Nonlinear Systems and Control
Lecture # 35
Tracking
Feedback Linearization &
Sliding Mode Control
– p. 1/11
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Nonlinear Systems and Control: Tracking, Feedback Linearization, and Sliding Mode Control, Slides of Nonlinear Control Systems
The tracking control of nonlinear systems using feedback linearization and sliding mode control. The concept of a siso relative-degree ρ system, the normal form, and the requirement for the reference signal. It also explains the goal of the control, the dynamics of the error system, and the local and global tracking. An example is provided to illustrate the concepts.
Typology: Slides
2011/2012
1 / 11
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Nonlinear Systems and Control
Lecture # 35
Tracking
Feedback Linearization &
Sliding Mode Control
Docsity.com
SISO relative-degree
ρ
system:
x
f
x
g
x
u,
y
h
x
f
h
L
g
L
i
−
1
f
h
x
for
i
ρ
L
g
L
ρ
−
1
f
h
x
Normal form:
η
f
0
η, ξ
ξ
i
ξ
i
i
ρ
ξ
ρ
L
ρ f
h
x
L
g
L
ρ
−
1
f
h
x
u
y
ξ
1
f
0
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η
f
0
η, e
R
e
A
c
e
B
c
[
L
ρ f
h
x
L
g
L
ρ
−
1
f
h
x
u
r
(
ρ
)
]
A
c
, B
c
u
L
g
L
ρ
−
1
f
h
x
[
L
ρ f
h
x
r
(
ρ
)
v
]
e
A
c
e
B
c
v
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v
Ke
e
A
c
B
c
K
H urwitz
e
lim t
→∞
e
t
lim t
→∞
[
y
t
r
t
)] = 0
e
t
is bounded
ξ
t
e
t
R
t
is bounded
What about
η
t
η
f
0
η, ξ
Local Tracking
(small
η
e
‖R
t
Minimum Phase
The origin of
η
f
0
η,
is
asymptotically stable
η
is bounded for sufficiently small
η
e
, and
‖R
t
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Sliding Mode Control
x
f
x
g
x
)[
u
δ
t, x, u
)]
y
h
x
L
g
h
x
L
g
L
ρ
−
2
f
h
x
L
g
L
ρ
−
1
f
h
x
a >
η
f
0
η, ξ
ξ
1
ξ
2
ξ
ρ
−
1
ξ
ρ
ξ
ρ
L
ρ f
h
x
L
g
L
ρ
−
1
f
h
x
)[
u
δ
t, x, u
)]
y
ξ
1
e
ξ
− R
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η
f
0
η, ξ
e
1
e
2
e
ρ
−
1
e
ρ
e
ρ
L
ρ f
h
x
L
g
L
ρ
−
1
f
h
x
)[
u
δ
t, x, u
)]
r
(
ρ
)
t
Sliding surface:
s
k
1
e
1
k
ρ
−
1
e
ρ
−
1
e
ρ
s
t
e
ρ
k
1
e
1
k
ρ
−
1
e
ρ
−
1
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s
k
1
e
1
k
ρ
−
1
e
ρ
−
1
e
ρ
ρ
−
1
∑ i
=
k
i
e
i
e
ρ
s
ρ
−
1
∑ i
=
k
i
e
i
L
ρ f
h
x
L
g
L
ρ
−
1
f
h
x
)[
u
δ
t, x, u
)]
r
(
ρ
)
t
u
L
g
L
ρ
−
1
f
h
x
[
ρ
−
1
∑ i
=
k
i
e
i
L
ρ f
h
x
r
(
ρ
)
t
]
v
s
L
g
L
ρ
−
1
f
h
x
v
t, x, v
t, x, v
L
g
L
ρ
−
1
f
h
x
x
κ
0
v
κ
0
- p. 10/
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v
β
x
) sat
s ε
ε >
β
x
x
κ
0
β
0
β
0
What properties can we prove for this control?
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