVLQ]]GOSFRV]DDGP[A
PSVLQ]]GOSFRV]DDGP[A PS]GA[- PSFRV]OSVLQ] DDGAP[APSP
[A]GAVLQ]AVLQ]DAPSVLQ]]GAOSFRV]DP[A PSVLQ]]GOSFRV]DDG
-PSJVLQ]- PSVLQ]OSFRV] DDGA-PSKPJ[FRV] PSKAP[]GAVLQ]
VLQ] DFRV]FRV] D PSPKOSFRV] D[GVLQ]DG PSJVLQ]P[AFRV]A
FRV] DAPSJVLQ]A[AFRV] DAPPSKPZJFVLQ] PSKP[]G[GPSP
[A]GA VLQ]AVLQ]DAPS[FRV]PZJF VLQ]VLQ]DAPS[FRV]APJ[PS
PKOSVLQ] D[GFRV]DG PSKPJ[FRV]AVLQ]VLQ] DFRV]DFRV]A
FRV]DPSAOS[VLQ]DA]GDGKFRV]FRV]DAPSAOS[AVLQ]A]GVLQ]DDG
FRV]FRV] DAPSAOS[VLQ]AK]GA FRV]FRV] DAPSA[GVLQ]DG[A
FRV]AFRV]DPSA]GVLQ] DDGK[AFRV]AFRV]DPSVLQ]D[GDG- FRV]
FRV]DAPSADGKVLQ]]G[A FRV]FRV]DPSA]GVLQ]DDG[AVLQ]FRV]A
FRV]DPSAVLQ] D[GDG[A PSFRV]OSVLQ] D]GAP[A PSKP[]G[G
FRV]AFRV]DAPSFRV]]GOSVLQ]DDG-PSPKA]GA[FRV]AFRV]DAPSP
KJ[FRV]AFRV]DAPSPKA]GA[VLQ]AVLQ]DAPSI[AVLQ]AFRV]DA
PSI[AFRV]AVLQ]DAPSFRV]OSVLQ]D]GAP[A PSAKOSFRV]DADGA[
FRV]APSAVLQ]]GOSFRV]DDG[A PSVLQ]]GAOSFRV] D-PSVLQ]]GAOS
FRV]DP[APSP[A]GAFRV]AFRV]DA PSPK[FRV]VLQ]DAJPSP[A
]GAVLQ]AFRV]DAPSPKOSFRV]DDGA[FRV] PSPKOSVLQ]DDGA[VLQ]
PSFRV]OSVLQ] D]GA- PSPK[FRV]AVLQ] DA[G]GPSPKA[FRV]
VLQ]DFRV] DDGVLQ]]G PJVLQ]P[APSPK[FRV]VLQ]DFRV]D[G
VLQ]DGPSAVLQ]A]GOSFRV]DADG[APSAVLQ]OSFRV]DADGA[AFRV]A
PJVLQ]-PSFRV]OSVLQ]DDGA-PSFRV]OSVLQ]DDGAP[APSAKAVLQ]
OSVLQ] DAFRV]AFRV] D]GDG PSAKAVLQ]]GOSFRV] DDG PSP[A]GA
FRV]AVLQ]DAPSFRV]]GOSVLQ] DDGP[AFRV]FRV]DAPSDGKVLQ]]G
P[A VLQ]AVLQ] DAPSAOS[AFRV]]GDGVLQ]AVLQ]DPSFRV]D[GDG-
VLQ]AVLQ] DPSFRV]D[GDGP[AVLQ]VLQ]DAPS[GFRV]]G-PA[A
]GAPSKAI FRV]FRV] DPSAVLQ]AOSVLQ]DAK]GA[ FRV]FRV]DPSAJ
VLQ]D[AFRV]AFRV]DPSVLQ]DK]GA- FRV]AFRV]DAPSAOS[AVLQ]D
DG]GFRV]AFRV]DAPSADG[A]G FRV]AFRV]DAPSAOS[VLQ]D[GVLQ]
DGFRV]FRV] DAPSAOS[VLQ]ADGK]GFRV]FRV]DPSAOSK]GA[FRV]A
FRV]DAPSAOSK]GA[FRV]AFRV]DPS]GVLQ]DDGKP[A VLQ]VLQ]DA
PSJP[A FRV]AFRV] DAPSAOS[AVLQ]DG]G FRV]AFRV] DPSAOS[
VLQ]DAK]GA FRV]AFRV]DPSAOS[VLQ]DA[GDGFRV]FRV]DAPSAOS[
VLQ]A[GDGPKAIPSKAIPKAII-PSA[APSA[AVLQ]AVLQ] DA
PSA[AFRV]AFRV]DA[AVLQ]AFRV]DAPSA[AFRV]AVLQ]DAPSAPSP
[AVLQ]AVLQ]DAPSP[AFRV]AFRV] DA -PSPS-VLQ]VLQ] DFRV]
FRV]DPS-FRV]AFRV]DAP[APS PSP[AVLQ]VLQ]DFRV]FRV]DP
[APS PS-VLQ]AVLQ]DAPSP[AVLQ]AVLQ]DAPSP[AFRV]AFRV]DA
[AFRV]AVLQ]DAPSP[AVLQ]AFRV]DAPSPP[AP-PPA[A
DGGRW PSOS[AFRV]AVLQ]DFRV]DDG]GPPSVLQ]VLQ]DI[APSAOS[FRV]
VLQ]DFRV] D[GVLQ]DG PSAOSAVLQ] D[GFRV]DG PSAVLQ ] AOSA
VLQ]DAFRV]FRV] D]GDG[ PSJVLQ] DP[A PSAVLQ]AOSAVLQ]D
FRV]FRV]DAK]GDG PSAVLQ]OSAVLQ]DAFRV]AFRV]DK]GDGPSAVLQ]
OSAVLQ]DFRV]AFRV]DADG[]G PSVLQ]VLQ]DAFRV]]GOSDGP[APS
VLQ]AVLQ]D]GOSFRV] DDGP[A PSAOSK]GA[PSFRV]AFRV] D]GOS
VLQ]DDGP[A PSAOS[FRV]VLQ] DFRV] DDGKVLQ]]GPSOS[FRV]
VLQ] DFRV] D[GVLQ]DGP PSAJVLQ] D[A PSVLQ]OSVLQ]DFRV]A
FRV]DJ[PPSVLQ]OSVLQ] DFRV]AFRV]DPJ[PSFRV]FRV]DI[A
PSAVLQ]AVLQ] DJ[A PSVLQ]AOSVLQ] DFRV]FRV] DPZJFPSA[A
FRV]AVLQ]DJPSAOS[G]G[ PSAOSJ[FRV] PSJVLQ]DP[APSVLQ]A
VLQ]DJ-FRV]FRV]DI-VLQ]AVLQ]DJPA[A PSOS[AVLQ]AFRV]D
]GVLQ]DDGP JVLQ] DP[AP FRV]FRV] DIP[A PSOS[VLQ]A
FRV]DADGK]GPPSJVLQ]D-JVLQ]DPA[AFRV]FRV]DIP[A VLQ]A
VLQ] DPJ-VLQ]VLQ]DIP[APSOS[FRV]AVLQ] DA]GDGKPVLQ]
VLQ]DIP[AVLQ]VLQ] DI- PSOS[AVLQ]FRV]DADGFRV]]GP[A
FRV]AVLQ] DPAJOSPAK[]GAOSPA[]G[GOSPAJ[FRV]PSOS[
FRV]VLQ]DFRV]DDGKVLQ]]GPPSVLQ]OSVLQ]DFRV]FRV]DP[]G[G
PSOS[AFRV]VLQ]DA]GDGVLQ]P PSVLQ]OSVLQ]DFRV]FRV]DKP[
]GA[VLQ]AFRV]DPZJFPJVLQ]DP- OSKP[]GAP[FRV]AVLQ]DP
J[POSP[]G[GP FRV] DDGKVLQ]]GP-FRV] DDG[AFRV]]GPA
FRV]D[GVLQ]DGP[AP]GVLQ]DDG[AVLQ]PAPSFRV]FRV]DAVLQ]
]GOSDGP[AFRV] D[GVLQ]DGP-[GFRV]VLQ]D]GP-[FRV]VLQ]D
PKI FRV] DDGKVLQ]]GPA[A[GFRV]VLQ] D]GP[AP [FRV]
VLQ]DKIP[VLQ]FRV] DPJ[FRV]P[VLQ]FRV] DKIPFRV]DK
VLQ]]GAP[AP FRV] DDG[FRV]]GP-[VLQ]FRV] DPKI OSPZJF
VLQ]POSPJ[FRV]P[FRV]VLQ]DP[]G[GPFRV]D[GVLQ]DGPA
[A[FRV]VLQ]DPZJFVLQ]P]GVLQ] DDGKFRV]P-[FRV]VLQ]DKP

[]GAP[VLQ]FRV]DP[]G[GP [VLQ]FRV]DKP[]GAP]GVLQ]D
DG[VLQ]P-FRV]FRV]DJVLQ]-P VLQ] D[GFRV]DGP[APFRV]DK
VLQ]]GAP- FRV]FRV] DJVLQ]P[AP[GVLQ]]GFRV]DP-PSFRV]
FRV]DAVLQ]]GAOS- PSVLQ]VLQ]DAFRV]]GOSDG-PSVLQ]AVLQ]DJP
[A PSVLQ]AVLQ] D]GOSFRV]DDG-PS]GVLQ] DDGKFRV]P[A PS
FRV]D[GVLQ]DGP[APSVLQ]AVLQ]DPJ[A PSFRV]AFRV] D]GOS
VLQ]DDG-PS[GFRV]VLQ]D]GP[APSFRV]DKVLQ]]GA-PSFRV]DDG[
FRV ] ]GP[A PSFRV] DDGKVLQ]]GP[A ]GVLQ] DDGKFRV]P[AP
FRV]DDG[FRV]]GP[APPSFRV]FRV]DJVLQ]-PS[GVLQ]]GFRV]D-
VLQ]DKFRV]]GAP- VLQ] D[GFRV]DGP-VLQ]AVLQ]DJP[AP[G
VLQ]]GFRV]DP[APVLQ] D[GFRV]DGPA[AVLQ]DKFRV]]GAP[A
PFRV]DDGKVLQ]]GP[AP]GVLQ]DDG[VLQ]P[AP PSVLQ]AVLQ]D
OSFRV]DDGA- PSAFRV]AOSFRV]DAJ[PSFRV]AFRV]DOSVLQ]D]GA-PS
FRV]FRV] DAVLQ]OSDGAP[A PS]GVLQ] DDGKFRV]- PSAFRV]AOSA
FRV]DADGA[PS]GVLQ] DDG[VLQ]- PSAOSAVLQ]VLQ]D]GA[PSAOSA
FRV]FRV]D]GA[PS]GVLQ]DDG[AVLQ]P PSFRV]FRV]DAVLQ]OSDGA
-OSKIPPSFRV]AFRV] DOSVLQ]DDGAP[A OSPKIPSFRV]FRV] DA
VLQ]]GAOSP[APSFRV]AFRV] DOSVLQ] DDGA-PSAOSAVLQ] DDGA[
VLQ]PSFRV]FRV]DAVLQ]]GOSDG-PSAOSAFRV]DDGA[FRV]PSVLQ]DK
FRV]]GA-PSVLQ]D[GFRV]DG-PSVLQ]AVLQ]D]GAOSFRV]D-PSAFRV]A
OSAFRV]DA]GA[PSVLQ]DKFRV]]GAP[APS]GVLQ]DDGKFRV]P[APS
VLQ] D[GFRV]DGP[APSAVLQ]AOSAVLQ] DADGA[PSFRV]FRV] DJ
VLQ]P[APSVLQ]VLQ] DAFRV]OSDGA-PSAVLQ]AOSAVLQ]DA]GA[PS
VLQ]VLQ]DAFRV]OS]GA-PSAVLQ]OSAVLQ] DFRV]AFRV]DA]GA[PSA
OSAFRV]D[GVLQ]DGPSAOSA]GVLQ] DDG[VLQ]PSAOSAKVLQ]]GFRV]D
DGPSVLQ]VLQ]DAFRV]OSDGAP[A PSAOS[VLQ]FRV] DJVLQ] D PSA
VLQ]AOSAVLQ]DAFRV]D[GDGPSVLQ]AVLQ] D]GAOSFRV] DP[APSA
VLQ]AOSAVLQ] DA[GFRV]DG PSVLQ]AVLQ] DOSFRV] DDGAP[A ]G
VLQ]DDGKFRV]PA[APSFRV]AFRV]DOSVLQ]D]GAP[APSAFRV]AOSA
FRV] DADG[]GPSAFRV] D[GVLQ]DG[APSAVLQ]AOSAVLQ] DFRV]
FRV] DA[GDGPSAOSAKFRV]]GVLQ] DDG PSAVLQ]OSAVLQ]DAFRV]A
FRV] D[GDG PSAOSAFRV] DDG[FRV]]G PSAVLQ]OSAVLQ] DFRV]A
FRV]DADGA[PSAOS[FRV]VLQ]DAJPSVLQ]D[GFRV]DGP[APSVLQ]
VLQ]DAFRV]OS]GAP[APSAFRV]AOSAFRV]DAKVLQ]]GDG PSAFRV]A
OSFRV]DA[G]G[PSAFRV]AOSFRV]DAK]GA[PSAFRV]AOSAFRV] DAK
]GVLQ]DDGPSAFRV]DDG[AFRV]]GPSAOSA[FRV]AVLQ] DAVLQ]DGA
PSOSPK]GA[PSAOS[FRV]AVLQ]DA[G]GPSAVLQ]AOSVLQ]DA[G]G
[PSAVLQ]OSVLQ]DFRV]AFRV]DJ[PSAVLQ]AOSVLQ] DAK]GA[ PSA
VLQ]AOSAVLQ]DAFRV]FRV]DDGA[PSAVLQ]D[GFRV]DG[APSAVLQ]A
OSAVLQ]DAK]GFRV] DDG PSAVLQ]AOSAVLQ] DA]GDG[PSAVLQ]AOSA
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50
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−100
−150
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L u
Frequency Response
120
100
80
Singular Values (dB)
60
40
20
0
−20
−40
−60
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Frequency Response
T reT
Frequency Response
30
30
20
20
10
Singular Values (dB)
0
−10
−20
−30
−40
Singular Values (dB)
10
0
−10
−20
−50
−30
−60
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
−40
10 −3 10 −2 10 −1 10 0 10 1 10 2
Frequency (rad/sec)
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T ru
Frequency Response
T ruf
Frequency Response
10
0
0
−10
−50
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−100
−150
−70
−200
−80
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nzp
Frequency Response
T neT
Frequency Response
40
30
20
20
Singular Values (dB)
0
−20
−40
−60
Singular Values (dB)
10
0
−10
−20
−80
−30
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−40
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T nu
Frequency Response
T nuf
Frequency Response
10
20
0
0
−10
−20
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−40
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di z p
Frequency Response
T di e T
Frequency Response
40
40
20
20
Singular Values (dB)
0
−20
−40
Singular Values (dB)
0
−20
−40
−60
−60
−80
−80
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−100
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T di
Frequency Response
u
T di u f
Frequency Response
5
0
0
−5
−50
Singular Values (dB)
−10
−15
−20
−25
−30
Singular Values (dB)
−100
−150
−35
−200
−40
−45
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Frequency (rad/sec)
−250
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T do z p
Frequency Response
T do e T
Frequency Response
30
30
20
20
Singular Values (dB)
10
0
−10
−20
Singular Values (dB)
10
0
−10
−20
−30
−30
−40
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−40
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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T Frequency Response
do u
T do u f
Frequency Response
10
20
0
0
−10
−20
Singular Values (dB)
−20
−30
−40
−50
−60
Singular Values (dB)
−40
−60
−80
−100
−120
−70
−140
−80
−160
−90
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
−180
10 −3 10 −2 10 −1 10 0 10 1 10 2 10 3
Frequency (rad/sec)
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18
16
Output Response to r=[1 0]
θ (deg)
x 2
(cm)
2
0
Tracking Error Response to r=[1 0]
e θ
(deg)
e x2
(cm)
14
−2
θ (deg);x 2
(cm);
12
10
8
6
e θ
(deg);e
x2
(cm);
−4
−6
−8
−10
−12
4
−14
2
−16
0
0 50 100 150
sec
−18
0 50 100 150
sec
2.5
2
Actuator Input Response to r=[1 0]
V p1
(volts)
V p2
(volts)
0.9
0.8
0.7
Actuator Output Response to r=[1 0]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
1.5
1
0.5
0
−0.5
F 1
(Pounds);F 2
(Pounds);
0.6
0.5
0.4
0.3
0.2
0.1
0
−1
0 50 100 150
sec
−0.1
0 50 100 150
sec
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7
6
Output Response to r=[0 1]
θ (deg)
x 2
(cm)
1
0
Tracking Error Response to r=[0 1]
e θ
(deg)
e x2
(cm)
5
−1
θ (deg);x 2
(cm);
4
3
e θ
(deg);e
x2
(cm);
−2
−3
2
−4
1
−5
0
0 50 100 150
sec
−6
0 50 100 150
sec
0.7
0.6
0.5
Actuator Input Response to r=[0 1]
V p1
(volts)
V p2
(volts)
0.3
0.25
Actuator Output Response to r=[0 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
0.4
0.3
0.2
0.1
0
−0.1
−0.2
F 1
(Pounds);F 2
(Pounds);
0.2
0.15
0.1
0.05
0
−0.3
0 50 100 150
sec
−0.05
0 50 100 150
sec
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25
20
Output Response to r=[1 1]
θ (deg)
x 2
(cm)
5
0
Tracking Error Response to r=[1 1]
e θ
(deg)
e x2
(cm)
θ (deg);x 2
(cm);
15
10
e θ
(deg);e
x2
(cm);
−5
−10
−15
5
−20
0
0 50 100 150
sec
−25
0 50 100 150
sec
3
2.5
Actuator Input Response to r=[1 1]
V p1
(volts)
V p2
(volts)
1.2
1
Actuator Output Response to r=[1 1]
F 1
(Pounds)
F 2
(Pounds)
V
p1
(volts);V
p2
(volts);
2
1.5
1
0.5
0
−0.5
F 1
(Pounds);F 2
(Pounds);
0.8
0.6
0.4
0.2
0
−1
0 50 100 150
sec
−0.2
0 50 100 150
sec
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12
10
Output Response to r=[1 −1]
θ (deg)
x 2
(cm)
2
0
Tracking Error Response to r=[1 −1]
e θ
(deg)
e x2
(cm)
8
−2
θ (deg);x 2
(cm);
6
4
e θ
(deg);e
x2
(cm);
−4
−6
2
−8
0
−10
−2
0 50 100 150
sec
−12
0 50 100 150
sec
2
Actuator Input Response to r=[1 −1]
V p1
(volts)
V p2
(volts)
0.7
0.6
Actuator Output Response to r=[1 −1]
F 1
(Pounds)
F 2
(Pounds)
1.5
0.5
V
p1
(volts);V
p2
(volts);
1
0.5
0
F 1
(Pounds);F 2
(Pounds);
0.4
0.3
0.2
0.1
0
−0.5
0 50 100 150
sec
−0.1
0 50 100 150
sec
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